mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -414,88 +414,88 @@ instance : AddGroupWithOne ℍ[R,c₁,c₂] :=
     intCast_negSucc := fun n => show ↑↑_ = -↑↑_ by rw [Int.cast_neg, Int.cast_natCast, coe_neg]
     one := 1 }
 
-#print QuaternionAlgebra.nat_cast_re /-
+#print QuaternionAlgebra.natCast_re /-
 @[simp, norm_cast]
-theorem nat_cast_re (n : ℕ) : (n : ℍ[R,c₁,c₂]).re = n :=
+theorem natCast_re (n : ℕ) : (n : ℍ[R,c₁,c₂]).re = n :=
   rfl
-#align quaternion_algebra.nat_cast_re QuaternionAlgebra.nat_cast_re
+#align quaternion_algebra.nat_cast_re QuaternionAlgebra.natCast_re
 -/
 
-#print QuaternionAlgebra.nat_cast_imI /-
+#print QuaternionAlgebra.natCast_imI /-
 @[simp, norm_cast]
-theorem nat_cast_imI (n : ℕ) : (n : ℍ[R,c₁,c₂]).imI = 0 :=
+theorem natCast_imI (n : ℕ) : (n : ℍ[R,c₁,c₂]).imI = 0 :=
   rfl
-#align quaternion_algebra.nat_cast_im_i QuaternionAlgebra.nat_cast_imI
+#align quaternion_algebra.nat_cast_im_i QuaternionAlgebra.natCast_imI
 -/
 
-#print QuaternionAlgebra.nat_cast_imJ /-
+#print QuaternionAlgebra.natCast_imJ /-
 @[simp, norm_cast]
-theorem nat_cast_imJ (n : ℕ) : (n : ℍ[R,c₁,c₂]).imJ = 0 :=
+theorem natCast_imJ (n : ℕ) : (n : ℍ[R,c₁,c₂]).imJ = 0 :=
   rfl
-#align quaternion_algebra.nat_cast_im_j QuaternionAlgebra.nat_cast_imJ
+#align quaternion_algebra.nat_cast_im_j QuaternionAlgebra.natCast_imJ
 -/
 
-#print QuaternionAlgebra.nat_cast_imK /-
+#print QuaternionAlgebra.natCast_imK /-
 @[simp, norm_cast]
-theorem nat_cast_imK (n : ℕ) : (n : ℍ[R,c₁,c₂]).imK = 0 :=
+theorem natCast_imK (n : ℕ) : (n : ℍ[R,c₁,c₂]).imK = 0 :=
   rfl
-#align quaternion_algebra.nat_cast_im_k QuaternionAlgebra.nat_cast_imK
+#align quaternion_algebra.nat_cast_im_k QuaternionAlgebra.natCast_imK
 -/
 
-#print QuaternionAlgebra.nat_cast_im /-
+#print QuaternionAlgebra.natCast_im /-
 @[simp, norm_cast]
-theorem nat_cast_im (n : ℕ) : (n : ℍ[R,c₁,c₂]).im = 0 :=
+theorem natCast_im (n : ℕ) : (n : ℍ[R,c₁,c₂]).im = 0 :=
   rfl
-#align quaternion_algebra.nat_cast_im QuaternionAlgebra.nat_cast_im
+#align quaternion_algebra.nat_cast_im QuaternionAlgebra.natCast_im
 -/
 
-#print QuaternionAlgebra.coe_nat_cast /-
+#print QuaternionAlgebra.coe_natCast /-
 @[norm_cast]
-theorem coe_nat_cast (n : ℕ) : ↑(n : R) = (n : ℍ[R,c₁,c₂]) :=
+theorem coe_natCast (n : ℕ) : ↑(n : R) = (n : ℍ[R,c₁,c₂]) :=
   rfl
-#align quaternion_algebra.coe_nat_cast QuaternionAlgebra.coe_nat_cast
+#align quaternion_algebra.coe_nat_cast QuaternionAlgebra.coe_natCast
 -/
 
-#print QuaternionAlgebra.int_cast_re /-
+#print QuaternionAlgebra.intCast_re /-
 @[simp, norm_cast]
-theorem int_cast_re (z : ℤ) : (z : ℍ[R,c₁,c₂]).re = z :=
+theorem intCast_re (z : ℤ) : (z : ℍ[R,c₁,c₂]).re = z :=
   rfl
-#align quaternion_algebra.int_cast_re QuaternionAlgebra.int_cast_re
+#align quaternion_algebra.int_cast_re QuaternionAlgebra.intCast_re
 -/
 
-#print QuaternionAlgebra.int_cast_imI /-
+#print QuaternionAlgebra.intCast_imI /-
 @[simp, norm_cast]
-theorem int_cast_imI (z : ℤ) : (z : ℍ[R,c₁,c₂]).imI = 0 :=
+theorem intCast_imI (z : ℤ) : (z : ℍ[R,c₁,c₂]).imI = 0 :=
   rfl
-#align quaternion_algebra.int_cast_im_i QuaternionAlgebra.int_cast_imI
+#align quaternion_algebra.int_cast_im_i QuaternionAlgebra.intCast_imI
 -/
 
-#print QuaternionAlgebra.int_cast_imJ /-
+#print QuaternionAlgebra.intCast_imJ /-
 @[simp, norm_cast]
-theorem int_cast_imJ (z : ℤ) : (z : ℍ[R,c₁,c₂]).imJ = 0 :=
+theorem intCast_imJ (z : ℤ) : (z : ℍ[R,c₁,c₂]).imJ = 0 :=
   rfl
-#align quaternion_algebra.int_cast_im_j QuaternionAlgebra.int_cast_imJ
+#align quaternion_algebra.int_cast_im_j QuaternionAlgebra.intCast_imJ
 -/
 
-#print QuaternionAlgebra.int_cast_imK /-
+#print QuaternionAlgebra.intCast_imK /-
 @[simp, norm_cast]
-theorem int_cast_imK (z : ℤ) : (z : ℍ[R,c₁,c₂]).imK = 0 :=
+theorem intCast_imK (z : ℤ) : (z : ℍ[R,c₁,c₂]).imK = 0 :=
   rfl
-#align quaternion_algebra.int_cast_im_k QuaternionAlgebra.int_cast_imK
+#align quaternion_algebra.int_cast_im_k QuaternionAlgebra.intCast_imK
 -/
 
-#print QuaternionAlgebra.int_cast_im /-
+#print QuaternionAlgebra.intCast_im /-
 @[simp, norm_cast]
-theorem int_cast_im (z : ℤ) : (z : ℍ[R,c₁,c₂]).im = 0 :=
+theorem intCast_im (z : ℤ) : (z : ℍ[R,c₁,c₂]).im = 0 :=
   rfl
-#align quaternion_algebra.int_cast_im QuaternionAlgebra.int_cast_im
+#align quaternion_algebra.int_cast_im QuaternionAlgebra.intCast_im
 -/
 
-#print QuaternionAlgebra.coe_int_cast /-
+#print QuaternionAlgebra.coe_intCast /-
 @[norm_cast]
-theorem coe_int_cast (z : ℤ) : ↑(z : R) = (z : ℍ[R,c₁,c₂]) :=
+theorem coe_intCast (z : ℤ) : ↑(z : R) = (z : ℍ[R,c₁,c₂]) :=
   rfl
-#align quaternion_algebra.coe_int_cast QuaternionAlgebra.coe_int_cast
+#align quaternion_algebra.coe_int_cast QuaternionAlgebra.coe_intCast
 -/
 
 instance : Ring ℍ[R,c₁,c₂] := by
@@ -1290,88 +1290,88 @@ theorem coe_pow (n : ℕ) : (↑(x ^ n) : ℍ[R]) = ↑x ^ n :=
 #align quaternion.coe_pow Quaternion.coe_pow
 -/
 
-#print Quaternion.nat_cast_re /-
+#print Quaternion.natCast_re /-
 @[simp, norm_cast]
-theorem nat_cast_re (n : ℕ) : (n : ℍ[R]).re = n :=
+theorem natCast_re (n : ℕ) : (n : ℍ[R]).re = n :=
   rfl
-#align quaternion.nat_cast_re Quaternion.nat_cast_re
+#align quaternion.nat_cast_re Quaternion.natCast_re
 -/
 
-#print Quaternion.nat_cast_imI /-
+#print Quaternion.natCast_imI /-
 @[simp, norm_cast]
-theorem nat_cast_imI (n : ℕ) : (n : ℍ[R]).imI = 0 :=
+theorem natCast_imI (n : ℕ) : (n : ℍ[R]).imI = 0 :=
   rfl
-#align quaternion.nat_cast_im_i Quaternion.nat_cast_imI
+#align quaternion.nat_cast_im_i Quaternion.natCast_imI
 -/
 
-#print Quaternion.nat_cast_imJ /-
+#print Quaternion.natCast_imJ /-
 @[simp, norm_cast]
-theorem nat_cast_imJ (n : ℕ) : (n : ℍ[R]).imJ = 0 :=
+theorem natCast_imJ (n : ℕ) : (n : ℍ[R]).imJ = 0 :=
   rfl
-#align quaternion.nat_cast_im_j Quaternion.nat_cast_imJ
+#align quaternion.nat_cast_im_j Quaternion.natCast_imJ
 -/
 
-#print Quaternion.nat_cast_imK /-
+#print Quaternion.natCast_imK /-
 @[simp, norm_cast]
-theorem nat_cast_imK (n : ℕ) : (n : ℍ[R]).imK = 0 :=
+theorem natCast_imK (n : ℕ) : (n : ℍ[R]).imK = 0 :=
   rfl
-#align quaternion.nat_cast_im_k Quaternion.nat_cast_imK
+#align quaternion.nat_cast_im_k Quaternion.natCast_imK
 -/
 
-#print Quaternion.nat_cast_im /-
+#print Quaternion.natCast_im /-
 @[simp, norm_cast]
-theorem nat_cast_im (n : ℕ) : (n : ℍ[R]).im = 0 :=
+theorem natCast_im (n : ℕ) : (n : ℍ[R]).im = 0 :=
   rfl
-#align quaternion.nat_cast_im Quaternion.nat_cast_im
+#align quaternion.nat_cast_im Quaternion.natCast_im
 -/
 
-#print Quaternion.coe_nat_cast /-
+#print Quaternion.coe_natCast /-
 @[norm_cast]
-theorem coe_nat_cast (n : ℕ) : ↑(n : R) = (n : ℍ[R]) :=
+theorem coe_natCast (n : ℕ) : ↑(n : R) = (n : ℍ[R]) :=
   rfl
-#align quaternion.coe_nat_cast Quaternion.coe_nat_cast
+#align quaternion.coe_nat_cast Quaternion.coe_natCast
 -/
 
-#print Quaternion.int_cast_re /-
+#print Quaternion.intCast_re /-
 @[simp, norm_cast]
-theorem int_cast_re (z : ℤ) : (z : ℍ[R]).re = z :=
+theorem intCast_re (z : ℤ) : (z : ℍ[R]).re = z :=
   rfl
-#align quaternion.int_cast_re Quaternion.int_cast_re
+#align quaternion.int_cast_re Quaternion.intCast_re
 -/
 
-#print Quaternion.int_cast_imI /-
+#print Quaternion.intCast_imI /-
 @[simp, norm_cast]
-theorem int_cast_imI (z : ℤ) : (z : ℍ[R]).imI = 0 :=
+theorem intCast_imI (z : ℤ) : (z : ℍ[R]).imI = 0 :=
   rfl
-#align quaternion.int_cast_im_i Quaternion.int_cast_imI
+#align quaternion.int_cast_im_i Quaternion.intCast_imI
 -/
 
-#print Quaternion.int_cast_imJ /-
+#print Quaternion.intCast_imJ /-
 @[simp, norm_cast]
-theorem int_cast_imJ (z : ℤ) : (z : ℍ[R]).imJ = 0 :=
+theorem intCast_imJ (z : ℤ) : (z : ℍ[R]).imJ = 0 :=
   rfl
-#align quaternion.int_cast_im_j Quaternion.int_cast_imJ
+#align quaternion.int_cast_im_j Quaternion.intCast_imJ
 -/
 
-#print Quaternion.int_cast_imK /-
+#print Quaternion.intCast_imK /-
 @[simp, norm_cast]
-theorem int_cast_imK (z : ℤ) : (z : ℍ[R]).imK = 0 :=
+theorem intCast_imK (z : ℤ) : (z : ℍ[R]).imK = 0 :=
   rfl
-#align quaternion.int_cast_im_k Quaternion.int_cast_imK
+#align quaternion.int_cast_im_k Quaternion.intCast_imK
 -/
 
-#print Quaternion.int_cast_im /-
+#print Quaternion.intCast_im /-
 @[simp, norm_cast]
-theorem int_cast_im (z : ℤ) : (z : ℍ[R]).im = 0 :=
+theorem intCast_im (z : ℤ) : (z : ℍ[R]).im = 0 :=
   rfl
-#align quaternion.int_cast_im Quaternion.int_cast_im
+#align quaternion.int_cast_im Quaternion.intCast_im
 -/
 
-#print Quaternion.coe_int_cast /-
+#print Quaternion.coe_intCast /-
 @[norm_cast]
-theorem coe_int_cast (z : ℤ) : ↑(z : R) = (z : ℍ[R]) :=
+theorem coe_intCast (z : ℤ) : ↑(z : R) = (z : ℍ[R]) :=
   rfl
-#align quaternion.coe_int_cast Quaternion.coe_int_cast
+#align quaternion.coe_int_cast Quaternion.coe_intCast
 -/
 
 #print Quaternion.coe_injective /-
@@ -1670,16 +1670,16 @@ theorem normSq_star : normSq (star a) = normSq a := by simp [norm_sq_def']
 #align quaternion.norm_sq_star Quaternion.normSq_star
 -/
 
-#print Quaternion.normSq_nat_cast /-
+#print Quaternion.normSq_natCast /-
 @[norm_cast]
-theorem normSq_nat_cast (n : ℕ) : normSq (n : ℍ[R]) = n ^ 2 := by rw [← coe_nat_cast, norm_sq_coe]
-#align quaternion.norm_sq_nat_cast Quaternion.normSq_nat_cast
+theorem normSq_natCast (n : ℕ) : normSq (n : ℍ[R]) = n ^ 2 := by rw [← coe_nat_cast, norm_sq_coe]
+#align quaternion.norm_sq_nat_cast Quaternion.normSq_natCast
 -/
 
-#print Quaternion.normSq_int_cast /-
+#print Quaternion.normSq_intCast /-
 @[norm_cast]
-theorem normSq_int_cast (z : ℤ) : normSq (z : ℍ[R]) = z ^ 2 := by rw [← coe_int_cast, norm_sq_coe]
-#align quaternion.norm_sq_int_cast Quaternion.normSq_int_cast
+theorem normSq_intCast (z : ℤ) : normSq (z : ℍ[R]) = z ^ 2 := by rw [← coe_int_cast, norm_sq_coe]
+#align quaternion.norm_sq_int_cast Quaternion.normSq_intCast
 -/
 
 #print Quaternion.normSq_neg /-
@@ -1850,46 +1850,46 @@ instance : DivisionRing ℍ[R] :=
       rw [coe_mul_eq_smul]
       ext <;> exact DivisionRing.qsmul_eq_mul' _ _ }
 
-#print Quaternion.rat_cast_re /-
+#print Quaternion.ratCast_re /-
 @[simp, norm_cast]
-theorem rat_cast_re (q : ℚ) : (q : ℍ[R]).re = q :=
+theorem ratCast_re (q : ℚ) : (q : ℍ[R]).re = q :=
   rfl
-#align quaternion.rat_cast_re Quaternion.rat_cast_re
+#align quaternion.rat_cast_re Quaternion.ratCast_re
 -/
 
-#print Quaternion.rat_cast_imI /-
+#print Quaternion.ratCast_imI /-
 @[simp, norm_cast]
-theorem rat_cast_imI (q : ℚ) : (q : ℍ[R]).imI = 0 :=
+theorem ratCast_imI (q : ℚ) : (q : ℍ[R]).imI = 0 :=
   rfl
-#align quaternion.rat_cast_im_i Quaternion.rat_cast_imI
+#align quaternion.rat_cast_im_i Quaternion.ratCast_imI
 -/
 
-#print Quaternion.rat_cast_imJ /-
+#print Quaternion.ratCast_imJ /-
 @[simp, norm_cast]
-theorem rat_cast_imJ (q : ℚ) : (q : ℍ[R]).imJ = 0 :=
+theorem ratCast_imJ (q : ℚ) : (q : ℍ[R]).imJ = 0 :=
   rfl
-#align quaternion.rat_cast_im_j Quaternion.rat_cast_imJ
+#align quaternion.rat_cast_im_j Quaternion.ratCast_imJ
 -/
 
-#print Quaternion.rat_cast_imK /-
+#print Quaternion.ratCast_imK /-
 @[simp, norm_cast]
-theorem rat_cast_imK (q : ℚ) : (q : ℍ[R]).imK = 0 :=
+theorem ratCast_imK (q : ℚ) : (q : ℍ[R]).imK = 0 :=
   rfl
-#align quaternion.rat_cast_im_k Quaternion.rat_cast_imK
+#align quaternion.rat_cast_im_k Quaternion.ratCast_imK
 -/
 
-#print Quaternion.rat_cast_im /-
+#print Quaternion.ratCast_im /-
 @[simp, norm_cast]
-theorem rat_cast_im (q : ℚ) : (q : ℍ[R]).im = 0 :=
+theorem ratCast_im (q : ℚ) : (q : ℍ[R]).im = 0 :=
   rfl
-#align quaternion.rat_cast_im Quaternion.rat_cast_im
+#align quaternion.rat_cast_im Quaternion.ratCast_im
 -/
 
-#print Quaternion.coe_rat_cast /-
+#print Quaternion.coe_ratCast /-
 @[norm_cast]
-theorem coe_rat_cast (q : ℚ) : ↑(q : R) = (q : ℍ[R]) :=
+theorem coe_ratCast (q : ℚ) : ↑(q : R) = (q : ℍ[R]) :=
   rfl
-#align quaternion.coe_rat_cast Quaternion.coe_rat_cast
+#align quaternion.coe_rat_cast Quaternion.coe_ratCast
 -/
 
 #print Quaternion.normSq_inv /-
@@ -1913,10 +1913,10 @@ theorem normSq_zpow (z : ℤ) : normSq (a ^ z) = normSq a ^ z :=
 #align quaternion.norm_sq_zpow Quaternion.normSq_zpow
 -/
 
-#print Quaternion.normSq_rat_cast /-
+#print Quaternion.normSq_ratCast /-
 @[norm_cast]
-theorem normSq_rat_cast (q : ℚ) : normSq (q : ℍ[R]) = q ^ 2 := by rw [← coe_rat_cast, norm_sq_coe]
-#align quaternion.norm_sq_rat_cast Quaternion.normSq_rat_cast
+theorem normSq_ratCast (q : ℚ) : normSq (q : ℍ[R]) = q ^ 2 := by rw [← coe_rat_cast, norm_sq_coe]
+#align quaternion.norm_sq_rat_cast Quaternion.normSq_ratCast
 -/
 
 end Field

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -410,8 +410,8 @@ instance : AddGroupWithOne ℍ[R,c₁,c₂] :=
     natCast_zero := by simp
     natCast_succ := by simp
     intCast := fun n => ((n : R) : ℍ[R,c₁,c₂])
-    intCast_ofNat := fun _ => congr_arg coe (Int.cast_ofNat _)
-    intCast_negSucc := fun n => show ↑↑_ = -↑↑_ by rw [Int.cast_neg, Int.cast_ofNat, coe_neg]
+    intCast_ofNat := fun _ => congr_arg coe (Int.cast_natCast _)
+    intCast_negSucc := fun n => show ↑↑_ = -↑↑_ by rw [Int.cast_neg, Int.cast_natCast, coe_neg]
     one := 1 }
 
 #print QuaternionAlgebra.nat_cast_re /-
@@ -1843,7 +1843,8 @@ instance : DivisionRing ℍ[R] :=
   { Quaternion.groupWithZero,
     Quaternion.ring with
     ratCast := fun q => ↑(q : R)
-    ratCast_mk := fun n d hd h => by rw [Rat.cast_mk', coe_mul, coe_int_cast, coe_inv, coe_nat_cast]
+    ratCast_def := fun n d hd h => by
+      rw [Rat.cast_mk', coe_mul, coe_int_cast, coe_inv, coe_nat_cast]
     qsmul := (· • ·)
     qsmul_eq_mul' := fun q x => by
       rw [coe_mul_eq_smul]

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 -/
 import Algebra.Algebra.Equiv
-import LinearAlgebra.Finrank
+import LinearAlgebra.Dimension.Finrank
 import LinearAlgebra.FreeModule.Basic
 import LinearAlgebra.FreeModule.Finite.Basic
 import SetTheory.Cardinal.Ordinal

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -1742,7 +1742,7 @@ variable [LinearOrderedCommRing R] {a : ℍ[R]}
 theorem normSq_eq_zero : normSq a = 0 ↔ a = 0 :=
   by
   refine' ⟨fun h => _, fun h => h.symm ▸ norm_sq.map_zero⟩
-  rw [norm_sq_def', add_eq_zero_iff', add_eq_zero_iff', add_eq_zero_iff'] at h 
+  rw [norm_sq_def', add_eq_zero_iff', add_eq_zero_iff', add_eq_zero_iff'] at h
   exact ext a 0 (pow_eq_zero h.1.1.1) (pow_eq_zero h.1.1.2) (pow_eq_zero h.1.2) (pow_eq_zero h.2)
   all_goals apply_rules [sq_nonneg, add_nonneg]
 #align quaternion.norm_sq_eq_zero Quaternion.normSq_eq_zero

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -638,7 +638,7 @@ theorem rank_eq_four [StrongRankCondition R] : Module.rank R ℍ[R,c₁,c₂] =
 theorem finrank_eq_four [StrongRankCondition R] : FiniteDimensional.finrank R ℍ[R,c₁,c₂] = 4 :=
   by
   have : Cardinal.toNat 4 = 4 := by
-    rw [← Cardinal.toNat_cast 4, Nat.cast_bit0, Nat.cast_bit0, Nat.cast_one]
+    rw [← Cardinal.toNat_natCast 4, Nat.cast_bit0, Nat.cast_bit0, Nat.cast_one]
   rw [FiniteDimensional.finrank, rank_eq_four, this]
 #align quaternion_algebra.finrank_eq_four QuaternionAlgebra.finrank_eq_four
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -56,7 +56,7 @@ quaternion
 
 
 #print QuaternionAlgebra /-
-/- ./././Mathport/Syntax/Translate/Command.lean:440:34: infer kinds are unsupported in Lean 4: mk {} -/
+/- ./././Mathport/Syntax/Translate/Command.lean:436:34: infer kinds are unsupported in Lean 4: mk {} -/
 /-- Quaternion algebra over a type with fixed coefficients $a=i^2$ and $b=j^2$.
 Implemented as a structure with four fields: `re`, `im_i`, `im_j`, and `im_k`. -/
 @[nolint unused_arguments, ext]

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -56,7 +56,7 @@ quaternion
 
 
 #print QuaternionAlgebra /-
-/- ./././Mathport/Syntax/Translate/Command.lean:430:34: infer kinds are unsupported in Lean 4: mk {} -/
+/- ./././Mathport/Syntax/Translate/Command.lean:440:34: infer kinds are unsupported in Lean 4: mk {} -/
 /-- Quaternion algebra over a type with fixed coefficients $a=i^2$ and $b=j^2$.
 Implemented as a structure with four fields: `re`, `im_i`, `im_j`, and `im_k`. -/
 @[nolint unused_arguments, ext]

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

@@ -3,12 +3,12 @@ Copyright (c) 2020 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 -/
-import Mathbin.Algebra.Algebra.Equiv
-import Mathbin.LinearAlgebra.Finrank
-import Mathbin.LinearAlgebra.FreeModule.Basic
-import Mathbin.LinearAlgebra.FreeModule.Finite.Basic
-import Mathbin.SetTheory.Cardinal.Ordinal
-import Mathbin.Tactic.RingExp
+import Algebra.Algebra.Equiv
+import LinearAlgebra.Finrank
+import LinearAlgebra.FreeModule.Basic
+import LinearAlgebra.FreeModule.Finite.Basic
+import SetTheory.Cardinal.Ordinal
+import Tactic.RingExp
 
 #align_import algebra.quaternion from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
 
@@ -56,7 +56,7 @@ quaternion
 
 
 #print QuaternionAlgebra /-
-/- ./././Mathport/Syntax/Translate/Command.lean:429:34: infer kinds are unsupported in Lean 4: mk {} -/
+/- ./././Mathport/Syntax/Translate/Command.lean:430:34: infer kinds are unsupported in Lean 4: mk {} -/
 /-- Quaternion algebra over a type with fixed coefficients $a=i^2$ and $b=j^2$.
 Implemented as a structure with four fields: `re`, `im_i`, `im_j`, and `im_k`. -/
 @[nolint unused_arguments, ext]

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

@@ -743,7 +743,7 @@ instance : StarRing ℍ[R,c₁,c₂]
     where
   star_involutive x := by simp [Star.star]
   star_add a b := by ext <;> simp [neg_add]
-  star_mul a b := by ext <;> simp <;> ring
+  star_hMul a b := by ext <;> simp <;> ring
 
 #print QuaternionAlgebra.self_add_star' /-
 theorem self_add_star' : a + star a = ↑(2 * a.re) := by ext <;> simp [two_mul]
@@ -1773,7 +1773,7 @@ instance : NoZeroDivisors ℍ[R] :=
   { Quaternion.nontrivial with
     eq_zero_or_eq_zero_of_mul_eq_zero := fun a b hab =>
       have : normSq a * normSq b = 0 := by rwa [← norm_sq.map_mul, norm_sq_eq_zero]
-      (eq_zero_or_eq_zero_of_mul_eq_zero this).imp normSq_eq_zero.1 normSq_eq_zero.1 }
+      (eq_zero_or_eq_zero_of_hMul_eq_zero this).imp normSq_eq_zero.1 normSq_eq_zero.1 }
 
 instance : IsDomain ℍ[R] :=
   NoZeroDivisors.to_isDomain _

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

@@ -2,11 +2,6 @@
 Copyright (c) 2020 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module algebra.quaternion
-! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Algebra.Equiv
 import Mathbin.LinearAlgebra.Finrank
@@ -15,6 +10,8 @@ import Mathbin.LinearAlgebra.FreeModule.Finite.Basic
 import Mathbin.SetTheory.Cardinal.Ordinal
 import Mathbin.Tactic.RingExp
 
+#align_import algebra.quaternion from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
+
 /-!
 # Quaternions
 

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

@@ -59,7 +59,7 @@ quaternion
 
 
 #print QuaternionAlgebra /-
-/- ./././Mathport/Syntax/Translate/Command.lean:430:34: infer kinds are unsupported in Lean 4: mk {} -/
+/- ./././Mathport/Syntax/Translate/Command.lean:429:34: infer kinds are unsupported in Lean 4: mk {} -/
 /-- Quaternion algebra over a type with fixed coefficients $a=i^2$ and $b=j^2$.
 Implemented as a structure with four fields: `re`, `im_i`, `im_j`, and `im_k`. -/
 @[nolint unused_arguments, ext]
@@ -71,7 +71,6 @@ structure QuaternionAlgebra (R : Type _) (a b : R) where mk ::
 #align quaternion_algebra QuaternionAlgebra
 -/
 
--- mathport name: quaternion_algebra
 scoped[Quaternion] notation "ℍ[" R "," a "," b "]" => QuaternionAlgebra R a b
 
 namespace QuaternionAlgebra
@@ -124,10 +123,12 @@ def im (x : ℍ[R,c₁,c₂]) : ℍ[R,c₁,c₂] :=
 #align quaternion_algebra.im QuaternionAlgebra.im
 -/
 
+#print QuaternionAlgebra.im_re /-
 @[simp]
 theorem im_re : a.im.re = 0 :=
   rfl
 #align quaternion_algebra.im_re QuaternionAlgebra.im_re
+-/
 
 #print QuaternionAlgebra.im_imI /-
 @[simp]
@@ -167,37 +168,49 @@ theorem coe_re : (x : ℍ[R,c₁,c₂]).re = x :=
 #align quaternion_algebra.coe_re QuaternionAlgebra.coe_re
 -/
 
+#print QuaternionAlgebra.coe_imI /-
 @[simp, norm_cast]
 theorem coe_imI : (x : ℍ[R,c₁,c₂]).imI = 0 :=
   rfl
 #align quaternion_algebra.coe_im_i QuaternionAlgebra.coe_imI
+-/
 
+#print QuaternionAlgebra.coe_imJ /-
 @[simp, norm_cast]
 theorem coe_imJ : (x : ℍ[R,c₁,c₂]).imJ = 0 :=
   rfl
 #align quaternion_algebra.coe_im_j QuaternionAlgebra.coe_imJ
+-/
 
+#print QuaternionAlgebra.coe_imK /-
 @[simp, norm_cast]
 theorem coe_imK : (x : ℍ[R,c₁,c₂]).imK = 0 :=
   rfl
 #align quaternion_algebra.coe_im_k QuaternionAlgebra.coe_imK
+-/
 
+#print QuaternionAlgebra.coe_injective /-
 theorem coe_injective : Function.Injective (coe : R → ℍ[R,c₁,c₂]) := fun x y h => congr_arg re h
 #align quaternion_algebra.coe_injective QuaternionAlgebra.coe_injective
+-/
 
+#print QuaternionAlgebra.coe_inj /-
 @[simp]
 theorem coe_inj {x y : R} : (x : ℍ[R,c₁,c₂]) = y ↔ x = y :=
   coe_injective.eq_iff
 #align quaternion_algebra.coe_inj QuaternionAlgebra.coe_inj
+-/
 
 @[simps]
 instance : Zero ℍ[R,c₁,c₂] :=
   ⟨⟨0, 0, 0, 0⟩⟩
 
+#print QuaternionAlgebra.coe_zero /-
 @[simp, norm_cast]
 theorem coe_zero : ((0 : R) : ℍ[R,c₁,c₂]) = 0 :=
   rfl
 #align quaternion_algebra.coe_zero QuaternionAlgebra.coe_zero
+-/
 
 instance : Inhabited ℍ[R,c₁,c₂] :=
   ⟨0⟩
@@ -206,67 +219,87 @@ instance : Inhabited ℍ[R,c₁,c₂] :=
 instance : One ℍ[R,c₁,c₂] :=
   ⟨⟨1, 0, 0, 0⟩⟩
 
+#print QuaternionAlgebra.coe_one /-
 @[simp, norm_cast]
 theorem coe_one : ((1 : R) : ℍ[R,c₁,c₂]) = 1 :=
   rfl
 #align quaternion_algebra.coe_one QuaternionAlgebra.coe_one
+-/
 
 @[simps]
 instance : Add ℍ[R,c₁,c₂] :=
   ⟨fun a b => ⟨a.1 + b.1, a.2 + b.2, a.3 + b.3, a.4 + b.4⟩⟩
 
+#print QuaternionAlgebra.mk_add_mk /-
 @[simp]
 theorem mk_add_mk (a₁ a₂ a₃ a₄ b₁ b₂ b₃ b₄ : R) :
     (mk a₁ a₂ a₃ a₄ : ℍ[R,c₁,c₂]) + mk b₁ b₂ b₃ b₄ = mk (a₁ + b₁) (a₂ + b₂) (a₃ + b₃) (a₄ + b₄) :=
   rfl
 #align quaternion_algebra.mk_add_mk QuaternionAlgebra.mk_add_mk
+-/
 
+#print QuaternionAlgebra.coe_add /-
 @[norm_cast, simp]
 theorem coe_add : ((x + y : R) : ℍ[R,c₁,c₂]) = x + y := by ext <;> simp
 #align quaternion_algebra.coe_add QuaternionAlgebra.coe_add
+-/
 
 @[simps]
 instance : Neg ℍ[R,c₁,c₂] :=
   ⟨fun a => ⟨-a.1, -a.2, -a.3, -a.4⟩⟩
 
+#print QuaternionAlgebra.neg_mk /-
 @[simp]
 theorem neg_mk (a₁ a₂ a₃ a₄ : R) : -(mk a₁ a₂ a₃ a₄ : ℍ[R,c₁,c₂]) = ⟨-a₁, -a₂, -a₃, -a₄⟩ :=
   rfl
 #align quaternion_algebra.neg_mk QuaternionAlgebra.neg_mk
+-/
 
+#print QuaternionAlgebra.coe_neg /-
 @[norm_cast, simp]
 theorem coe_neg : ((-x : R) : ℍ[R,c₁,c₂]) = -x := by ext <;> simp
 #align quaternion_algebra.coe_neg QuaternionAlgebra.coe_neg
+-/
 
 @[simps]
 instance : Sub ℍ[R,c₁,c₂] :=
   ⟨fun a b => ⟨a.1 - b.1, a.2 - b.2, a.3 - b.3, a.4 - b.4⟩⟩
 
+#print QuaternionAlgebra.mk_sub_mk /-
 @[simp]
 theorem mk_sub_mk (a₁ a₂ a₃ a₄ b₁ b₂ b₃ b₄ : R) :
     (mk a₁ a₂ a₃ a₄ : ℍ[R,c₁,c₂]) - mk b₁ b₂ b₃ b₄ = mk (a₁ - b₁) (a₂ - b₂) (a₃ - b₃) (a₄ - b₄) :=
   rfl
 #align quaternion_algebra.mk_sub_mk QuaternionAlgebra.mk_sub_mk
+-/
 
+#print QuaternionAlgebra.coe_im /-
 @[simp, norm_cast]
 theorem coe_im : (x : ℍ[R,c₁,c₂]).im = 0 :=
   rfl
 #align quaternion_algebra.coe_im QuaternionAlgebra.coe_im
+-/
 
+#print QuaternionAlgebra.re_add_im /-
 @[simp]
 theorem re_add_im : ↑a.re + a.im = a :=
   ext _ _ (add_zero _) (zero_add _) (zero_add _) (zero_add _)
 #align quaternion_algebra.re_add_im QuaternionAlgebra.re_add_im
+-/
 
+#print QuaternionAlgebra.sub_self_im /-
 @[simp]
 theorem sub_self_im : a - a.im = a.re :=
   ext _ _ (sub_zero _) (sub_self _) (sub_self _) (sub_self _)
 #align quaternion_algebra.sub_self_im QuaternionAlgebra.sub_self_im
+-/
 
+#print QuaternionAlgebra.sub_self_re /-
 @[simp]
 theorem sub_self_re : a - a.re = a.im :=
   ext _ _ (sub_self _) (sub_zero _) (sub_zero _) (sub_zero _)
 #align quaternion_algebra.sub_self_re QuaternionAlgebra.sub_self_re
+-/
 
 /-- Multiplication is given by
 
@@ -285,6 +318,7 @@ instance : Mul ℍ[R,c₁,c₂] :=
       a.1 * b.3 + c₁ * a.2 * b.4 + a.3 * b.1 - c₁ * a.4 * b.2,
       a.1 * b.4 + a.2 * b.3 - a.3 * b.2 + a.4 * b.1⟩⟩
 
+#print QuaternionAlgebra.mk_mul_mk /-
 @[simp]
 theorem mk_mul_mk (a₁ a₂ a₃ a₄ b₁ b₂ b₃ b₄ : R) :
     (mk a₁ a₂ a₃ a₄ : ℍ[R,c₁,c₂]) * mk b₁ b₂ b₃ b₄ =
@@ -293,6 +327,7 @@ theorem mk_mul_mk (a₁ a₂ a₃ a₄ b₁ b₂ b₃ b₄ : R) :
         a₁ * b₃ + c₁ * a₂ * b₄ + a₃ * b₁ - c₁ * a₄ * b₂, a₁ * b₄ + a₂ * b₃ - a₃ * b₂ + a₄ * b₁⟩ :=
   rfl
 #align quaternion_algebra.mk_mul_mk QuaternionAlgebra.mk_mul_mk
+-/
 
 section
 
@@ -312,38 +347,50 @@ instance [SMul S T] [IsScalarTower S T R] : IsScalarTower S T ℍ[R,c₁,c₂]
 instance [SMulCommClass S T R] : SMulCommClass S T ℍ[R,c₁,c₂]
     where smul_comm s t x := by ext <;> exact smul_comm _ _ _
 
+#print QuaternionAlgebra.smul_re /-
 @[simp]
 theorem smul_re : (s • a).re = s • a.re :=
   rfl
 #align quaternion_algebra.smul_re QuaternionAlgebra.smul_re
+-/
 
+#print QuaternionAlgebra.smul_imI /-
 @[simp]
 theorem smul_imI : (s • a).imI = s • a.imI :=
   rfl
 #align quaternion_algebra.smul_im_i QuaternionAlgebra.smul_imI
+-/
 
+#print QuaternionAlgebra.smul_imJ /-
 @[simp]
 theorem smul_imJ : (s • a).imJ = s • a.imJ :=
   rfl
 #align quaternion_algebra.smul_im_j QuaternionAlgebra.smul_imJ
+-/
 
+#print QuaternionAlgebra.smul_imK /-
 @[simp]
 theorem smul_imK : (s • a).imK = s • a.imK :=
   rfl
 #align quaternion_algebra.smul_im_k QuaternionAlgebra.smul_imK
+-/
 
+#print QuaternionAlgebra.smul_mk /-
 @[simp]
 theorem smul_mk (re im_i im_j im_k : R) :
     s • (⟨re, im_i, im_j, im_k⟩ : ℍ[R,c₁,c₂]) = ⟨s • re, s • im_i, s • im_j, s • im_k⟩ :=
   rfl
 #align quaternion_algebra.smul_mk QuaternionAlgebra.smul_mk
+-/
 
 end
 
+#print QuaternionAlgebra.coe_smul /-
 @[simp, norm_cast]
 theorem coe_smul [SMulZeroClass S R] (s : S) (r : R) : (↑(s • r) : ℍ[R,c₁,c₂]) = s • ↑r :=
   ext _ _ rfl (smul_zero s).symm (smul_zero s).symm (smul_zero s).symm
 #align quaternion_algebra.coe_smul QuaternionAlgebra.coe_smul
+-/
 
 instance : AddCommGroup ℍ[R,c₁,c₂] := by
   refine_struct {
@@ -370,65 +417,89 @@ instance : AddGroupWithOne ℍ[R,c₁,c₂] :=
     intCast_negSucc := fun n => show ↑↑_ = -↑↑_ by rw [Int.cast_neg, Int.cast_ofNat, coe_neg]
     one := 1 }
 
+#print QuaternionAlgebra.nat_cast_re /-
 @[simp, norm_cast]
 theorem nat_cast_re (n : ℕ) : (n : ℍ[R,c₁,c₂]).re = n :=
   rfl
 #align quaternion_algebra.nat_cast_re QuaternionAlgebra.nat_cast_re
+-/
 
+#print QuaternionAlgebra.nat_cast_imI /-
 @[simp, norm_cast]
 theorem nat_cast_imI (n : ℕ) : (n : ℍ[R,c₁,c₂]).imI = 0 :=
   rfl
 #align quaternion_algebra.nat_cast_im_i QuaternionAlgebra.nat_cast_imI
+-/
 
+#print QuaternionAlgebra.nat_cast_imJ /-
 @[simp, norm_cast]
 theorem nat_cast_imJ (n : ℕ) : (n : ℍ[R,c₁,c₂]).imJ = 0 :=
   rfl
 #align quaternion_algebra.nat_cast_im_j QuaternionAlgebra.nat_cast_imJ
+-/
 
+#print QuaternionAlgebra.nat_cast_imK /-
 @[simp, norm_cast]
 theorem nat_cast_imK (n : ℕ) : (n : ℍ[R,c₁,c₂]).imK = 0 :=
   rfl
 #align quaternion_algebra.nat_cast_im_k QuaternionAlgebra.nat_cast_imK
+-/
 
+#print QuaternionAlgebra.nat_cast_im /-
 @[simp, norm_cast]
 theorem nat_cast_im (n : ℕ) : (n : ℍ[R,c₁,c₂]).im = 0 :=
   rfl
 #align quaternion_algebra.nat_cast_im QuaternionAlgebra.nat_cast_im
+-/
 
+#print QuaternionAlgebra.coe_nat_cast /-
 @[norm_cast]
 theorem coe_nat_cast (n : ℕ) : ↑(n : R) = (n : ℍ[R,c₁,c₂]) :=
   rfl
 #align quaternion_algebra.coe_nat_cast QuaternionAlgebra.coe_nat_cast
+-/
 
+#print QuaternionAlgebra.int_cast_re /-
 @[simp, norm_cast]
 theorem int_cast_re (z : ℤ) : (z : ℍ[R,c₁,c₂]).re = z :=
   rfl
 #align quaternion_algebra.int_cast_re QuaternionAlgebra.int_cast_re
+-/
 
+#print QuaternionAlgebra.int_cast_imI /-
 @[simp, norm_cast]
 theorem int_cast_imI (z : ℤ) : (z : ℍ[R,c₁,c₂]).imI = 0 :=
   rfl
 #align quaternion_algebra.int_cast_im_i QuaternionAlgebra.int_cast_imI
+-/
 
+#print QuaternionAlgebra.int_cast_imJ /-
 @[simp, norm_cast]
 theorem int_cast_imJ (z : ℤ) : (z : ℍ[R,c₁,c₂]).imJ = 0 :=
   rfl
 #align quaternion_algebra.int_cast_im_j QuaternionAlgebra.int_cast_imJ
+-/
 
+#print QuaternionAlgebra.int_cast_imK /-
 @[simp, norm_cast]
 theorem int_cast_imK (z : ℤ) : (z : ℍ[R,c₁,c₂]).imK = 0 :=
   rfl
 #align quaternion_algebra.int_cast_im_k QuaternionAlgebra.int_cast_imK
+-/
 
+#print QuaternionAlgebra.int_cast_im /-
 @[simp, norm_cast]
 theorem int_cast_im (z : ℤ) : (z : ℍ[R,c₁,c₂]).im = 0 :=
   rfl
 #align quaternion_algebra.int_cast_im QuaternionAlgebra.int_cast_im
+-/
 
+#print QuaternionAlgebra.coe_int_cast /-
 @[norm_cast]
 theorem coe_int_cast (z : ℤ) : ↑(z : R) = (z : ℍ[R,c₁,c₂]) :=
   rfl
 #align quaternion_algebra.coe_int_cast QuaternionAlgebra.coe_int_cast
+-/
 
 instance : Ring ℍ[R,c₁,c₂] := by
   refine_struct
@@ -444,9 +515,11 @@ instance : Ring ℍ[R,c₁,c₂] := by
       simp <;>
     ring
 
+#print QuaternionAlgebra.coe_mul /-
 @[norm_cast, simp]
 theorem coe_mul : ((x * y : R) : ℍ[R,c₁,c₂]) = x * y := by ext <;> simp
 #align quaternion_algebra.coe_mul QuaternionAlgebra.coe_mul
+-/
 
 -- TODO: add weaker `mul_action`, `distrib_mul_action`, and `module` instances (and repeat them
 -- for `ℍ[R]`)
@@ -461,14 +534,17 @@ instance [CommSemiring S] [Algebra S R] : Algebra S ℍ[R,c₁,c₂]
   smul_def' s x := by ext <;> simp [Algebra.smul_def]
   commutes' s x := by ext <;> simp [Algebra.commutes]
 
+#print QuaternionAlgebra.algebraMap_eq /-
 theorem algebraMap_eq (r : R) : algebraMap R ℍ[R,c₁,c₂] r = ⟨r, 0, 0, 0⟩ :=
   rfl
 #align quaternion_algebra.algebra_map_eq QuaternionAlgebra.algebraMap_eq
+-/
 
 section
 
 variable (c₁ c₂)
 
+#print QuaternionAlgebra.reₗ /-
 /-- `quaternion_algebra.re` as a `linear_map`-/
 @[simps]
 def reₗ : ℍ[R,c₁,c₂] →ₗ[R] R where
@@ -476,7 +552,9 @@ def reₗ : ℍ[R,c₁,c₂] →ₗ[R] R where
   map_add' x y := rfl
   map_smul' r x := rfl
 #align quaternion_algebra.re_lm QuaternionAlgebra.reₗ
+-/
 
+#print QuaternionAlgebra.imIₗ /-
 /-- `quaternion_algebra.im_i` as a `linear_map`-/
 @[simps]
 def imIₗ : ℍ[R,c₁,c₂] →ₗ[R] R where
@@ -484,7 +562,9 @@ def imIₗ : ℍ[R,c₁,c₂] →ₗ[R] R where
   map_add' x y := rfl
   map_smul' r x := rfl
 #align quaternion_algebra.im_i_lm QuaternionAlgebra.imIₗ
+-/
 
+#print QuaternionAlgebra.imJₗ /-
 /-- `quaternion_algebra.im_j` as a `linear_map`-/
 @[simps]
 def imJₗ : ℍ[R,c₁,c₂] →ₗ[R] R where
@@ -492,7 +572,9 @@ def imJₗ : ℍ[R,c₁,c₂] →ₗ[R] R where
   map_add' x y := rfl
   map_smul' r x := rfl
 #align quaternion_algebra.im_j_lm QuaternionAlgebra.imJₗ
+-/
 
+#print QuaternionAlgebra.imKₗ /-
 /-- `quaternion_algebra.im_k` as a `linear_map`-/
 @[simps]
 def imKₗ : ℍ[R,c₁,c₂] →ₗ[R] R where
@@ -500,7 +582,9 @@ def imKₗ : ℍ[R,c₁,c₂] →ₗ[R] R where
   map_add' x y := rfl
   map_smul' r x := rfl
 #align quaternion_algebra.im_k_lm QuaternionAlgebra.imKₗ
+-/
 
+#print QuaternionAlgebra.linearEquivTuple /-
 /-- `quaternion_algebra.equiv_tuple` as a linear equivalence. -/
 def linearEquivTuple : ℍ[R,c₁,c₂] ≃ₗ[R] Fin 4 → R :=
   LinearEquiv.symm-- proofs are not `rfl` in the forward direction
@@ -510,27 +594,36 @@ def linearEquivTuple : ℍ[R,c₁,c₂] ≃ₗ[R] Fin 4 → R :=
       map_add' := fun v₁ v₂ => rfl
       map_smul' := fun v₁ v₂ => rfl }
 #align quaternion_algebra.linear_equiv_tuple QuaternionAlgebra.linearEquivTuple
+-/
 
+#print QuaternionAlgebra.coe_linearEquivTuple /-
 @[simp]
 theorem coe_linearEquivTuple : ⇑(linearEquivTuple c₁ c₂) = equivTuple c₁ c₂ :=
   rfl
 #align quaternion_algebra.coe_linear_equiv_tuple QuaternionAlgebra.coe_linearEquivTuple
+-/
 
+#print QuaternionAlgebra.coe_linearEquivTuple_symm /-
 @[simp]
 theorem coe_linearEquivTuple_symm : ⇑(linearEquivTuple c₁ c₂).symm = (equivTuple c₁ c₂).symm :=
   rfl
 #align quaternion_algebra.coe_linear_equiv_tuple_symm QuaternionAlgebra.coe_linearEquivTuple_symm
+-/
 
+#print QuaternionAlgebra.basisOneIJK /-
 /-- `ℍ[R, c₁, c₂]` has a basis over `R` given by `1`, `i`, `j`, and `k`. -/
 noncomputable def basisOneIJK : Basis (Fin 4) R ℍ[R,c₁,c₂] :=
   Basis.ofEquivFun <| linearEquivTuple c₁ c₂
 #align quaternion_algebra.basis_one_i_j_k QuaternionAlgebra.basisOneIJK
+-/
 
+#print QuaternionAlgebra.coe_basisOneIJK_repr /-
 @[simp]
 theorem coe_basisOneIJK_repr (q : ℍ[R,c₁,c₂]) :
     ⇑((basisOneIJK c₁ c₂).repr q) = ![q.re, q.imI, q.imJ, q.imK] :=
   rfl
 #align quaternion_algebra.coe_basis_one_i_j_k_repr QuaternionAlgebra.coe_basisOneIJK_repr
+-/
 
 instance : Module.Finite R ℍ[R,c₁,c₂] :=
   Module.Finite.of_basis (basisOneIJK c₁ c₂)
@@ -538,51 +631,71 @@ instance : Module.Finite R ℍ[R,c₁,c₂] :=
 instance : Module.Free R ℍ[R,c₁,c₂] :=
   Module.Free.of_basis (basisOneIJK c₁ c₂)
 
+#print QuaternionAlgebra.rank_eq_four /-
 theorem rank_eq_four [StrongRankCondition R] : Module.rank R ℍ[R,c₁,c₂] = 4 := by
   rw [rank_eq_card_basis (basis_one_i_j_k c₁ c₂), Fintype.card_fin]; norm_num
 #align quaternion_algebra.rank_eq_four QuaternionAlgebra.rank_eq_four
+-/
 
+#print QuaternionAlgebra.finrank_eq_four /-
 theorem finrank_eq_four [StrongRankCondition R] : FiniteDimensional.finrank R ℍ[R,c₁,c₂] = 4 :=
   by
   have : Cardinal.toNat 4 = 4 := by
     rw [← Cardinal.toNat_cast 4, Nat.cast_bit0, Nat.cast_bit0, Nat.cast_one]
   rw [FiniteDimensional.finrank, rank_eq_four, this]
 #align quaternion_algebra.finrank_eq_four QuaternionAlgebra.finrank_eq_four
+-/
 
 end
 
+#print QuaternionAlgebra.coe_sub /-
 @[norm_cast, simp]
 theorem coe_sub : ((x - y : R) : ℍ[R,c₁,c₂]) = x - y :=
   (algebraMap R ℍ[R,c₁,c₂]).map_sub x y
 #align quaternion_algebra.coe_sub QuaternionAlgebra.coe_sub
+-/
 
+#print QuaternionAlgebra.coe_pow /-
 @[norm_cast, simp]
 theorem coe_pow (n : ℕ) : (↑(x ^ n) : ℍ[R,c₁,c₂]) = ↑x ^ n :=
   (algebraMap R ℍ[R,c₁,c₂]).map_pow x n
 #align quaternion_algebra.coe_pow QuaternionAlgebra.coe_pow
+-/
 
+#print QuaternionAlgebra.coe_commutes /-
 theorem coe_commutes : ↑r * a = a * r :=
   Algebra.commutes r a
 #align quaternion_algebra.coe_commutes QuaternionAlgebra.coe_commutes
+-/
 
+#print QuaternionAlgebra.coe_commute /-
 theorem coe_commute : Commute (↑r) a :=
   coe_commutes r a
 #align quaternion_algebra.coe_commute QuaternionAlgebra.coe_commute
+-/
 
+#print QuaternionAlgebra.coe_mul_eq_smul /-
 theorem coe_mul_eq_smul : ↑r * a = r • a :=
   (Algebra.smul_def r a).symm
 #align quaternion_algebra.coe_mul_eq_smul QuaternionAlgebra.coe_mul_eq_smul
+-/
 
+#print QuaternionAlgebra.mul_coe_eq_smul /-
 theorem mul_coe_eq_smul : a * r = r • a := by rw [← coe_commutes, coe_mul_eq_smul]
 #align quaternion_algebra.mul_coe_eq_smul QuaternionAlgebra.mul_coe_eq_smul
+-/
 
+#print QuaternionAlgebra.coe_algebraMap /-
 @[norm_cast, simp]
 theorem coe_algebraMap : ⇑(algebraMap R ℍ[R,c₁,c₂]) = coe :=
   rfl
 #align quaternion_algebra.coe_algebra_map QuaternionAlgebra.coe_algebraMap
+-/
 
+#print QuaternionAlgebra.smul_coe /-
 theorem smul_coe : x • (y : ℍ[R,c₁,c₂]) = ↑(x * y) := by rw [coe_mul, coe_mul_eq_smul]
 #align quaternion_algebra.smul_coe QuaternionAlgebra.smul_coe
+-/
 
 /-- Quaternion conjugate. -/
 instance : Star ℍ[R,c₁,c₂] where unit a := ⟨a.1, -a.2, -a.3, -a.4⟩
@@ -594,30 +707,40 @@ theorem re_star : (star a).re = a.re :=
 #align quaternion_algebra.re_star QuaternionAlgebra.re_star
 -/
 
+#print QuaternionAlgebra.imI_star /-
 @[simp]
 theorem imI_star : (star a).imI = -a.imI :=
   rfl
 #align quaternion_algebra.im_i_star QuaternionAlgebra.imI_star
+-/
 
+#print QuaternionAlgebra.imJ_star /-
 @[simp]
 theorem imJ_star : (star a).imJ = -a.imJ :=
   rfl
 #align quaternion_algebra.im_j_star QuaternionAlgebra.imJ_star
+-/
 
+#print QuaternionAlgebra.imK_star /-
 @[simp]
 theorem imK_star : (star a).imK = -a.imK :=
   rfl
 #align quaternion_algebra.im_k_star QuaternionAlgebra.imK_star
+-/
 
+#print QuaternionAlgebra.im_star /-
 @[simp]
 theorem im_star : (star a).im = -a.im :=
   ext _ _ neg_zero.symm rfl rfl rfl
 #align quaternion_algebra.im_star QuaternionAlgebra.im_star
+-/
 
+#print QuaternionAlgebra.star_mk /-
 @[simp]
 theorem star_mk (a₁ a₂ a₃ a₄ : R) : star (mk a₁ a₂ a₃ a₄ : ℍ[R,c₁,c₂]) = ⟨a₁, -a₂, -a₃, -a₄⟩ :=
   rfl
 #align quaternion_algebra.star_mk QuaternionAlgebra.star_mk
+-/
 
 instance : StarRing ℍ[R,c₁,c₂]
     where
@@ -625,75 +748,104 @@ instance : StarRing ℍ[R,c₁,c₂]
   star_add a b := by ext <;> simp [neg_add]
   star_mul a b := by ext <;> simp <;> ring
 
+#print QuaternionAlgebra.self_add_star' /-
 theorem self_add_star' : a + star a = ↑(2 * a.re) := by ext <;> simp [two_mul]
 #align quaternion_algebra.self_add_star' QuaternionAlgebra.self_add_star'
+-/
 
+#print QuaternionAlgebra.self_add_star /-
 theorem self_add_star : a + star a = 2 * a.re := by simp only [self_add_star', two_mul, coe_add]
 #align quaternion_algebra.self_add_star QuaternionAlgebra.self_add_star
+-/
 
+#print QuaternionAlgebra.star_add_self' /-
 theorem star_add_self' : star a + a = ↑(2 * a.re) := by rw [add_comm, self_add_star']
 #align quaternion_algebra.star_add_self' QuaternionAlgebra.star_add_self'
+-/
 
+#print QuaternionAlgebra.star_add_self /-
 theorem star_add_self : star a + a = 2 * a.re := by rw [add_comm, self_add_star]
 #align quaternion_algebra.star_add_self QuaternionAlgebra.star_add_self
+-/
 
+#print QuaternionAlgebra.star_eq_two_re_sub /-
 theorem star_eq_two_re_sub : star a = ↑(2 * a.re) - a :=
   eq_sub_iff_add_eq.2 a.star_add_self'
 #align quaternion_algebra.star_eq_two_re_sub QuaternionAlgebra.star_eq_two_re_sub
+-/
 
 instance : IsStarNormal a :=
   ⟨by
     rw [a.star_eq_two_re_sub]
     exact (coe_commute (2 * a.re) a).sub_left (Commute.refl a)⟩
 
+#print QuaternionAlgebra.star_coe /-
 @[simp, norm_cast]
 theorem star_coe : star (x : ℍ[R,c₁,c₂]) = x := by ext <;> simp
 #align quaternion_algebra.star_coe QuaternionAlgebra.star_coe
+-/
 
+#print QuaternionAlgebra.star_im /-
 @[simp]
 theorem star_im : star a.im = -a.im :=
   im_star _
 #align quaternion_algebra.star_im QuaternionAlgebra.star_im
+-/
 
+#print QuaternionAlgebra.star_smul /-
 @[simp]
 theorem star_smul [Monoid S] [DistribMulAction S R] (s : S) (a : ℍ[R,c₁,c₂]) :
     star (s • a) = s • star a :=
   ext _ _ rfl (smul_neg _ _).symm (smul_neg _ _).symm (smul_neg _ _).symm
 #align quaternion_algebra.star_smul QuaternionAlgebra.star_smul
+-/
 
+#print QuaternionAlgebra.eq_re_of_eq_coe /-
 theorem eq_re_of_eq_coe {a : ℍ[R,c₁,c₂]} {x : R} (h : a = x) : a = a.re := by rw [h, coe_re]
 #align quaternion_algebra.eq_re_of_eq_coe QuaternionAlgebra.eq_re_of_eq_coe
+-/
 
+#print QuaternionAlgebra.eq_re_iff_mem_range_coe /-
 theorem eq_re_iff_mem_range_coe {a : ℍ[R,c₁,c₂]} :
     a = a.re ↔ a ∈ Set.range (coe : R → ℍ[R,c₁,c₂]) :=
   ⟨fun h => ⟨a.re, h.symm⟩, fun ⟨x, h⟩ => eq_re_of_eq_coe h.symm⟩
 #align quaternion_algebra.eq_re_iff_mem_range_coe QuaternionAlgebra.eq_re_iff_mem_range_coe
+-/
 
 section CharZero
 
 variable [NoZeroDivisors R] [CharZero R]
 
+#print QuaternionAlgebra.star_eq_self /-
 @[simp]
 theorem star_eq_self {c₁ c₂ : R} {a : ℍ[R,c₁,c₂]} : star a = a ↔ a = a.re := by
   simp [ext_iff, neg_eq_iff_add_eq_zero, add_self_eq_zero]
 #align quaternion_algebra.star_eq_self QuaternionAlgebra.star_eq_self
+-/
 
+#print QuaternionAlgebra.star_eq_neg /-
 theorem star_eq_neg {c₁ c₂ : R} {a : ℍ[R,c₁,c₂]} : star a = -a ↔ a.re = 0 := by
   simp [ext_iff, eq_neg_iff_add_eq_zero]
 #align quaternion_algebra.star_eq_neg QuaternionAlgebra.star_eq_neg
+-/
 
 end CharZero
 
+#print QuaternionAlgebra.star_mul_eq_coe /-
 -- Can't use `rw ← star_eq_self` in the proof without additional assumptions
 theorem star_mul_eq_coe : star a * a = (star a * a).re := by ext <;> simp <;> ring
 #align quaternion_algebra.star_mul_eq_coe QuaternionAlgebra.star_mul_eq_coe
+-/
 
+#print QuaternionAlgebra.mul_star_eq_coe /-
 theorem mul_star_eq_coe : a * star a = (a * star a).re := by rw [← star_comm_self'];
   exact a.star_mul_eq_coe
 #align quaternion_algebra.mul_star_eq_coe QuaternionAlgebra.mul_star_eq_coe
+-/
 
 open MulOpposite
 
+#print QuaternionAlgebra.starAe /-
 /-- Quaternion conjugate as an `alg_equiv` to the opposite ring. -/
 def starAe : ℍ[R,c₁,c₂] ≃ₐ[R] ℍ[R,c₁,c₂]ᵐᵒᵖ :=
   { starAddEquiv.trans opAddEquiv with
@@ -702,11 +854,14 @@ def starAe : ℍ[R,c₁,c₂] ≃ₐ[R] ℍ[R,c₁,c₂]ᵐᵒᵖ :=
     map_mul' := fun x y => by simp
     commutes' := fun r => by simp }
 #align quaternion_algebra.star_ae QuaternionAlgebra.starAe
+-/
 
+#print QuaternionAlgebra.coe_starAe /-
 @[simp]
 theorem coe_starAe : ⇑(starAe : ℍ[R,c₁,c₂] ≃ₐ[R] _) = op ∘ star :=
   rfl
 #align quaternion_algebra.coe_star_ae QuaternionAlgebra.coe_starAe
+-/
 
 end QuaternionAlgebra
 
@@ -718,7 +873,6 @@ def Quaternion (R : Type _) [One R] [Neg R] :=
 #align quaternion Quaternion
 -/
 
--- mathport name: quaternion
 scoped[Quaternion] notation "ℍ[" R "]" => Quaternion R
 
 #print Quaternion.equivProd /-
@@ -775,60 +929,82 @@ instance [CommSemiring S] [Algebra S R] : Algebra S ℍ[R] :=
 instance : StarRing ℍ[R] :=
   QuaternionAlgebra.starRing
 
+#print Quaternion.ext /-
 @[ext]
 theorem ext : a.re = b.re → a.imI = b.imI → a.imJ = b.imJ → a.imK = b.imK → a = b :=
   QuaternionAlgebra.ext a b
 #align quaternion.ext Quaternion.ext
+-/
 
+#print Quaternion.ext_iff /-
 theorem ext_iff {a b : ℍ[R]} :
     a = b ↔ a.re = b.re ∧ a.imI = b.imI ∧ a.imJ = b.imJ ∧ a.imK = b.imK :=
   QuaternionAlgebra.ext_iff a b
 #align quaternion.ext_iff Quaternion.ext_iff
+-/
 
+#print Quaternion.im /-
 /-- The imaginary part of a quaternion. -/
 def im (x : ℍ[R]) : ℍ[R] :=
   x.im
 #align quaternion.im Quaternion.im
+-/
 
+#print Quaternion.im_re /-
 @[simp]
 theorem im_re : a.im.re = 0 :=
   rfl
 #align quaternion.im_re Quaternion.im_re
+-/
 
+#print Quaternion.im_imI /-
 @[simp]
 theorem im_imI : a.im.imI = a.imI :=
   rfl
 #align quaternion.im_im_i Quaternion.im_imI
+-/
 
+#print Quaternion.im_imJ /-
 @[simp]
 theorem im_imJ : a.im.imJ = a.imJ :=
   rfl
 #align quaternion.im_im_j Quaternion.im_imJ
+-/
 
+#print Quaternion.im_imK /-
 @[simp]
 theorem im_imK : a.im.imK = a.imK :=
   rfl
 #align quaternion.im_im_k Quaternion.im_imK
+-/
 
+#print Quaternion.im_idem /-
 @[simp]
 theorem im_idem : a.im.im = a.im :=
   rfl
 #align quaternion.im_idem Quaternion.im_idem
+-/
 
+#print Quaternion.re_add_im /-
 @[simp]
 theorem re_add_im : ↑a.re + a.im = a :=
   a.re_add_im
 #align quaternion.re_add_im Quaternion.re_add_im
+-/
 
+#print Quaternion.sub_self_im /-
 @[simp]
 theorem sub_self_im : a - a.im = a.re :=
   a.sub_self_im
 #align quaternion.sub_self_im Quaternion.sub_self_im
+-/
 
+#print Quaternion.sub_self_re /-
 @[simp]
 theorem sub_self_re : a - a.re = a.im :=
   a.sub_self_re
 #align quaternion.sub_self_re Quaternion.sub_self_re
+-/
 
 #print Quaternion.coe_re /-
 @[simp, norm_cast]
@@ -837,329 +1013,461 @@ theorem coe_re : (x : ℍ[R]).re = x :=
 #align quaternion.coe_re Quaternion.coe_re
 -/
 
+#print Quaternion.coe_imI /-
 @[simp, norm_cast]
 theorem coe_imI : (x : ℍ[R]).imI = 0 :=
   rfl
 #align quaternion.coe_im_i Quaternion.coe_imI
+-/
 
+#print Quaternion.coe_imJ /-
 @[simp, norm_cast]
 theorem coe_imJ : (x : ℍ[R]).imJ = 0 :=
   rfl
 #align quaternion.coe_im_j Quaternion.coe_imJ
+-/
 
+#print Quaternion.coe_imK /-
 @[simp, norm_cast]
 theorem coe_imK : (x : ℍ[R]).imK = 0 :=
   rfl
 #align quaternion.coe_im_k Quaternion.coe_imK
+-/
 
+#print Quaternion.coe_im /-
 @[simp, norm_cast]
 theorem coe_im : (x : ℍ[R]).im = 0 :=
   rfl
 #align quaternion.coe_im Quaternion.coe_im
+-/
 
+#print Quaternion.zero_re /-
 @[simp]
 theorem zero_re : (0 : ℍ[R]).re = 0 :=
   rfl
 #align quaternion.zero_re Quaternion.zero_re
+-/
 
+#print Quaternion.zero_imI /-
 @[simp]
 theorem zero_imI : (0 : ℍ[R]).imI = 0 :=
   rfl
 #align quaternion.zero_im_i Quaternion.zero_imI
+-/
 
+#print Quaternion.zero_imJ /-
 @[simp]
 theorem zero_imJ : (0 : ℍ[R]).imJ = 0 :=
   rfl
 #align quaternion.zero_im_j Quaternion.zero_imJ
+-/
 
+#print Quaternion.zero_imK /-
 @[simp]
 theorem zero_imK : (0 : ℍ[R]).imK = 0 :=
   rfl
 #align quaternion.zero_im_k Quaternion.zero_imK
+-/
 
+#print Quaternion.zero_im /-
 @[simp]
 theorem zero_im : (0 : ℍ[R]).im = 0 :=
   rfl
 #align quaternion.zero_im Quaternion.zero_im
+-/
 
+#print Quaternion.coe_zero /-
 @[simp, norm_cast]
 theorem coe_zero : ((0 : R) : ℍ[R]) = 0 :=
   rfl
 #align quaternion.coe_zero Quaternion.coe_zero
+-/
 
+#print Quaternion.one_re /-
 @[simp]
 theorem one_re : (1 : ℍ[R]).re = 1 :=
   rfl
 #align quaternion.one_re Quaternion.one_re
+-/
 
+#print Quaternion.one_imI /-
 @[simp]
 theorem one_imI : (1 : ℍ[R]).imI = 0 :=
   rfl
 #align quaternion.one_im_i Quaternion.one_imI
+-/
 
+#print Quaternion.one_imJ /-
 @[simp]
 theorem one_imJ : (1 : ℍ[R]).imJ = 0 :=
   rfl
 #align quaternion.one_im_j Quaternion.one_imJ
+-/
 
+#print Quaternion.one_imK /-
 @[simp]
 theorem one_imK : (1 : ℍ[R]).imK = 0 :=
   rfl
 #align quaternion.one_im_k Quaternion.one_imK
+-/
 
+#print Quaternion.one_im /-
 @[simp]
 theorem one_im : (1 : ℍ[R]).im = 0 :=
   rfl
 #align quaternion.one_im Quaternion.one_im
+-/
 
+#print Quaternion.coe_one /-
 @[simp, norm_cast]
 theorem coe_one : ((1 : R) : ℍ[R]) = 1 :=
   rfl
 #align quaternion.coe_one Quaternion.coe_one
+-/
 
+#print Quaternion.add_re /-
 @[simp]
 theorem add_re : (a + b).re = a.re + b.re :=
   rfl
 #align quaternion.add_re Quaternion.add_re
+-/
 
+#print Quaternion.add_imI /-
 @[simp]
 theorem add_imI : (a + b).imI = a.imI + b.imI :=
   rfl
 #align quaternion.add_im_i Quaternion.add_imI
+-/
 
+#print Quaternion.add_imJ /-
 @[simp]
 theorem add_imJ : (a + b).imJ = a.imJ + b.imJ :=
   rfl
 #align quaternion.add_im_j Quaternion.add_imJ
+-/
 
+#print Quaternion.add_imK /-
 @[simp]
 theorem add_imK : (a + b).imK = a.imK + b.imK :=
   rfl
 #align quaternion.add_im_k Quaternion.add_imK
+-/
 
+#print Quaternion.add_im /-
 @[simp]
 theorem add_im : (a + b).im = a.im + b.im :=
   ext _ _ (add_zero _).symm rfl rfl rfl
 #align quaternion.add_im Quaternion.add_im
+-/
 
+#print Quaternion.coe_add /-
 @[simp, norm_cast]
 theorem coe_add : ((x + y : R) : ℍ[R]) = x + y :=
   QuaternionAlgebra.coe_add x y
 #align quaternion.coe_add Quaternion.coe_add
+-/
 
+#print Quaternion.neg_re /-
 @[simp]
 theorem neg_re : (-a).re = -a.re :=
   rfl
 #align quaternion.neg_re Quaternion.neg_re
+-/
 
+#print Quaternion.neg_imI /-
 @[simp]
 theorem neg_imI : (-a).imI = -a.imI :=
   rfl
 #align quaternion.neg_im_i Quaternion.neg_imI
+-/
 
+#print Quaternion.neg_imJ /-
 @[simp]
 theorem neg_imJ : (-a).imJ = -a.imJ :=
   rfl
 #align quaternion.neg_im_j Quaternion.neg_imJ
+-/
 
+#print Quaternion.neg_imK /-
 @[simp]
 theorem neg_imK : (-a).imK = -a.imK :=
   rfl
 #align quaternion.neg_im_k Quaternion.neg_imK
+-/
 
+#print Quaternion.neg_im /-
 @[simp]
 theorem neg_im : (-a).im = -a.im :=
   ext _ _ neg_zero.symm rfl rfl rfl
 #align quaternion.neg_im Quaternion.neg_im
+-/
 
+#print Quaternion.coe_neg /-
 @[simp, norm_cast]
 theorem coe_neg : ((-x : R) : ℍ[R]) = -x :=
   QuaternionAlgebra.coe_neg x
 #align quaternion.coe_neg Quaternion.coe_neg
+-/
 
+#print Quaternion.sub_re /-
 @[simp]
 theorem sub_re : (a - b).re = a.re - b.re :=
   rfl
 #align quaternion.sub_re Quaternion.sub_re
+-/
 
+#print Quaternion.sub_imI /-
 @[simp]
 theorem sub_imI : (a - b).imI = a.imI - b.imI :=
   rfl
 #align quaternion.sub_im_i Quaternion.sub_imI
+-/
 
+#print Quaternion.sub_imJ /-
 @[simp]
 theorem sub_imJ : (a - b).imJ = a.imJ - b.imJ :=
   rfl
 #align quaternion.sub_im_j Quaternion.sub_imJ
+-/
 
+#print Quaternion.sub_imK /-
 @[simp]
 theorem sub_imK : (a - b).imK = a.imK - b.imK :=
   rfl
 #align quaternion.sub_im_k Quaternion.sub_imK
+-/
 
+#print Quaternion.sub_im /-
 @[simp]
 theorem sub_im : (a - b).im = a.im - b.im :=
   ext _ _ (sub_zero _).symm rfl rfl rfl
 #align quaternion.sub_im Quaternion.sub_im
+-/
 
+#print Quaternion.coe_sub /-
 @[simp, norm_cast]
 theorem coe_sub : ((x - y : R) : ℍ[R]) = x - y :=
   QuaternionAlgebra.coe_sub x y
 #align quaternion.coe_sub Quaternion.coe_sub
+-/
 
+#print Quaternion.mul_re /-
 @[simp]
 theorem mul_re : (a * b).re = a.re * b.re - a.imI * b.imI - a.imJ * b.imJ - a.imK * b.imK :=
   (QuaternionAlgebra.mul_re a b).trans <| by simp only [one_mul, neg_mul, sub_eq_add_neg, neg_neg]
 #align quaternion.mul_re Quaternion.mul_re
+-/
 
+#print Quaternion.mul_imI /-
 @[simp]
 theorem mul_imI : (a * b).imI = a.re * b.imI + a.imI * b.re + a.imJ * b.imK - a.imK * b.imJ :=
   (QuaternionAlgebra.mul_imI a b).trans <| by simp only [one_mul, neg_mul, sub_eq_add_neg, neg_neg]
 #align quaternion.mul_im_i Quaternion.mul_imI
+-/
 
+#print Quaternion.mul_imJ /-
 @[simp]
 theorem mul_imJ : (a * b).imJ = a.re * b.imJ - a.imI * b.imK + a.imJ * b.re + a.imK * b.imI :=
   (QuaternionAlgebra.mul_imJ a b).trans <| by simp only [one_mul, neg_mul, sub_eq_add_neg, neg_neg]
 #align quaternion.mul_im_j Quaternion.mul_imJ
+-/
 
+#print Quaternion.mul_imK /-
 @[simp]
 theorem mul_imK : (a * b).imK = a.re * b.imK + a.imI * b.imJ - a.imJ * b.imI + a.imK * b.re :=
   (QuaternionAlgebra.mul_imK a b).trans <| by simp only [one_mul, neg_mul, sub_eq_add_neg, neg_neg]
 #align quaternion.mul_im_k Quaternion.mul_imK
+-/
 
+#print Quaternion.coe_mul /-
 @[simp, norm_cast]
 theorem coe_mul : ((x * y : R) : ℍ[R]) = x * y :=
   QuaternionAlgebra.coe_mul x y
 #align quaternion.coe_mul Quaternion.coe_mul
+-/
 
+#print Quaternion.coe_pow /-
 @[norm_cast, simp]
 theorem coe_pow (n : ℕ) : (↑(x ^ n) : ℍ[R]) = ↑x ^ n :=
   QuaternionAlgebra.coe_pow x n
 #align quaternion.coe_pow Quaternion.coe_pow
+-/
 
+#print Quaternion.nat_cast_re /-
 @[simp, norm_cast]
 theorem nat_cast_re (n : ℕ) : (n : ℍ[R]).re = n :=
   rfl
 #align quaternion.nat_cast_re Quaternion.nat_cast_re
+-/
 
+#print Quaternion.nat_cast_imI /-
 @[simp, norm_cast]
 theorem nat_cast_imI (n : ℕ) : (n : ℍ[R]).imI = 0 :=
   rfl
 #align quaternion.nat_cast_im_i Quaternion.nat_cast_imI
+-/
 
+#print Quaternion.nat_cast_imJ /-
 @[simp, norm_cast]
 theorem nat_cast_imJ (n : ℕ) : (n : ℍ[R]).imJ = 0 :=
   rfl
 #align quaternion.nat_cast_im_j Quaternion.nat_cast_imJ
+-/
 
+#print Quaternion.nat_cast_imK /-
 @[simp, norm_cast]
 theorem nat_cast_imK (n : ℕ) : (n : ℍ[R]).imK = 0 :=
   rfl
 #align quaternion.nat_cast_im_k Quaternion.nat_cast_imK
+-/
 
+#print Quaternion.nat_cast_im /-
 @[simp, norm_cast]
 theorem nat_cast_im (n : ℕ) : (n : ℍ[R]).im = 0 :=
   rfl
 #align quaternion.nat_cast_im Quaternion.nat_cast_im
+-/
 
+#print Quaternion.coe_nat_cast /-
 @[norm_cast]
 theorem coe_nat_cast (n : ℕ) : ↑(n : R) = (n : ℍ[R]) :=
   rfl
 #align quaternion.coe_nat_cast Quaternion.coe_nat_cast
+-/
 
+#print Quaternion.int_cast_re /-
 @[simp, norm_cast]
 theorem int_cast_re (z : ℤ) : (z : ℍ[R]).re = z :=
   rfl
 #align quaternion.int_cast_re Quaternion.int_cast_re
+-/
 
+#print Quaternion.int_cast_imI /-
 @[simp, norm_cast]
 theorem int_cast_imI (z : ℤ) : (z : ℍ[R]).imI = 0 :=
   rfl
 #align quaternion.int_cast_im_i Quaternion.int_cast_imI
+-/
 
+#print Quaternion.int_cast_imJ /-
 @[simp, norm_cast]
 theorem int_cast_imJ (z : ℤ) : (z : ℍ[R]).imJ = 0 :=
   rfl
 #align quaternion.int_cast_im_j Quaternion.int_cast_imJ
+-/
 
+#print Quaternion.int_cast_imK /-
 @[simp, norm_cast]
 theorem int_cast_imK (z : ℤ) : (z : ℍ[R]).imK = 0 :=
   rfl
 #align quaternion.int_cast_im_k Quaternion.int_cast_imK
+-/
 
+#print Quaternion.int_cast_im /-
 @[simp, norm_cast]
 theorem int_cast_im (z : ℤ) : (z : ℍ[R]).im = 0 :=
   rfl
 #align quaternion.int_cast_im Quaternion.int_cast_im
+-/
 
+#print Quaternion.coe_int_cast /-
 @[norm_cast]
 theorem coe_int_cast (z : ℤ) : ↑(z : R) = (z : ℍ[R]) :=
   rfl
 #align quaternion.coe_int_cast Quaternion.coe_int_cast
+-/
 
+#print Quaternion.coe_injective /-
 theorem coe_injective : Function.Injective (coe : R → ℍ[R]) :=
   QuaternionAlgebra.coe_injective
 #align quaternion.coe_injective Quaternion.coe_injective
+-/
 
+#print Quaternion.coe_inj /-
 @[simp]
 theorem coe_inj {x y : R} : (x : ℍ[R]) = y ↔ x = y :=
   coe_injective.eq_iff
 #align quaternion.coe_inj Quaternion.coe_inj
+-/
 
+#print Quaternion.smul_re /-
 @[simp]
 theorem smul_re [SMul S R] (s : S) : (s • a).re = s • a.re :=
   rfl
 #align quaternion.smul_re Quaternion.smul_re
+-/
 
+#print Quaternion.smul_imI /-
 @[simp]
 theorem smul_imI [SMul S R] (s : S) : (s • a).imI = s • a.imI :=
   rfl
 #align quaternion.smul_im_i Quaternion.smul_imI
+-/
 
+#print Quaternion.smul_imJ /-
 @[simp]
 theorem smul_imJ [SMul S R] (s : S) : (s • a).imJ = s • a.imJ :=
   rfl
 #align quaternion.smul_im_j Quaternion.smul_imJ
+-/
 
+#print Quaternion.smul_imK /-
 @[simp]
 theorem smul_imK [SMul S R] (s : S) : (s • a).imK = s • a.imK :=
   rfl
 #align quaternion.smul_im_k Quaternion.smul_imK
+-/
 
+#print Quaternion.smul_im /-
 @[simp]
 theorem smul_im [SMulZeroClass S R] (s : S) : (s • a).im = s • a.im :=
   ext _ _ (smul_zero _).symm rfl rfl rfl
 #align quaternion.smul_im Quaternion.smul_im
+-/
 
+#print Quaternion.coe_smul /-
 @[simp, norm_cast]
 theorem coe_smul [SMulZeroClass S R] (s : S) (r : R) : (↑(s • r) : ℍ[R]) = s • ↑r :=
   QuaternionAlgebra.coe_smul _ _
 #align quaternion.coe_smul Quaternion.coe_smul
+-/
 
+#print Quaternion.coe_commutes /-
 theorem coe_commutes : ↑r * a = a * r :=
   QuaternionAlgebra.coe_commutes r a
 #align quaternion.coe_commutes Quaternion.coe_commutes
+-/
 
+#print Quaternion.coe_commute /-
 theorem coe_commute : Commute (↑r) a :=
   QuaternionAlgebra.coe_commute r a
 #align quaternion.coe_commute Quaternion.coe_commute
+-/
 
+#print Quaternion.coe_mul_eq_smul /-
 theorem coe_mul_eq_smul : ↑r * a = r • a :=
   QuaternionAlgebra.coe_mul_eq_smul r a
 #align quaternion.coe_mul_eq_smul Quaternion.coe_mul_eq_smul
+-/
 
+#print Quaternion.mul_coe_eq_smul /-
 theorem mul_coe_eq_smul : a * r = r • a :=
   QuaternionAlgebra.mul_coe_eq_smul r a
 #align quaternion.mul_coe_eq_smul Quaternion.mul_coe_eq_smul
+-/
 
+#print Quaternion.algebraMap_def /-
 @[simp]
 theorem algebraMap_def : ⇑(algebraMap R ℍ[R]) = coe :=
   rfl
 #align quaternion.algebra_map_def Quaternion.algebraMap_def
+-/
 
+#print Quaternion.smul_coe /-
 theorem smul_coe : x • (y : ℍ[R]) = ↑(x * y) :=
   QuaternionAlgebra.smul_coe x y
 #align quaternion.smul_coe Quaternion.smul_coe
+-/
 
 instance : Module.Finite R ℍ[R] :=
   QuaternionAlgebra.Module.finite _ _
@@ -1167,119 +1475,166 @@ instance : Module.Finite R ℍ[R] :=
 instance : Module.Free R ℍ[R] :=
   QuaternionAlgebra.Module.free _ _
 
+#print Quaternion.rank_eq_four /-
 theorem rank_eq_four [StrongRankCondition R] : Module.rank R ℍ[R] = 4 :=
   QuaternionAlgebra.rank_eq_four _ _
 #align quaternion.rank_eq_four Quaternion.rank_eq_four
+-/
 
+#print Quaternion.finrank_eq_four /-
 theorem finrank_eq_four [StrongRankCondition R] : FiniteDimensional.finrank R ℍ[R] = 4 :=
   QuaternionAlgebra.finrank_eq_four _ _
 #align quaternion.finrank_eq_four Quaternion.finrank_eq_four
+-/
 
+#print Quaternion.star_re /-
 @[simp]
 theorem star_re : (star a).re = a.re :=
   rfl
 #align quaternion.star_re Quaternion.star_re
+-/
 
+#print Quaternion.star_imI /-
 @[simp]
 theorem star_imI : (star a).imI = -a.imI :=
   rfl
 #align quaternion.star_im_i Quaternion.star_imI
+-/
 
+#print Quaternion.star_imJ /-
 @[simp]
 theorem star_imJ : (star a).imJ = -a.imJ :=
   rfl
 #align quaternion.star_im_j Quaternion.star_imJ
+-/
 
+#print Quaternion.star_imK /-
 @[simp]
 theorem star_imK : (star a).imK = -a.imK :=
   rfl
 #align quaternion.star_im_k Quaternion.star_imK
+-/
 
+#print Quaternion.star_im /-
 @[simp]
 theorem star_im : (star a).im = -a.im :=
   a.im_star
 #align quaternion.star_im Quaternion.star_im
+-/
 
+#print Quaternion.self_add_star' /-
 theorem self_add_star' : a + star a = ↑(2 * a.re) :=
   a.self_add_star'
 #align quaternion.self_add_star' Quaternion.self_add_star'
+-/
 
+#print Quaternion.self_add_star /-
 theorem self_add_star : a + star a = 2 * a.re :=
   a.self_add_star
 #align quaternion.self_add_star Quaternion.self_add_star
+-/
 
+#print Quaternion.star_add_self' /-
 theorem star_add_self' : star a + a = ↑(2 * a.re) :=
   a.star_add_self'
 #align quaternion.star_add_self' Quaternion.star_add_self'
+-/
 
+#print Quaternion.star_add_self /-
 theorem star_add_self : star a + a = 2 * a.re :=
   a.star_add_self
 #align quaternion.star_add_self Quaternion.star_add_self
+-/
 
+#print Quaternion.star_eq_two_re_sub /-
 theorem star_eq_two_re_sub : star a = ↑(2 * a.re) - a :=
   a.star_eq_two_re_sub
 #align quaternion.star_eq_two_re_sub Quaternion.star_eq_two_re_sub
+-/
 
+#print Quaternion.star_coe /-
 @[simp, norm_cast]
 theorem star_coe : star (x : ℍ[R]) = x :=
   QuaternionAlgebra.star_coe x
 #align quaternion.star_coe Quaternion.star_coe
+-/
 
+#print Quaternion.im_star /-
 @[simp]
 theorem im_star : star a.im = -a.im :=
   QuaternionAlgebra.im_star _
 #align quaternion.im_star Quaternion.im_star
+-/
 
+#print Quaternion.star_smul /-
 @[simp]
 theorem star_smul [Monoid S] [DistribMulAction S R] (s : S) (a : ℍ[R]) :
     star (s • a) = s • star a :=
   QuaternionAlgebra.star_smul _ _
 #align quaternion.star_smul Quaternion.star_smul
+-/
 
+#print Quaternion.eq_re_of_eq_coe /-
 theorem eq_re_of_eq_coe {a : ℍ[R]} {x : R} (h : a = x) : a = a.re :=
   QuaternionAlgebra.eq_re_of_eq_coe h
 #align quaternion.eq_re_of_eq_coe Quaternion.eq_re_of_eq_coe
+-/
 
+#print Quaternion.eq_re_iff_mem_range_coe /-
 theorem eq_re_iff_mem_range_coe {a : ℍ[R]} : a = a.re ↔ a ∈ Set.range (coe : R → ℍ[R]) :=
   QuaternionAlgebra.eq_re_iff_mem_range_coe
 #align quaternion.eq_re_iff_mem_range_coe Quaternion.eq_re_iff_mem_range_coe
+-/
 
 section CharZero
 
 variable [NoZeroDivisors R] [CharZero R]
 
+#print Quaternion.star_eq_self /-
 @[simp]
 theorem star_eq_self {a : ℍ[R]} : star a = a ↔ a = a.re :=
   QuaternionAlgebra.star_eq_self
 #align quaternion.star_eq_self Quaternion.star_eq_self
+-/
 
+#print Quaternion.star_eq_neg /-
 @[simp]
 theorem star_eq_neg {a : ℍ[R]} : star a = -a ↔ a.re = 0 :=
   QuaternionAlgebra.star_eq_neg
 #align quaternion.star_eq_neg Quaternion.star_eq_neg
+-/
 
 end CharZero
 
+#print Quaternion.star_mul_eq_coe /-
 theorem star_mul_eq_coe : star a * a = (star a * a).re :=
   a.star_mul_eq_coe
 #align quaternion.star_mul_eq_coe Quaternion.star_mul_eq_coe
+-/
 
+#print Quaternion.mul_star_eq_coe /-
 theorem mul_star_eq_coe : a * star a = (a * star a).re :=
   a.mul_star_eq_coe
 #align quaternion.mul_star_eq_coe Quaternion.mul_star_eq_coe
+-/
 
 open MulOpposite
 
+#print Quaternion.starAe /-
 /-- Quaternion conjugate as an `alg_equiv` to the opposite ring. -/
 def starAe : ℍ[R] ≃ₐ[R] ℍ[R]ᵐᵒᵖ :=
   QuaternionAlgebra.starAe
 #align quaternion.star_ae Quaternion.starAe
+-/
 
+#print Quaternion.coe_starAe /-
 @[simp]
 theorem coe_starAe : ⇑(starAe : ℍ[R] ≃ₐ[R] ℍ[R]ᵐᵒᵖ) = op ∘ star :=
   rfl
 #align quaternion.coe_star_ae Quaternion.coe_starAe
+-/
 
+#print Quaternion.normSq /-
 /-- Square of the norm. -/
 def normSq : ℍ[R] →*₀ R where
   toFun a := (a * star a).re
@@ -1291,54 +1646,80 @@ def normSq : ℍ[R] →*₀ R where
         rw [← mul_star_eq_coe, star_mul, mul_assoc, ← mul_assoc y, y.mul_star_eq_coe, coe_commutes,
           ← mul_assoc, x.mul_star_eq_coe, ← coe_mul]
 #align quaternion.norm_sq Quaternion.normSq
+-/
 
+#print Quaternion.normSq_def /-
 theorem normSq_def : normSq a = (a * star a).re :=
   rfl
 #align quaternion.norm_sq_def Quaternion.normSq_def
+-/
 
+#print Quaternion.normSq_def' /-
 theorem normSq_def' : normSq a = a.1 ^ 2 + a.2 ^ 2 + a.3 ^ 2 + a.4 ^ 2 := by
   simp only [norm_sq_def, sq, mul_neg, sub_neg_eq_add, mul_re, star_re, star_im_i, star_im_j,
     star_im_k]
 #align quaternion.norm_sq_def' Quaternion.normSq_def'
+-/
 
+#print Quaternion.normSq_coe /-
 theorem normSq_coe : normSq (x : ℍ[R]) = x ^ 2 := by
   rw [norm_sq_def, star_coe, ← coe_mul, coe_re, sq]
 #align quaternion.norm_sq_coe Quaternion.normSq_coe
+-/
 
+#print Quaternion.normSq_star /-
 @[simp]
 theorem normSq_star : normSq (star a) = normSq a := by simp [norm_sq_def']
 #align quaternion.norm_sq_star Quaternion.normSq_star
+-/
 
+#print Quaternion.normSq_nat_cast /-
 @[norm_cast]
 theorem normSq_nat_cast (n : ℕ) : normSq (n : ℍ[R]) = n ^ 2 := by rw [← coe_nat_cast, norm_sq_coe]
 #align quaternion.norm_sq_nat_cast Quaternion.normSq_nat_cast
+-/
 
+#print Quaternion.normSq_int_cast /-
 @[norm_cast]
 theorem normSq_int_cast (z : ℤ) : normSq (z : ℍ[R]) = z ^ 2 := by rw [← coe_int_cast, norm_sq_coe]
 #align quaternion.norm_sq_int_cast Quaternion.normSq_int_cast
+-/
 
+#print Quaternion.normSq_neg /-
 @[simp]
 theorem normSq_neg : normSq (-a) = normSq a := by simp only [norm_sq_def, star_neg, neg_mul_neg]
 #align quaternion.norm_sq_neg Quaternion.normSq_neg
+-/
 
+#print Quaternion.self_mul_star /-
 theorem self_mul_star : a * star a = normSq a := by rw [mul_star_eq_coe, norm_sq_def]
 #align quaternion.self_mul_star Quaternion.self_mul_star
+-/
 
+#print Quaternion.star_mul_self /-
 theorem star_mul_self : star a * a = normSq a := by rw [star_comm_self', self_mul_star]
 #align quaternion.star_mul_self Quaternion.star_mul_self
+-/
 
+#print Quaternion.im_sq /-
 theorem im_sq : a.im ^ 2 = -normSq a.im := by
   simp_rw [sq, ← star_mul_self, im_star, neg_mul, neg_neg]
 #align quaternion.im_sq Quaternion.im_sq
+-/
 
+#print Quaternion.coe_normSq_add /-
 theorem coe_normSq_add : (normSq (a + b) : ℍ[R]) = normSq a + a * star b + b * star a + normSq b :=
   by simp [← self_mul_star, mul_add, add_mul, add_assoc]
 #align quaternion.coe_norm_sq_add Quaternion.coe_normSq_add
+-/
 
+#print Quaternion.normSq_smul /-
 theorem normSq_smul (r : R) (q : ℍ[R]) : normSq (r • q) = r ^ 2 * normSq q := by
   simp_rw [norm_sq_def, star_smul, smul_mul_smul, smul_re, sq, smul_eq_mul]
 #align quaternion.norm_sq_smul Quaternion.normSq_smul
+-/
 
+#print Quaternion.normSq_add /-
 theorem normSq_add (a b : ℍ[R]) : normSq (a + b) = normSq a + normSq b + 2 * (a * star b).re :=
   calc
     normSq (a + b) = normSq a + (a * star b).re + ((b * star a).re + normSq b) := by
@@ -1347,6 +1728,7 @@ theorem normSq_add (a b : ℍ[R]) : normSq (a + b) = normSq a + normSq b + 2 * (
     _ = normSq a + normSq b + 2 * (a * star b).re := by
       rw [← add_re, ← star_mul_star a b, self_add_star', coe_re]
 #align quaternion.norm_sq_add Quaternion.normSq_add
+-/
 
 end Quaternion
 
@@ -1358,6 +1740,7 @@ section LinearOrderedCommRing
 
 variable [LinearOrderedCommRing R] {a : ℍ[R]}
 
+#print Quaternion.normSq_eq_zero /-
 @[simp]
 theorem normSq_eq_zero : normSq a = 0 ↔ a = 0 :=
   by
@@ -1366,19 +1749,26 @@ theorem normSq_eq_zero : normSq a = 0 ↔ a = 0 :=
   exact ext a 0 (pow_eq_zero h.1.1.1) (pow_eq_zero h.1.1.2) (pow_eq_zero h.1.2) (pow_eq_zero h.2)
   all_goals apply_rules [sq_nonneg, add_nonneg]
 #align quaternion.norm_sq_eq_zero Quaternion.normSq_eq_zero
+-/
 
+#print Quaternion.normSq_ne_zero /-
 theorem normSq_ne_zero : normSq a ≠ 0 ↔ a ≠ 0 :=
   not_congr normSq_eq_zero
 #align quaternion.norm_sq_ne_zero Quaternion.normSq_ne_zero
+-/
 
+#print Quaternion.normSq_nonneg /-
 @[simp]
 theorem normSq_nonneg : 0 ≤ normSq a := by rw [norm_sq_def']; apply_rules [sq_nonneg, add_nonneg]
 #align quaternion.norm_sq_nonneg Quaternion.normSq_nonneg
+-/
 
+#print Quaternion.normSq_le_zero /-
 @[simp]
 theorem normSq_le_zero : normSq a ≤ 0 ↔ a = 0 := by
   simpa only [le_antisymm_iff, norm_sq_nonneg, and_true_iff] using @norm_sq_eq_zero _ _ a
 #align quaternion.norm_sq_le_zero Quaternion.normSq_le_zero
+-/
 
 instance : Nontrivial ℍ[R] where exists_pair_ne := ⟨0, 1, mt (congr_arg re) zero_ne_one⟩
 
@@ -1391,6 +1781,7 @@ instance : NoZeroDivisors ℍ[R] :=
 instance : IsDomain ℍ[R] :=
   NoZeroDivisors.to_isDomain _
 
+#print Quaternion.sq_eq_normSq /-
 theorem sq_eq_normSq : a ^ 2 = normSq a ↔ a = a.re :=
   by
   simp_rw [← star_eq_self]
@@ -1398,7 +1789,9 @@ theorem sq_eq_normSq : a ^ 2 = normSq a ↔ a = a.re :=
   · simp
   · rw [← star_mul_self, sq, mul_left_inj' hq0, eq_comm]
 #align quaternion.sq_eq_norm_sq Quaternion.sq_eq_normSq
+-/
 
+#print Quaternion.sq_eq_neg_normSq /-
 theorem sq_eq_neg_normSq : a ^ 2 = -normSq a ↔ a.re = 0 :=
   by
   simp_rw [← star_eq_neg]
@@ -1406,6 +1799,7 @@ theorem sq_eq_neg_normSq : a ^ 2 = -normSq a ↔ a.re = 0 :=
   · simp
   rw [← star_mul_self, ← mul_neg, ← neg_sq, sq, mul_left_inj' (neg_ne_zero.mpr hq0), eq_comm]
 #align quaternion.sq_eq_neg_norm_sq Quaternion.sq_eq_neg_normSq
+-/
 
 end LinearOrderedCommRing
 
@@ -1427,20 +1821,26 @@ instance : GroupWithZero ℍ[R] :=
       rw [has_inv_inv, Algebra.mul_smul_comm, self_mul_star, smul_coe,
         inv_mul_cancel (norm_sq_ne_zero.2 ha), coe_one] }
 
+#print Quaternion.coe_inv /-
 @[norm_cast, simp]
 theorem coe_inv (x : R) : ((x⁻¹ : R) : ℍ[R]) = x⁻¹ :=
   map_inv₀ (algebraMap R ℍ[R]) _
 #align quaternion.coe_inv Quaternion.coe_inv
+-/
 
+#print Quaternion.coe_div /-
 @[norm_cast, simp]
 theorem coe_div (x y : R) : ((x / y : R) : ℍ[R]) = x / y :=
   map_div₀ (algebraMap R ℍ[R]) x y
 #align quaternion.coe_div Quaternion.coe_div
+-/
 
+#print Quaternion.coe_zpow /-
 @[norm_cast, simp]
 theorem coe_zpow (x : R) (z : ℤ) : ((x ^ z : R) : ℍ[R]) = x ^ z :=
   map_zpow₀ (algebraMap R ℍ[R]) x z
 #align quaternion.coe_zpow Quaternion.coe_zpow
+-/
 
 instance : DivisionRing ℍ[R] :=
   { Quaternion.groupWithZero,
@@ -1452,54 +1852,74 @@ instance : DivisionRing ℍ[R] :=
       rw [coe_mul_eq_smul]
       ext <;> exact DivisionRing.qsmul_eq_mul' _ _ }
 
+#print Quaternion.rat_cast_re /-
 @[simp, norm_cast]
 theorem rat_cast_re (q : ℚ) : (q : ℍ[R]).re = q :=
   rfl
 #align quaternion.rat_cast_re Quaternion.rat_cast_re
+-/
 
+#print Quaternion.rat_cast_imI /-
 @[simp, norm_cast]
 theorem rat_cast_imI (q : ℚ) : (q : ℍ[R]).imI = 0 :=
   rfl
 #align quaternion.rat_cast_im_i Quaternion.rat_cast_imI
+-/
 
+#print Quaternion.rat_cast_imJ /-
 @[simp, norm_cast]
 theorem rat_cast_imJ (q : ℚ) : (q : ℍ[R]).imJ = 0 :=
   rfl
 #align quaternion.rat_cast_im_j Quaternion.rat_cast_imJ
+-/
 
+#print Quaternion.rat_cast_imK /-
 @[simp, norm_cast]
 theorem rat_cast_imK (q : ℚ) : (q : ℍ[R]).imK = 0 :=
   rfl
 #align quaternion.rat_cast_im_k Quaternion.rat_cast_imK
+-/
 
+#print Quaternion.rat_cast_im /-
 @[simp, norm_cast]
 theorem rat_cast_im (q : ℚ) : (q : ℍ[R]).im = 0 :=
   rfl
 #align quaternion.rat_cast_im Quaternion.rat_cast_im
+-/
 
+#print Quaternion.coe_rat_cast /-
 @[norm_cast]
 theorem coe_rat_cast (q : ℚ) : ↑(q : R) = (q : ℍ[R]) :=
   rfl
 #align quaternion.coe_rat_cast Quaternion.coe_rat_cast
+-/
 
+#print Quaternion.normSq_inv /-
 @[simp]
 theorem normSq_inv : normSq a⁻¹ = (normSq a)⁻¹ :=
   map_inv₀ normSq _
 #align quaternion.norm_sq_inv Quaternion.normSq_inv
+-/
 
+#print Quaternion.normSq_div /-
 @[simp]
 theorem normSq_div : normSq (a / b) = normSq a / normSq b :=
   map_div₀ normSq a b
 #align quaternion.norm_sq_div Quaternion.normSq_div
+-/
 
+#print Quaternion.normSq_zpow /-
 @[simp]
 theorem normSq_zpow (z : ℤ) : normSq (a ^ z) = normSq a ^ z :=
   map_zpow₀ normSq a z
 #align quaternion.norm_sq_zpow Quaternion.normSq_zpow
+-/
 
+#print Quaternion.normSq_rat_cast /-
 @[norm_cast]
 theorem normSq_rat_cast (q : ℚ) : normSq (q : ℍ[R]) = q ^ 2 := by rw [← coe_rat_cast, norm_sq_coe]
 #align quaternion.norm_sq_rat_cast Quaternion.normSq_rat_cast
+-/
 
 end Field
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

@@ -1346,7 +1346,6 @@ theorem normSq_add (a b : ℍ[R]) : normSq (a + b) = normSq a + normSq b + 2 * (
     _ = normSq a + normSq b + ((a * star b).re + (b * star a).re) := by abel
     _ = normSq a + normSq b + 2 * (a * star b).re := by
       rw [← add_re, ← star_mul_star a b, self_add_star', coe_re]
-    
 #align quaternion.norm_sq_add Quaternion.normSq_add
 
 end Quaternion

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

@@ -59,7 +59,7 @@ quaternion
 
 
 #print QuaternionAlgebra /-
-/- ./././Mathport/Syntax/Translate/Command.lean:429:34: infer kinds are unsupported in Lean 4: mk {} -/
+/- ./././Mathport/Syntax/Translate/Command.lean:430:34: infer kinds are unsupported in Lean 4: mk {} -/
 /-- Quaternion algebra over a type with fixed coefficients $a=i^2$ and $b=j^2$.
 Implemented as a structure with four fields: `re`, `im_i`, `im_j`, and `im_k`. -/
 @[nolint unused_arguments, ext]

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

@@ -1363,7 +1363,7 @@ variable [LinearOrderedCommRing R] {a : ℍ[R]}
 theorem normSq_eq_zero : normSq a = 0 ↔ a = 0 :=
   by
   refine' ⟨fun h => _, fun h => h.symm ▸ norm_sq.map_zero⟩
-  rw [norm_sq_def', add_eq_zero_iff', add_eq_zero_iff', add_eq_zero_iff'] at h
+  rw [norm_sq_def', add_eq_zero_iff', add_eq_zero_iff', add_eq_zero_iff'] at h 
   exact ext a 0 (pow_eq_zero h.1.1.1) (pow_eq_zero h.1.1.2) (pow_eq_zero h.1.2) (pow_eq_zero h.2)
   all_goals apply_rules [sq_nonneg, add_nonneg]
 #align quaternion.norm_sq_eq_zero Quaternion.normSq_eq_zero

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

@@ -1508,7 +1508,7 @@ end Quaternion
 
 namespace Cardinal
 
-open Cardinal Quaternion
+open scoped Cardinal Quaternion
 
 section QuaternionAlgebra
 

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

@@ -124,12 +124,6 @@ def im (x : ℍ[R,c₁,c₂]) : ℍ[R,c₁,c₂] :=
 #align quaternion_algebra.im QuaternionAlgebra.im
 -/
 
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 @[simp]
 theorem im_re : a.im.re = 0 :=
   rfl
@@ -173,54 +167,24 @@ theorem coe_re : (x : ℍ[R,c₁,c₂]).re = x :=
 #align quaternion_algebra.coe_re QuaternionAlgebra.coe_re
 -/
 
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 @[simp, norm_cast]
 theorem coe_imI : (x : ℍ[R,c₁,c₂]).imI = 0 :=
   rfl
 #align quaternion_algebra.coe_im_i QuaternionAlgebra.coe_imI
 
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 @[simp, norm_cast]
 theorem coe_imJ : (x : ℍ[R,c₁,c₂]).imJ = 0 :=
   rfl
 #align quaternion_algebra.coe_im_j QuaternionAlgebra.coe_imJ
 
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 @[simp, norm_cast]
 theorem coe_imK : (x : ℍ[R,c₁,c₂]).imK = 0 :=
   rfl
 #align quaternion_algebra.coe_im_k QuaternionAlgebra.coe_imK
 
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 theorem coe_injective : Function.Injective (coe : R → ℍ[R,c₁,c₂]) := fun x y h => congr_arg re h
 #align quaternion_algebra.coe_injective QuaternionAlgebra.coe_injective
 
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 @[simp]
 theorem coe_inj {x y : R} : (x : ℍ[R,c₁,c₂]) = y ↔ x = y :=
   coe_injective.eq_iff
@@ -230,12 +194,6 @@ theorem coe_inj {x y : R} : (x : ℍ[R,c₁,c₂]) = y ↔ x = y :=
 instance : Zero ℍ[R,c₁,c₂] :=
   ⟨⟨0, 0, 0, 0⟩⟩
 
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 @[simp, norm_cast]
 theorem coe_zero : ((0 : R) : ℍ[R,c₁,c₂]) = 0 :=
   rfl
@@ -248,12 +206,6 @@ instance : Inhabited ℍ[R,c₁,c₂] :=
 instance : One ℍ[R,c₁,c₂] :=
   ⟨⟨1, 0, 0, 0⟩⟩
 
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 @[simp, norm_cast]
 theorem coe_one : ((1 : R) : ℍ[R,c₁,c₂]) = 1 :=
   rfl
@@ -263,24 +215,12 @@ theorem coe_one : ((1 : R) : ℍ[R,c₁,c₂]) = 1 :=
 instance : Add ℍ[R,c₁,c₂] :=
   ⟨fun a b => ⟨a.1 + b.1, a.2 + b.2, a.3 + b.3, a.4 + b.4⟩⟩
 
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 @[simp]
 theorem mk_add_mk (a₁ a₂ a₃ a₄ b₁ b₂ b₃ b₄ : R) :
     (mk a₁ a₂ a₃ a₄ : ℍ[R,c₁,c₂]) + mk b₁ b₂ b₃ b₄ = mk (a₁ + b₁) (a₂ + b₂) (a₃ + b₃) (a₄ + b₄) :=
   rfl
 #align quaternion_algebra.mk_add_mk QuaternionAlgebra.mk_add_mk
 
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 @[norm_cast, simp]
 theorem coe_add : ((x + y : R) : ℍ[R,c₁,c₂]) = x + y := by ext <;> simp
 #align quaternion_algebra.coe_add QuaternionAlgebra.coe_add
@@ -289,23 +229,11 @@ theorem coe_add : ((x + y : R) : ℍ[R,c₁,c₂]) = x + y := by ext <;> simp
 instance : Neg ℍ[R,c₁,c₂] :=
   ⟨fun a => ⟨-a.1, -a.2, -a.3, -a.4⟩⟩
 
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 @[simp]
 theorem neg_mk (a₁ a₂ a₃ a₄ : R) : -(mk a₁ a₂ a₃ a₄ : ℍ[R,c₁,c₂]) = ⟨-a₁, -a₂, -a₃, -a₄⟩ :=
   rfl
 #align quaternion_algebra.neg_mk QuaternionAlgebra.neg_mk
 
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 @[norm_cast, simp]
 theorem coe_neg : ((-x : R) : ℍ[R,c₁,c₂]) = -x := by ext <;> simp
 #align quaternion_algebra.coe_neg QuaternionAlgebra.coe_neg
@@ -314,57 +242,27 @@ theorem coe_neg : ((-x : R) : ℍ[R,c₁,c₂]) = -x := by ext <;> simp
 instance : Sub ℍ[R,c₁,c₂] :=
   ⟨fun a b => ⟨a.1 - b.1, a.2 - b.2, a.3 - b.3, a.4 - b.4⟩⟩
 
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 @[simp]
 theorem mk_sub_mk (a₁ a₂ a₃ a₄ b₁ b₂ b₃ b₄ : R) :
     (mk a₁ a₂ a₃ a₄ : ℍ[R,c₁,c₂]) - mk b₁ b₂ b₃ b₄ = mk (a₁ - b₁) (a₂ - b₂) (a₃ - b₃) (a₄ - b₄) :=
   rfl
 #align quaternion_algebra.mk_sub_mk QuaternionAlgebra.mk_sub_mk
 
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 @[simp, norm_cast]
 theorem coe_im : (x : ℍ[R,c₁,c₂]).im = 0 :=
   rfl
 #align quaternion_algebra.coe_im QuaternionAlgebra.coe_im
 
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 @[simp]
 theorem re_add_im : ↑a.re + a.im = a :=
   ext _ _ (add_zero _) (zero_add _) (zero_add _) (zero_add _)
 #align quaternion_algebra.re_add_im QuaternionAlgebra.re_add_im
 
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 @[simp]
 theorem sub_self_im : a - a.im = a.re :=
   ext _ _ (sub_zero _) (sub_self _) (sub_self _) (sub_self _)
 #align quaternion_algebra.sub_self_im QuaternionAlgebra.sub_self_im
 
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 @[simp]
 theorem sub_self_re : a - a.re = a.im :=
   ext _ _ (sub_self _) (sub_zero _) (sub_zero _) (sub_zero _)
@@ -387,9 +285,6 @@ instance : Mul ℍ[R,c₁,c₂] :=
       a.1 * b.3 + c₁ * a.2 * b.4 + a.3 * b.1 - c₁ * a.4 * b.2,
       a.1 * b.4 + a.2 * b.3 - a.3 * b.2 + a.4 * b.1⟩⟩
 
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 @[simp]
 theorem mk_mul_mk (a₁ a₂ a₃ a₄ b₁ b₂ b₃ b₄ : R) :
     (mk a₁ a₂ a₃ a₄ : ℍ[R,c₁,c₂]) * mk b₁ b₂ b₃ b₄ =
@@ -417,56 +312,26 @@ instance [SMul S T] [IsScalarTower S T R] : IsScalarTower S T ℍ[R,c₁,c₂]
 instance [SMulCommClass S T R] : SMulCommClass S T ℍ[R,c₁,c₂]
     where smul_comm s t x := by ext <;> exact smul_comm _ _ _
 
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 @[simp]
 theorem smul_re : (s • a).re = s • a.re :=
   rfl
 #align quaternion_algebra.smul_re QuaternionAlgebra.smul_re
 
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 @[simp]
 theorem smul_imI : (s • a).imI = s • a.imI :=
   rfl
 #align quaternion_algebra.smul_im_i QuaternionAlgebra.smul_imI
 
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 @[simp]
 theorem smul_imJ : (s • a).imJ = s • a.imJ :=
   rfl
 #align quaternion_algebra.smul_im_j QuaternionAlgebra.smul_imJ
 
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 @[simp]
 theorem smul_imK : (s • a).imK = s • a.imK :=
   rfl
 #align quaternion_algebra.smul_im_k QuaternionAlgebra.smul_imK
 
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 @[simp]
 theorem smul_mk (re im_i im_j im_k : R) :
     s • (⟨re, im_i, im_j, im_k⟩ : ℍ[R,c₁,c₂]) = ⟨s • re, s • im_i, s • im_j, s • im_k⟩ :=
@@ -475,12 +340,6 @@ theorem smul_mk (re im_i im_j im_k : R) :
 
 end
 
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 @[simp, norm_cast]
 theorem coe_smul [SMulZeroClass S R] (s : S) (r : R) : (↑(s • r) : ℍ[R,c₁,c₂]) = s • ↑r :=
   ext _ _ rfl (smul_zero s).symm (smul_zero s).symm (smul_zero s).symm
@@ -511,133 +370,61 @@ instance : AddGroupWithOne ℍ[R,c₁,c₂] :=
     intCast_negSucc := fun n => show ↑↑_ = -↑↑_ by rw [Int.cast_neg, Int.cast_ofNat, coe_neg]
     one := 1 }
 
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 @[simp, norm_cast]
 theorem nat_cast_re (n : ℕ) : (n : ℍ[R,c₁,c₂]).re = n :=
   rfl
 #align quaternion_algebra.nat_cast_re QuaternionAlgebra.nat_cast_re
 
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 @[simp, norm_cast]
 theorem nat_cast_imI (n : ℕ) : (n : ℍ[R,c₁,c₂]).imI = 0 :=
   rfl
 #align quaternion_algebra.nat_cast_im_i QuaternionAlgebra.nat_cast_imI
 
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 @[simp, norm_cast]
 theorem nat_cast_imJ (n : ℕ) : (n : ℍ[R,c₁,c₂]).imJ = 0 :=
   rfl
 #align quaternion_algebra.nat_cast_im_j QuaternionAlgebra.nat_cast_imJ
 
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 @[simp, norm_cast]
 theorem nat_cast_imK (n : ℕ) : (n : ℍ[R,c₁,c₂]).imK = 0 :=
   rfl
 #align quaternion_algebra.nat_cast_im_k QuaternionAlgebra.nat_cast_imK
 
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 @[simp, norm_cast]
 theorem nat_cast_im (n : ℕ) : (n : ℍ[R,c₁,c₂]).im = 0 :=
   rfl
 #align quaternion_algebra.nat_cast_im QuaternionAlgebra.nat_cast_im
 
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 @[norm_cast]
 theorem coe_nat_cast (n : ℕ) : ↑(n : R) = (n : ℍ[R,c₁,c₂]) :=
   rfl
 #align quaternion_algebra.coe_nat_cast QuaternionAlgebra.coe_nat_cast
 
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 @[simp, norm_cast]
 theorem int_cast_re (z : ℤ) : (z : ℍ[R,c₁,c₂]).re = z :=
   rfl
 #align quaternion_algebra.int_cast_re QuaternionAlgebra.int_cast_re
 
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 @[simp, norm_cast]
 theorem int_cast_imI (z : ℤ) : (z : ℍ[R,c₁,c₂]).imI = 0 :=
   rfl
 #align quaternion_algebra.int_cast_im_i QuaternionAlgebra.int_cast_imI
 
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 @[simp, norm_cast]
 theorem int_cast_imJ (z : ℤ) : (z : ℍ[R,c₁,c₂]).imJ = 0 :=
   rfl
 #align quaternion_algebra.int_cast_im_j QuaternionAlgebra.int_cast_imJ
 
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 @[simp, norm_cast]
 theorem int_cast_imK (z : ℤ) : (z : ℍ[R,c₁,c₂]).imK = 0 :=
   rfl
 #align quaternion_algebra.int_cast_im_k QuaternionAlgebra.int_cast_imK
 
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 @[simp, norm_cast]
 theorem int_cast_im (z : ℤ) : (z : ℍ[R,c₁,c₂]).im = 0 :=
   rfl
 #align quaternion_algebra.int_cast_im QuaternionAlgebra.int_cast_im
 
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 @[norm_cast]
 theorem coe_int_cast (z : ℤ) : ↑(z : R) = (z : ℍ[R,c₁,c₂]) :=
   rfl
@@ -657,12 +444,6 @@ instance : Ring ℍ[R,c₁,c₂] := by
       simp <;>
     ring
 
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 @[norm_cast, simp]
 theorem coe_mul : ((x * y : R) : ℍ[R,c₁,c₂]) = x * y := by ext <;> simp
 #align quaternion_algebra.coe_mul QuaternionAlgebra.coe_mul
@@ -680,12 +461,6 @@ instance [CommSemiring S] [Algebra S R] : Algebra S ℍ[R,c₁,c₂]
   smul_def' s x := by ext <;> simp [Algebra.smul_def]
   commutes' s x := by ext <;> simp [Algebra.commutes]
 
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-Case conversion may be inaccurate. Consider using '#align quaternion_algebra.algebra_map_eq QuaternionAlgebra.algebraMap_eqₓ'. -/
 theorem algebraMap_eq (r : R) : algebraMap R ℍ[R,c₁,c₂] r = ⟨r, 0, 0, 0⟩ :=
   rfl
 #align quaternion_algebra.algebra_map_eq QuaternionAlgebra.algebraMap_eq
@@ -694,12 +469,6 @@ section
 
 variable (c₁ c₂)
 
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-Case conversion may be inaccurate. Consider using '#align quaternion_algebra.re_lm QuaternionAlgebra.reₗₓ'. -/
 /-- `quaternion_algebra.re` as a `linear_map`-/
 @[simps]
 def reₗ : ℍ[R,c₁,c₂] →ₗ[R] R where
@@ -708,12 +477,6 @@ def reₗ : ℍ[R,c₁,c₂] →ₗ[R] R where
   map_smul' r x := rfl
 #align quaternion_algebra.re_lm QuaternionAlgebra.reₗ
 
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 /-- `quaternion_algebra.im_i` as a `linear_map`-/
 @[simps]
 def imIₗ : ℍ[R,c₁,c₂] →ₗ[R] R where
@@ -722,12 +485,6 @@ def imIₗ : ℍ[R,c₁,c₂] →ₗ[R] R where
   map_smul' r x := rfl
 #align quaternion_algebra.im_i_lm QuaternionAlgebra.imIₗ
 
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 /-- `quaternion_algebra.im_j` as a `linear_map`-/
 @[simps]
 def imJₗ : ℍ[R,c₁,c₂] →ₗ[R] R where
@@ -736,12 +493,6 @@ def imJₗ : ℍ[R,c₁,c₂] →ₗ[R] R where
   map_smul' r x := rfl
 #align quaternion_algebra.im_j_lm QuaternionAlgebra.imJₗ
 
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 /-- `quaternion_algebra.im_k` as a `linear_map`-/
 @[simps]
 def imKₗ : ℍ[R,c₁,c₂] →ₗ[R] R where
@@ -750,12 +501,6 @@ def imKₗ : ℍ[R,c₁,c₂] →ₗ[R] R where
   map_smul' r x := rfl
 #align quaternion_algebra.im_k_lm QuaternionAlgebra.imKₗ
 
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 /-- `quaternion_algebra.equiv_tuple` as a linear equivalence. -/
 def linearEquivTuple : ℍ[R,c₁,c₂] ≃ₗ[R] Fin 4 → R :=
   LinearEquiv.symm-- proofs are not `rfl` in the forward direction
@@ -766,36 +511,21 @@ def linearEquivTuple : ℍ[R,c₁,c₂] ≃ₗ[R] Fin 4 → R :=
       map_smul' := fun v₁ v₂ => rfl }
 #align quaternion_algebra.linear_equiv_tuple QuaternionAlgebra.linearEquivTuple
 
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 @[simp]
 theorem coe_linearEquivTuple : ⇑(linearEquivTuple c₁ c₂) = equivTuple c₁ c₂ :=
   rfl
 #align quaternion_algebra.coe_linear_equiv_tuple QuaternionAlgebra.coe_linearEquivTuple
 
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 @[simp]
 theorem coe_linearEquivTuple_symm : ⇑(linearEquivTuple c₁ c₂).symm = (equivTuple c₁ c₂).symm :=
   rfl
 #align quaternion_algebra.coe_linear_equiv_tuple_symm QuaternionAlgebra.coe_linearEquivTuple_symm
 
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 /-- `ℍ[R, c₁, c₂]` has a basis over `R` given by `1`, `i`, `j`, and `k`. -/
 noncomputable def basisOneIJK : Basis (Fin 4) R ℍ[R,c₁,c₂] :=
   Basis.ofEquivFun <| linearEquivTuple c₁ c₂
 #align quaternion_algebra.basis_one_i_j_k QuaternionAlgebra.basisOneIJK
 
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 @[simp]
 theorem coe_basisOneIJK_repr (q : ℍ[R,c₁,c₂]) :
     ⇑((basisOneIJK c₁ c₂).repr q) = ![q.re, q.imI, q.imJ, q.imK] :=
@@ -808,22 +538,10 @@ instance : Module.Finite R ℍ[R,c₁,c₂] :=
 instance : Module.Free R ℍ[R,c₁,c₂] :=
   Module.Free.of_basis (basisOneIJK c₁ c₂)
 
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 theorem rank_eq_four [StrongRankCondition R] : Module.rank R ℍ[R,c₁,c₂] = 4 := by
   rw [rank_eq_card_basis (basis_one_i_j_k c₁ c₂), Fintype.card_fin]; norm_num
 #align quaternion_algebra.rank_eq_four QuaternionAlgebra.rank_eq_four
 
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 theorem finrank_eq_four [StrongRankCondition R] : FiniteDimensional.finrank R ℍ[R,c₁,c₂] = 4 :=
   by
   have : Cardinal.toNat 4 = 4 := by
@@ -833,84 +551,36 @@ theorem finrank_eq_four [StrongRankCondition R] : FiniteDimensional.finrank R 
 
 end
 
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 @[norm_cast, simp]
 theorem coe_sub : ((x - y : R) : ℍ[R,c₁,c₂]) = x - y :=
   (algebraMap R ℍ[R,c₁,c₂]).map_sub x y
 #align quaternion_algebra.coe_sub QuaternionAlgebra.coe_sub
 
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 @[norm_cast, simp]
 theorem coe_pow (n : ℕ) : (↑(x ^ n) : ℍ[R,c₁,c₂]) = ↑x ^ n :=
   (algebraMap R ℍ[R,c₁,c₂]).map_pow x n
 #align quaternion_algebra.coe_pow QuaternionAlgebra.coe_pow
 
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 theorem coe_commutes : ↑r * a = a * r :=
   Algebra.commutes r a
 #align quaternion_algebra.coe_commutes QuaternionAlgebra.coe_commutes
 
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 theorem coe_commute : Commute (↑r) a :=
   coe_commutes r a
 #align quaternion_algebra.coe_commute QuaternionAlgebra.coe_commute
 
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 theorem coe_mul_eq_smul : ↑r * a = r • a :=
   (Algebra.smul_def r a).symm
 #align quaternion_algebra.coe_mul_eq_smul QuaternionAlgebra.coe_mul_eq_smul
 
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 theorem mul_coe_eq_smul : a * r = r • a := by rw [← coe_commutes, coe_mul_eq_smul]
 #align quaternion_algebra.mul_coe_eq_smul QuaternionAlgebra.mul_coe_eq_smul
 
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 @[norm_cast, simp]
 theorem coe_algebraMap : ⇑(algebraMap R ℍ[R,c₁,c₂]) = coe :=
   rfl
 #align quaternion_algebra.coe_algebra_map QuaternionAlgebra.coe_algebraMap
 
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 theorem smul_coe : x • (y : ℍ[R,c₁,c₂]) = ↑(x * y) := by rw [coe_mul, coe_mul_eq_smul]
 #align quaternion_algebra.smul_coe QuaternionAlgebra.smul_coe
 
@@ -924,56 +594,26 @@ theorem re_star : (star a).re = a.re :=
 #align quaternion_algebra.re_star QuaternionAlgebra.re_star
 -/
 
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 @[simp]
 theorem imI_star : (star a).imI = -a.imI :=
   rfl
 #align quaternion_algebra.im_i_star QuaternionAlgebra.imI_star
 
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 @[simp]
 theorem imJ_star : (star a).imJ = -a.imJ :=
   rfl
 #align quaternion_algebra.im_j_star QuaternionAlgebra.imJ_star
 
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 @[simp]
 theorem imK_star : (star a).imK = -a.imK :=
   rfl
 #align quaternion_algebra.im_k_star QuaternionAlgebra.imK_star
 
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 @[simp]
 theorem im_star : (star a).im = -a.im :=
   ext _ _ neg_zero.symm rfl rfl rfl
 #align quaternion_algebra.im_star QuaternionAlgebra.im_star
 
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 @[simp]
 theorem star_mk (a₁ a₂ a₃ a₄ : R) : star (mk a₁ a₂ a₃ a₄ : ℍ[R,c₁,c₂]) = ⟨a₁, -a₂, -a₃, -a₄⟩ :=
   rfl
@@ -985,48 +625,18 @@ instance : StarRing ℍ[R,c₁,c₂]
   star_add a b := by ext <;> simp [neg_add]
   star_mul a b := by ext <;> simp <;> ring
 
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 theorem self_add_star' : a + star a = ↑(2 * a.re) := by ext <;> simp [two_mul]
 #align quaternion_algebra.self_add_star' QuaternionAlgebra.self_add_star'
 
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 theorem self_add_star : a + star a = 2 * a.re := by simp only [self_add_star', two_mul, coe_add]
 #align quaternion_algebra.self_add_star QuaternionAlgebra.self_add_star
 
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 theorem star_add_self' : star a + a = ↑(2 * a.re) := by rw [add_comm, self_add_star']
 #align quaternion_algebra.star_add_self' QuaternionAlgebra.star_add_self'
 
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 theorem star_add_self : star a + a = 2 * a.re := by rw [add_comm, self_add_star]
 #align quaternion_algebra.star_add_self QuaternionAlgebra.star_add_self
 
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 theorem star_eq_two_re_sub : star a = ↑(2 * a.re) - a :=
   eq_sub_iff_add_eq.2 a.star_add_self'
 #align quaternion_algebra.star_eq_two_re_sub QuaternionAlgebra.star_eq_two_re_sub
@@ -1036,54 +646,24 @@ instance : IsStarNormal a :=
     rw [a.star_eq_two_re_sub]
     exact (coe_commute (2 * a.re) a).sub_left (Commute.refl a)⟩
 
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 @[simp, norm_cast]
 theorem star_coe : star (x : ℍ[R,c₁,c₂]) = x := by ext <;> simp
 #align quaternion_algebra.star_coe QuaternionAlgebra.star_coe
 
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 @[simp]
 theorem star_im : star a.im = -a.im :=
   im_star _
 #align quaternion_algebra.star_im QuaternionAlgebra.star_im
 
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 @[simp]
 theorem star_smul [Monoid S] [DistribMulAction S R] (s : S) (a : ℍ[R,c₁,c₂]) :
     star (s • a) = s • star a :=
   ext _ _ rfl (smul_neg _ _).symm (smul_neg _ _).symm (smul_neg _ _).symm
 #align quaternion_algebra.star_smul QuaternionAlgebra.star_smul
 
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 theorem eq_re_of_eq_coe {a : ℍ[R,c₁,c₂]} {x : R} (h : a = x) : a = a.re := by rw [h, coe_re]
 #align quaternion_algebra.eq_re_of_eq_coe QuaternionAlgebra.eq_re_of_eq_coe
 
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 theorem eq_re_iff_mem_range_coe {a : ℍ[R,c₁,c₂]} :
     a = a.re ↔ a ∈ Set.range (coe : R → ℍ[R,c₁,c₂]) :=
   ⟨fun h => ⟨a.re, h.symm⟩, fun ⟨x, h⟩ => eq_re_of_eq_coe h.symm⟩
@@ -1093,57 +673,27 @@ section CharZero
 
 variable [NoZeroDivisors R] [CharZero R]
 
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 @[simp]
 theorem star_eq_self {c₁ c₂ : R} {a : ℍ[R,c₁,c₂]} : star a = a ↔ a = a.re := by
   simp [ext_iff, neg_eq_iff_add_eq_zero, add_self_eq_zero]
 #align quaternion_algebra.star_eq_self QuaternionAlgebra.star_eq_self
 
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 theorem star_eq_neg {c₁ c₂ : R} {a : ℍ[R,c₁,c₂]} : star a = -a ↔ a.re = 0 := by
   simp [ext_iff, eq_neg_iff_add_eq_zero]
 #align quaternion_algebra.star_eq_neg QuaternionAlgebra.star_eq_neg
 
 end CharZero
 
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 -- Can't use `rw ← star_eq_self` in the proof without additional assumptions
 theorem star_mul_eq_coe : star a * a = (star a * a).re := by ext <;> simp <;> ring
 #align quaternion_algebra.star_mul_eq_coe QuaternionAlgebra.star_mul_eq_coe
 
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 theorem mul_star_eq_coe : a * star a = (a * star a).re := by rw [← star_comm_self'];
   exact a.star_mul_eq_coe
 #align quaternion_algebra.mul_star_eq_coe QuaternionAlgebra.mul_star_eq_coe
 
 open MulOpposite
 
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 /-- Quaternion conjugate as an `alg_equiv` to the opposite ring. -/
 def starAe : ℍ[R,c₁,c₂] ≃ₐ[R] ℍ[R,c₁,c₂]ᵐᵒᵖ :=
   { starAddEquiv.trans opAddEquiv with
@@ -1153,9 +703,6 @@ def starAe : ℍ[R,c₁,c₂] ≃ₐ[R] ℍ[R,c₁,c₂]ᵐᵒᵖ :=
     commutes' := fun r => by simp }
 #align quaternion_algebra.star_ae QuaternionAlgebra.starAe
 
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 @[simp]
 theorem coe_starAe : ⇑(starAe : ℍ[R,c₁,c₂] ≃ₐ[R] _) = op ∘ star :=
   rfl
@@ -1228,116 +775,56 @@ instance [CommSemiring S] [Algebra S R] : Algebra S ℍ[R] :=
 instance : StarRing ℍ[R] :=
   QuaternionAlgebra.starRing
 
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 @[ext]
 theorem ext : a.re = b.re → a.imI = b.imI → a.imJ = b.imJ → a.imK = b.imK → a = b :=
   QuaternionAlgebra.ext a b
 #align quaternion.ext Quaternion.ext
 
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 theorem ext_iff {a b : ℍ[R]} :
     a = b ↔ a.re = b.re ∧ a.imI = b.imI ∧ a.imJ = b.imJ ∧ a.imK = b.imK :=
   QuaternionAlgebra.ext_iff a b
 #align quaternion.ext_iff Quaternion.ext_iff
 
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 /-- The imaginary part of a quaternion. -/
 def im (x : ℍ[R]) : ℍ[R] :=
   x.im
 #align quaternion.im Quaternion.im
 
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 @[simp]
 theorem im_re : a.im.re = 0 :=
   rfl
 #align quaternion.im_re Quaternion.im_re
 
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 @[simp]
 theorem im_imI : a.im.imI = a.imI :=
   rfl
 #align quaternion.im_im_i Quaternion.im_imI
 
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 @[simp]
 theorem im_imJ : a.im.imJ = a.imJ :=
   rfl
 #align quaternion.im_im_j Quaternion.im_imJ
 
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 @[simp]
 theorem im_imK : a.im.imK = a.imK :=
   rfl
 #align quaternion.im_im_k Quaternion.im_imK
 
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 @[simp]
 theorem im_idem : a.im.im = a.im :=
   rfl
 #align quaternion.im_idem Quaternion.im_idem
 
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-Case conversion may be inaccurate. Consider using '#align quaternion.re_add_im Quaternion.re_add_imₓ'. -/
 @[simp]
 theorem re_add_im : ↑a.re + a.im = a :=
   a.re_add_im
 #align quaternion.re_add_im Quaternion.re_add_im
 
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 @[simp]
 theorem sub_self_im : a - a.im = a.re :=
   a.sub_self_im
 #align quaternion.sub_self_im Quaternion.sub_self_im
 
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 @[simp]
 theorem sub_self_re : a - a.re = a.im :=
   a.sub_self_re
@@ -1350,665 +837,326 @@ theorem coe_re : (x : ℍ[R]).re = x :=
 #align quaternion.coe_re Quaternion.coe_re
 -/
 
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 @[simp, norm_cast]
 theorem coe_imI : (x : ℍ[R]).imI = 0 :=
   rfl
 #align quaternion.coe_im_i Quaternion.coe_imI
 
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 @[simp, norm_cast]
 theorem coe_imJ : (x : ℍ[R]).imJ = 0 :=
   rfl
 #align quaternion.coe_im_j Quaternion.coe_imJ
 
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 @[simp, norm_cast]
 theorem coe_imK : (x : ℍ[R]).imK = 0 :=
   rfl
 #align quaternion.coe_im_k Quaternion.coe_imK
 
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 @[simp, norm_cast]
 theorem coe_im : (x : ℍ[R]).im = 0 :=
   rfl
 #align quaternion.coe_im Quaternion.coe_im
 
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 @[simp]
 theorem zero_re : (0 : ℍ[R]).re = 0 :=
   rfl
 #align quaternion.zero_re Quaternion.zero_re
 
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 @[simp]
 theorem zero_imI : (0 : ℍ[R]).imI = 0 :=
   rfl
 #align quaternion.zero_im_i Quaternion.zero_imI
 
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 @[simp]
 theorem zero_imJ : (0 : ℍ[R]).imJ = 0 :=
   rfl
 #align quaternion.zero_im_j Quaternion.zero_imJ
 
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 @[simp]
 theorem zero_imK : (0 : ℍ[R]).imK = 0 :=
   rfl
 #align quaternion.zero_im_k Quaternion.zero_imK
 
-/- warning: quaternion.zero_im -> Quaternion.zero_im is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.zero_im Quaternion.zero_imₓ'. -/
 @[simp]
 theorem zero_im : (0 : ℍ[R]).im = 0 :=
   rfl
 #align quaternion.zero_im Quaternion.zero_im
 
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 @[simp, norm_cast]
 theorem coe_zero : ((0 : R) : ℍ[R]) = 0 :=
   rfl
 #align quaternion.coe_zero Quaternion.coe_zero
 
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 @[simp]
 theorem one_re : (1 : ℍ[R]).re = 1 :=
   rfl
 #align quaternion.one_re Quaternion.one_re
 
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 @[simp]
 theorem one_imI : (1 : ℍ[R]).imI = 0 :=
   rfl
 #align quaternion.one_im_i Quaternion.one_imI
 
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-Case conversion may be inaccurate. Consider using '#align quaternion.one_im_j Quaternion.one_imJₓ'. -/
 @[simp]
 theorem one_imJ : (1 : ℍ[R]).imJ = 0 :=
   rfl
 #align quaternion.one_im_j Quaternion.one_imJ
 
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-Case conversion may be inaccurate. Consider using '#align quaternion.one_im_k Quaternion.one_imKₓ'. -/
 @[simp]
 theorem one_imK : (1 : ℍ[R]).imK = 0 :=
   rfl
 #align quaternion.one_im_k Quaternion.one_imK
 
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 @[simp]
 theorem one_im : (1 : ℍ[R]).im = 0 :=
   rfl
 #align quaternion.one_im Quaternion.one_im
 
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 @[simp, norm_cast]
 theorem coe_one : ((1 : R) : ℍ[R]) = 1 :=
   rfl
 #align quaternion.coe_one Quaternion.coe_one
 
-/- warning: quaternion.add_re -> Quaternion.add_re is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.add_re Quaternion.add_reₓ'. -/
 @[simp]
 theorem add_re : (a + b).re = a.re + b.re :=
   rfl
 #align quaternion.add_re Quaternion.add_re
 
-/- warning: quaternion.add_im_i -> Quaternion.add_imI is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.add_im_i Quaternion.add_imIₓ'. -/
 @[simp]
 theorem add_imI : (a + b).imI = a.imI + b.imI :=
   rfl
 #align quaternion.add_im_i Quaternion.add_imI
 
-/- warning: quaternion.add_im_j -> Quaternion.add_imJ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.add_im_j Quaternion.add_imJₓ'. -/
 @[simp]
 theorem add_imJ : (a + b).imJ = a.imJ + b.imJ :=
   rfl
 #align quaternion.add_im_j Quaternion.add_imJ
 
-/- warning: quaternion.add_im_k -> Quaternion.add_imK is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.add_im_k Quaternion.add_imKₓ'. -/
 @[simp]
 theorem add_imK : (a + b).imK = a.imK + b.imK :=
   rfl
 #align quaternion.add_im_k Quaternion.add_imK
 
-/- warning: quaternion.add_im -> Quaternion.add_im is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.add_im Quaternion.add_imₓ'. -/
 @[simp]
 theorem add_im : (a + b).im = a.im + b.im :=
   ext _ _ (add_zero _).symm rfl rfl rfl
 #align quaternion.add_im Quaternion.add_im
 
-/- warning: quaternion.coe_add -> Quaternion.coe_add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.coe_add Quaternion.coe_addₓ'. -/
 @[simp, norm_cast]
 theorem coe_add : ((x + y : R) : ℍ[R]) = x + y :=
   QuaternionAlgebra.coe_add x y
 #align quaternion.coe_add Quaternion.coe_add
 
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 @[simp]
 theorem neg_re : (-a).re = -a.re :=
   rfl
 #align quaternion.neg_re Quaternion.neg_re
 
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 @[simp]
 theorem neg_imI : (-a).imI = -a.imI :=
   rfl
 #align quaternion.neg_im_i Quaternion.neg_imI
 
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 @[simp]
 theorem neg_imJ : (-a).imJ = -a.imJ :=
   rfl
 #align quaternion.neg_im_j Quaternion.neg_imJ
 
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 @[simp]
 theorem neg_imK : (-a).imK = -a.imK :=
   rfl
 #align quaternion.neg_im_k Quaternion.neg_imK
 
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 @[simp]
 theorem neg_im : (-a).im = -a.im :=
   ext _ _ neg_zero.symm rfl rfl rfl
 #align quaternion.neg_im Quaternion.neg_im
 
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-Case conversion may be inaccurate. Consider using '#align quaternion.coe_neg Quaternion.coe_negₓ'. -/
 @[simp, norm_cast]
 theorem coe_neg : ((-x : R) : ℍ[R]) = -x :=
   QuaternionAlgebra.coe_neg x
 #align quaternion.coe_neg Quaternion.coe_neg
 
-/- warning: quaternion.sub_re -> Quaternion.sub_re is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.sub_re Quaternion.sub_reₓ'. -/
 @[simp]
 theorem sub_re : (a - b).re = a.re - b.re :=
   rfl
 #align quaternion.sub_re Quaternion.sub_re
 
-/- warning: quaternion.sub_im_i -> Quaternion.sub_imI is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.sub_im_i Quaternion.sub_imIₓ'. -/
 @[simp]
 theorem sub_imI : (a - b).imI = a.imI - b.imI :=
   rfl
 #align quaternion.sub_im_i Quaternion.sub_imI
 
-/- warning: quaternion.sub_im_j -> Quaternion.sub_imJ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.sub_im_j Quaternion.sub_imJₓ'. -/
 @[simp]
 theorem sub_imJ : (a - b).imJ = a.imJ - b.imJ :=
   rfl
 #align quaternion.sub_im_j Quaternion.sub_imJ
 
-/- warning: quaternion.sub_im_k -> Quaternion.sub_imK is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.sub_im_k Quaternion.sub_imKₓ'. -/
 @[simp]
 theorem sub_imK : (a - b).imK = a.imK - b.imK :=
   rfl
 #align quaternion.sub_im_k Quaternion.sub_imK
 
-/- warning: quaternion.sub_im -> Quaternion.sub_im is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.sub_im Quaternion.sub_imₓ'. -/
 @[simp]
 theorem sub_im : (a - b).im = a.im - b.im :=
   ext _ _ (sub_zero _).symm rfl rfl rfl
 #align quaternion.sub_im Quaternion.sub_im
 
-/- warning: quaternion.coe_sub -> Quaternion.coe_sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.coe_sub Quaternion.coe_subₓ'. -/
 @[simp, norm_cast]
 theorem coe_sub : ((x - y : R) : ℍ[R]) = x - y :=
   QuaternionAlgebra.coe_sub x y
 #align quaternion.coe_sub Quaternion.coe_sub
 
-/- warning: quaternion.mul_re -> Quaternion.mul_re is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.mul_re Quaternion.mul_reₓ'. -/
 @[simp]
 theorem mul_re : (a * b).re = a.re * b.re - a.imI * b.imI - a.imJ * b.imJ - a.imK * b.imK :=
   (QuaternionAlgebra.mul_re a b).trans <| by simp only [one_mul, neg_mul, sub_eq_add_neg, neg_neg]
 #align quaternion.mul_re Quaternion.mul_re
 
-/- warning: quaternion.mul_im_i -> Quaternion.mul_imI is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.mul_im_i Quaternion.mul_imIₓ'. -/
 @[simp]
 theorem mul_imI : (a * b).imI = a.re * b.imI + a.imI * b.re + a.imJ * b.imK - a.imK * b.imJ :=
   (QuaternionAlgebra.mul_imI a b).trans <| by simp only [one_mul, neg_mul, sub_eq_add_neg, neg_neg]
 #align quaternion.mul_im_i Quaternion.mul_imI
 
-/- warning: quaternion.mul_im_j -> Quaternion.mul_imJ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.mul_im_j Quaternion.mul_imJₓ'. -/
 @[simp]
 theorem mul_imJ : (a * b).imJ = a.re * b.imJ - a.imI * b.imK + a.imJ * b.re + a.imK * b.imI :=
   (QuaternionAlgebra.mul_imJ a b).trans <| by simp only [one_mul, neg_mul, sub_eq_add_neg, neg_neg]
 #align quaternion.mul_im_j Quaternion.mul_imJ
 
-/- warning: quaternion.mul_im_k -> Quaternion.mul_imK is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.mul_im_k Quaternion.mul_imKₓ'. -/
 @[simp]
 theorem mul_imK : (a * b).imK = a.re * b.imK + a.imI * b.imJ - a.imJ * b.imI + a.imK * b.re :=
   (QuaternionAlgebra.mul_imK a b).trans <| by simp only [one_mul, neg_mul, sub_eq_add_neg, neg_neg]
 #align quaternion.mul_im_k Quaternion.mul_imK
 
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 @[simp, norm_cast]
 theorem coe_mul : ((x * y : R) : ℍ[R]) = x * y :=
   QuaternionAlgebra.coe_mul x y
 #align quaternion.coe_mul Quaternion.coe_mul
 
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 @[norm_cast, simp]
 theorem coe_pow (n : ℕ) : (↑(x ^ n) : ℍ[R]) = ↑x ^ n :=
   QuaternionAlgebra.coe_pow x n
 #align quaternion.coe_pow Quaternion.coe_pow
 
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 @[simp, norm_cast]
 theorem nat_cast_re (n : ℕ) : (n : ℍ[R]).re = n :=
   rfl
 #align quaternion.nat_cast_re Quaternion.nat_cast_re
 
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 @[simp, norm_cast]
 theorem nat_cast_imI (n : ℕ) : (n : ℍ[R]).imI = 0 :=
   rfl
 #align quaternion.nat_cast_im_i Quaternion.nat_cast_imI
 
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 @[simp, norm_cast]
 theorem nat_cast_imJ (n : ℕ) : (n : ℍ[R]).imJ = 0 :=
   rfl
 #align quaternion.nat_cast_im_j Quaternion.nat_cast_imJ
 
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 @[simp, norm_cast]
 theorem nat_cast_imK (n : ℕ) : (n : ℍ[R]).imK = 0 :=
   rfl
 #align quaternion.nat_cast_im_k Quaternion.nat_cast_imK
 
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 @[simp, norm_cast]
 theorem nat_cast_im (n : ℕ) : (n : ℍ[R]).im = 0 :=
   rfl
 #align quaternion.nat_cast_im Quaternion.nat_cast_im
 
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 @[norm_cast]
 theorem coe_nat_cast (n : ℕ) : ↑(n : R) = (n : ℍ[R]) :=
   rfl
 #align quaternion.coe_nat_cast Quaternion.coe_nat_cast
 
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 @[simp, norm_cast]
 theorem int_cast_re (z : ℤ) : (z : ℍ[R]).re = z :=
   rfl
 #align quaternion.int_cast_re Quaternion.int_cast_re
 
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 @[simp, norm_cast]
 theorem int_cast_imI (z : ℤ) : (z : ℍ[R]).imI = 0 :=
   rfl
 #align quaternion.int_cast_im_i Quaternion.int_cast_imI
 
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 @[simp, norm_cast]
 theorem int_cast_imJ (z : ℤ) : (z : ℍ[R]).imJ = 0 :=
   rfl
 #align quaternion.int_cast_im_j Quaternion.int_cast_imJ
 
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-Case conversion may be inaccurate. Consider using '#align quaternion.int_cast_im_k Quaternion.int_cast_imKₓ'. -/
 @[simp, norm_cast]
 theorem int_cast_imK (z : ℤ) : (z : ℍ[R]).imK = 0 :=
   rfl
 #align quaternion.int_cast_im_k Quaternion.int_cast_imK
 
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 @[simp, norm_cast]
 theorem int_cast_im (z : ℤ) : (z : ℍ[R]).im = 0 :=
   rfl
 #align quaternion.int_cast_im Quaternion.int_cast_im
 
-/- warning: quaternion.coe_int_cast -> Quaternion.coe_int_cast is a dubious translation:
-lean 3 declaration is
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 @[norm_cast]
 theorem coe_int_cast (z : ℤ) : ↑(z : R) = (z : ℍ[R]) :=
   rfl
 #align quaternion.coe_int_cast Quaternion.coe_int_cast
 
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 theorem coe_injective : Function.Injective (coe : R → ℍ[R]) :=
   QuaternionAlgebra.coe_injective
 #align quaternion.coe_injective Quaternion.coe_injective
 
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 @[simp]
 theorem coe_inj {x y : R} : (x : ℍ[R]) = y ↔ x = y :=
   coe_injective.eq_iff
 #align quaternion.coe_inj Quaternion.coe_inj
 
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 @[simp]
 theorem smul_re [SMul S R] (s : S) : (s • a).re = s • a.re :=
   rfl
 #align quaternion.smul_re Quaternion.smul_re
 
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 @[simp]
 theorem smul_imI [SMul S R] (s : S) : (s • a).imI = s • a.imI :=
   rfl
 #align quaternion.smul_im_i Quaternion.smul_imI
 
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 @[simp]
 theorem smul_imJ [SMul S R] (s : S) : (s • a).imJ = s • a.imJ :=
   rfl
 #align quaternion.smul_im_j Quaternion.smul_imJ
 
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 @[simp]
 theorem smul_imK [SMul S R] (s : S) : (s • a).imK = s • a.imK :=
   rfl
 #align quaternion.smul_im_k Quaternion.smul_imK
 
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 @[simp]
 theorem smul_im [SMulZeroClass S R] (s : S) : (s • a).im = s • a.im :=
   ext _ _ (smul_zero _).symm rfl rfl rfl
 #align quaternion.smul_im Quaternion.smul_im
 
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 @[simp, norm_cast]
 theorem coe_smul [SMulZeroClass S R] (s : S) (r : R) : (↑(s • r) : ℍ[R]) = s • ↑r :=
   QuaternionAlgebra.coe_smul _ _
 #align quaternion.coe_smul Quaternion.coe_smul
 
-/- warning: quaternion.coe_commutes -> Quaternion.coe_commutes is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.coe_commutes Quaternion.coe_commutesₓ'. -/
 theorem coe_commutes : ↑r * a = a * r :=
   QuaternionAlgebra.coe_commutes r a
 #align quaternion.coe_commutes Quaternion.coe_commutes
 
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 theorem coe_commute : Commute (↑r) a :=
   QuaternionAlgebra.coe_commute r a
 #align quaternion.coe_commute Quaternion.coe_commute
 
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 theorem coe_mul_eq_smul : ↑r * a = r • a :=
   QuaternionAlgebra.coe_mul_eq_smul r a
 #align quaternion.coe_mul_eq_smul Quaternion.coe_mul_eq_smul
 
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 theorem mul_coe_eq_smul : a * r = r • a :=
   QuaternionAlgebra.mul_coe_eq_smul r a
 #align quaternion.mul_coe_eq_smul Quaternion.mul_coe_eq_smul
 
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 @[simp]
 theorem algebraMap_def : ⇑(algebraMap R ℍ[R]) = coe :=
   rfl
 #align quaternion.algebra_map_def Quaternion.algebraMap_def
 
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-Case conversion may be inaccurate. Consider using '#align quaternion.smul_coe Quaternion.smul_coeₓ'. -/
 theorem smul_coe : x • (y : ℍ[R]) = ↑(x * y) :=
   QuaternionAlgebra.smul_coe x y
 #align quaternion.smul_coe Quaternion.smul_coe
@@ -2019,157 +1167,79 @@ instance : Module.Finite R ℍ[R] :=
 instance : Module.Free R ℍ[R] :=
   QuaternionAlgebra.Module.free _ _
 
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 theorem rank_eq_four [StrongRankCondition R] : Module.rank R ℍ[R] = 4 :=
   QuaternionAlgebra.rank_eq_four _ _
 #align quaternion.rank_eq_four Quaternion.rank_eq_four
 
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 theorem finrank_eq_four [StrongRankCondition R] : FiniteDimensional.finrank R ℍ[R] = 4 :=
   QuaternionAlgebra.finrank_eq_four _ _
 #align quaternion.finrank_eq_four Quaternion.finrank_eq_four
 
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-Case conversion may be inaccurate. Consider using '#align quaternion.star_re Quaternion.star_reₓ'. -/
 @[simp]
 theorem star_re : (star a).re = a.re :=
   rfl
 #align quaternion.star_re Quaternion.star_re
 
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-Case conversion may be inaccurate. Consider using '#align quaternion.star_im_i Quaternion.star_imIₓ'. -/
 @[simp]
 theorem star_imI : (star a).imI = -a.imI :=
   rfl
 #align quaternion.star_im_i Quaternion.star_imI
 
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-Case conversion may be inaccurate. Consider using '#align quaternion.star_im_j Quaternion.star_imJₓ'. -/
 @[simp]
 theorem star_imJ : (star a).imJ = -a.imJ :=
   rfl
 #align quaternion.star_im_j Quaternion.star_imJ
 
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(CommRing.toRing.{u1} R _inst_1)))))) (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) a))
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-Case conversion may be inaccurate. Consider using '#align quaternion.star_im_k Quaternion.star_imKₓ'. -/
 @[simp]
 theorem star_imK : (star a).imK = -a.imK :=
   rfl
 #align quaternion.star_im_k Quaternion.star_imK
 
-/- warning: quaternion.star_im -> Quaternion.star_im is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.star_im Quaternion.star_imₓ'. -/
 @[simp]
 theorem star_im : (star a).im = -a.im :=
   a.im_star
 #align quaternion.star_im Quaternion.star_im
 
-/- warning: quaternion.self_add_star' -> Quaternion.self_add_star' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.self_add_star' Quaternion.self_add_star'ₓ'. -/
 theorem self_add_star' : a + star a = ↑(2 * a.re) :=
   a.self_add_star'
 #align quaternion.self_add_star' Quaternion.self_add_star'
 
-/- warning: quaternion.self_add_star -> Quaternion.self_add_star is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.self_add_star Quaternion.self_add_starₓ'. -/
 theorem self_add_star : a + star a = 2 * a.re :=
   a.self_add_star
 #align quaternion.self_add_star Quaternion.self_add_star
 
-/- warning: quaternion.star_add_self' -> Quaternion.star_add_self' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.star_add_self' Quaternion.star_add_self'ₓ'. -/
 theorem star_add_self' : star a + a = ↑(2 * a.re) :=
   a.star_add_self'
 #align quaternion.star_add_self' Quaternion.star_add_self'
 
-/- warning: quaternion.star_add_self -> Quaternion.star_add_self is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.star_add_self Quaternion.star_add_selfₓ'. -/
 theorem star_add_self : star a + a = 2 * a.re :=
   a.star_add_self
 #align quaternion.star_add_self Quaternion.star_add_self
 
-/- warning: quaternion.star_eq_two_re_sub -> Quaternion.star_eq_two_re_sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.star_eq_two_re_sub Quaternion.star_eq_two_re_subₓ'. -/
 theorem star_eq_two_re_sub : star a = ↑(2 * a.re) - a :=
   a.star_eq_two_re_sub
 #align quaternion.star_eq_two_re_sub Quaternion.star_eq_two_re_sub
 
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-Case conversion may be inaccurate. Consider using '#align quaternion.star_coe Quaternion.star_coeₓ'. -/
 @[simp, norm_cast]
 theorem star_coe : star (x : ℍ[R]) = x :=
   QuaternionAlgebra.star_coe x
 #align quaternion.star_coe Quaternion.star_coe
 
-/- warning: quaternion.im_star -> Quaternion.im_star is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.im_star Quaternion.im_starₓ'. -/
 @[simp]
 theorem im_star : star a.im = -a.im :=
   QuaternionAlgebra.im_star _
 #align quaternion.im_star Quaternion.im_star
 
-/- warning: quaternion.star_smul -> Quaternion.star_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.star_smul Quaternion.star_smulₓ'. -/
 @[simp]
 theorem star_smul [Monoid S] [DistribMulAction S R] (s : S) (a : ℍ[R]) :
     star (s • a) = s • star a :=
   QuaternionAlgebra.star_smul _ _
 #align quaternion.star_smul Quaternion.star_smul
 
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 theorem eq_re_of_eq_coe {a : ℍ[R]} {x : R} (h : a = x) : a = a.re :=
   QuaternionAlgebra.eq_re_of_eq_coe h
 #align quaternion.eq_re_of_eq_coe Quaternion.eq_re_of_eq_coe
 
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 theorem eq_re_iff_mem_range_coe {a : ℍ[R]} : a = a.re ↔ a ∈ Set.range (coe : R → ℍ[R]) :=
   QuaternionAlgebra.eq_re_iff_mem_range_coe
 #align quaternion.eq_re_iff_mem_range_coe Quaternion.eq_re_iff_mem_range_coe
@@ -2178,17 +1248,11 @@ section CharZero
 
 variable [NoZeroDivisors R] [CharZero R]
 
-/- warning: quaternion.star_eq_self -> Quaternion.star_eq_self is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.star_eq_self Quaternion.star_eq_selfₓ'. -/
 @[simp]
 theorem star_eq_self {a : ℍ[R]} : star a = a ↔ a = a.re :=
   QuaternionAlgebra.star_eq_self
 #align quaternion.star_eq_self Quaternion.star_eq_self
 
-/- warning: quaternion.star_eq_neg -> Quaternion.star_eq_neg is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.star_eq_neg Quaternion.star_eq_negₓ'. -/
 @[simp]
 theorem star_eq_neg {a : ℍ[R]} : star a = -a ↔ a.re = 0 :=
   QuaternionAlgebra.star_eq_neg
@@ -2196,47 +1260,26 @@ theorem star_eq_neg {a : ℍ[R]} : star a = -a ↔ a.re = 0 :=
 
 end CharZero
 
-/- warning: quaternion.star_mul_eq_coe -> Quaternion.star_mul_eq_coe is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.star_mul_eq_coe Quaternion.star_mul_eq_coeₓ'. -/
 theorem star_mul_eq_coe : star a * a = (star a * a).re :=
   a.star_mul_eq_coe
 #align quaternion.star_mul_eq_coe Quaternion.star_mul_eq_coe
 
-/- warning: quaternion.mul_star_eq_coe -> Quaternion.mul_star_eq_coe is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.mul_star_eq_coe Quaternion.mul_star_eq_coeₓ'. -/
 theorem mul_star_eq_coe : a * star a = (a * star a).re :=
   a.mul_star_eq_coe
 #align quaternion.mul_star_eq_coe Quaternion.mul_star_eq_coe
 
 open MulOpposite
 
-/- warning: quaternion.star_ae -> Quaternion.starAe is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align quaternion.star_ae Quaternion.starAeₓ'. -/
 /-- Quaternion conjugate as an `alg_equiv` to the opposite ring. -/
 def starAe : ℍ[R] ≃ₐ[R] ℍ[R]ᵐᵒᵖ :=
   QuaternionAlgebra.starAe
 #align quaternion.star_ae Quaternion.starAe
 
-/- warning: quaternion.coe_star_ae -> Quaternion.coe_starAe is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.coe_star_ae Quaternion.coe_starAeₓ'. -/
 @[simp]
 theorem coe_starAe : ⇑(starAe : ℍ[R] ≃ₐ[R] ℍ[R]ᵐᵒᵖ) = op ∘ star :=
   rfl
 #align quaternion.coe_star_ae Quaternion.coe_starAe
 
-/- warning: quaternion.norm_sq -> Quaternion.normSq is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq Quaternion.normSqₓ'. -/
 /-- Square of the norm. -/
 def normSq : ℍ[R] →*₀ R where
   toFun a := (a * star a).re
@@ -2249,92 +1292,53 @@ def normSq : ℍ[R] →*₀ R where
           ← mul_assoc, x.mul_star_eq_coe, ← coe_mul]
 #align quaternion.norm_sq Quaternion.normSq
 
-/- warning: quaternion.norm_sq_def -> Quaternion.normSq_def is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_def Quaternion.normSq_defₓ'. -/
 theorem normSq_def : normSq a = (a * star a).re :=
   rfl
 #align quaternion.norm_sq_def Quaternion.normSq_def
 
-/- warning: quaternion.norm_sq_def' -> Quaternion.normSq_def' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_def' Quaternion.normSq_def'ₓ'. -/
 theorem normSq_def' : normSq a = a.1 ^ 2 + a.2 ^ 2 + a.3 ^ 2 + a.4 ^ 2 := by
   simp only [norm_sq_def, sq, mul_neg, sub_neg_eq_add, mul_re, star_re, star_im_i, star_im_j,
     star_im_k]
 #align quaternion.norm_sq_def' Quaternion.normSq_def'
 
-/- warning: quaternion.norm_sq_coe -> Quaternion.normSq_coe is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_coe Quaternion.normSq_coeₓ'. -/
 theorem normSq_coe : normSq (x : ℍ[R]) = x ^ 2 := by
   rw [norm_sq_def, star_coe, ← coe_mul, coe_re, sq]
 #align quaternion.norm_sq_coe Quaternion.normSq_coe
 
-/- warning: quaternion.norm_sq_star -> Quaternion.normSq_star is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_star Quaternion.normSq_starₓ'. -/
 @[simp]
 theorem normSq_star : normSq (star a) = normSq a := by simp [norm_sq_def']
 #align quaternion.norm_sq_star Quaternion.normSq_star
 
-/- warning: quaternion.norm_sq_nat_cast -> Quaternion.normSq_nat_cast is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_nat_cast Quaternion.normSq_nat_castₓ'. -/
 @[norm_cast]
 theorem normSq_nat_cast (n : ℕ) : normSq (n : ℍ[R]) = n ^ 2 := by rw [← coe_nat_cast, norm_sq_coe]
 #align quaternion.norm_sq_nat_cast Quaternion.normSq_nat_cast
 
-/- warning: quaternion.norm_sq_int_cast -> Quaternion.normSq_int_cast is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_int_cast Quaternion.normSq_int_castₓ'. -/
 @[norm_cast]
 theorem normSq_int_cast (z : ℤ) : normSq (z : ℍ[R]) = z ^ 2 := by rw [← coe_int_cast, norm_sq_coe]
 #align quaternion.norm_sq_int_cast Quaternion.normSq_int_cast
 
-/- warning: quaternion.norm_sq_neg -> Quaternion.normSq_neg is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_neg Quaternion.normSq_negₓ'. -/
 @[simp]
 theorem normSq_neg : normSq (-a) = normSq a := by simp only [norm_sq_def, star_neg, neg_mul_neg]
 #align quaternion.norm_sq_neg Quaternion.normSq_neg
 
-/- warning: quaternion.self_mul_star -> Quaternion.self_mul_star is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.self_mul_star Quaternion.self_mul_starₓ'. -/
 theorem self_mul_star : a * star a = normSq a := by rw [mul_star_eq_coe, norm_sq_def]
 #align quaternion.self_mul_star Quaternion.self_mul_star
 
-/- warning: quaternion.star_mul_self -> Quaternion.star_mul_self is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.star_mul_self Quaternion.star_mul_selfₓ'. -/
 theorem star_mul_self : star a * a = normSq a := by rw [star_comm_self', self_mul_star]
 #align quaternion.star_mul_self Quaternion.star_mul_self
 
-/- warning: quaternion.im_sq -> Quaternion.im_sq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.im_sq Quaternion.im_sqₓ'. -/
 theorem im_sq : a.im ^ 2 = -normSq a.im := by
   simp_rw [sq, ← star_mul_self, im_star, neg_mul, neg_neg]
 #align quaternion.im_sq Quaternion.im_sq
 
-/- warning: quaternion.coe_norm_sq_add -> Quaternion.coe_normSq_add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.coe_norm_sq_add Quaternion.coe_normSq_addₓ'. -/
 theorem coe_normSq_add : (normSq (a + b) : ℍ[R]) = normSq a + a * star b + b * star a + normSq b :=
   by simp [← self_mul_star, mul_add, add_mul, add_assoc]
 #align quaternion.coe_norm_sq_add Quaternion.coe_normSq_add
 
-/- warning: quaternion.norm_sq_smul -> Quaternion.normSq_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_smul Quaternion.normSq_smulₓ'. -/
 theorem normSq_smul (r : R) (q : ℍ[R]) : normSq (r • q) = r ^ 2 * normSq q := by
   simp_rw [norm_sq_def, star_smul, smul_mul_smul, smul_re, sq, smul_eq_mul]
 #align quaternion.norm_sq_smul Quaternion.normSq_smul
 
-/- warning: quaternion.norm_sq_add -> Quaternion.normSq_add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_add Quaternion.normSq_addₓ'. -/
 theorem normSq_add (a b : ℍ[R]) : normSq (a + b) = normSq a + normSq b + 2 * (a * star b).re :=
   calc
     normSq (a + b) = normSq a + (a * star b).re + ((b * star a).re + normSq b) := by
@@ -2355,9 +1359,6 @@ section LinearOrderedCommRing
 
 variable [LinearOrderedCommRing R] {a : ℍ[R]}
 
-/- warning: quaternion.norm_sq_eq_zero -> Quaternion.normSq_eq_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_eq_zero Quaternion.normSq_eq_zeroₓ'. -/
 @[simp]
 theorem normSq_eq_zero : normSq a = 0 ↔ a = 0 :=
   by
@@ -2367,23 +1368,14 @@ theorem normSq_eq_zero : normSq a = 0 ↔ a = 0 :=
   all_goals apply_rules [sq_nonneg, add_nonneg]
 #align quaternion.norm_sq_eq_zero Quaternion.normSq_eq_zero
 
-/- warning: quaternion.norm_sq_ne_zero -> Quaternion.normSq_ne_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_ne_zero Quaternion.normSq_ne_zeroₓ'. -/
 theorem normSq_ne_zero : normSq a ≠ 0 ↔ a ≠ 0 :=
   not_congr normSq_eq_zero
 #align quaternion.norm_sq_ne_zero Quaternion.normSq_ne_zero
 
-/- warning: quaternion.norm_sq_nonneg -> Quaternion.normSq_nonneg is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_nonneg Quaternion.normSq_nonnegₓ'. -/
 @[simp]
 theorem normSq_nonneg : 0 ≤ normSq a := by rw [norm_sq_def']; apply_rules [sq_nonneg, add_nonneg]
 #align quaternion.norm_sq_nonneg Quaternion.normSq_nonneg
 
-/- warning: quaternion.norm_sq_le_zero -> Quaternion.normSq_le_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_le_zero Quaternion.normSq_le_zeroₓ'. -/
 @[simp]
 theorem normSq_le_zero : normSq a ≤ 0 ↔ a = 0 := by
   simpa only [le_antisymm_iff, norm_sq_nonneg, and_true_iff] using @norm_sq_eq_zero _ _ a
@@ -2400,9 +1392,6 @@ instance : NoZeroDivisors ℍ[R] :=
 instance : IsDomain ℍ[R] :=
   NoZeroDivisors.to_isDomain _
 
-/- warning: quaternion.sq_eq_norm_sq -> Quaternion.sq_eq_normSq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.sq_eq_norm_sq Quaternion.sq_eq_normSqₓ'. -/
 theorem sq_eq_normSq : a ^ 2 = normSq a ↔ a = a.re :=
   by
   simp_rw [← star_eq_self]
@@ -2411,9 +1400,6 @@ theorem sq_eq_normSq : a ^ 2 = normSq a ↔ a = a.re :=
   · rw [← star_mul_self, sq, mul_left_inj' hq0, eq_comm]
 #align quaternion.sq_eq_norm_sq Quaternion.sq_eq_normSq
 
-/- warning: quaternion.sq_eq_neg_norm_sq -> Quaternion.sq_eq_neg_normSq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.sq_eq_neg_norm_sq Quaternion.sq_eq_neg_normSqₓ'. -/
 theorem sq_eq_neg_normSq : a ^ 2 = -normSq a ↔ a.re = 0 :=
   by
   simp_rw [← star_eq_neg]
@@ -2442,28 +1428,16 @@ instance : GroupWithZero ℍ[R] :=
       rw [has_inv_inv, Algebra.mul_smul_comm, self_mul_star, smul_coe,
         inv_mul_cancel (norm_sq_ne_zero.2 ha), coe_one] }
 
-/- warning: quaternion.coe_inv -> Quaternion.coe_inv is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align quaternion.coe_inv Quaternion.coe_invₓ'. -/
 @[norm_cast, simp]
 theorem coe_inv (x : R) : ((x⁻¹ : R) : ℍ[R]) = x⁻¹ :=
   map_inv₀ (algebraMap R ℍ[R]) _
 #align quaternion.coe_inv Quaternion.coe_inv
 
-/- warning: quaternion.coe_div -> Quaternion.coe_div is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.coe_div Quaternion.coe_divₓ'. -/
 @[norm_cast, simp]
 theorem coe_div (x y : R) : ((x / y : R) : ℍ[R]) = x / y :=
   map_div₀ (algebraMap R ℍ[R]) x y
 #align quaternion.coe_div Quaternion.coe_div
 
-/- warning: quaternion.coe_zpow -> Quaternion.coe_zpow is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.coe_zpow Quaternion.coe_zpowₓ'. -/
 @[norm_cast, simp]
 theorem coe_zpow (x : R) (z : ℤ) : ((x ^ z : R) : ℍ[R]) = x ^ z :=
   map_zpow₀ (algebraMap R ℍ[R]) x z
@@ -2479,96 +1453,51 @@ instance : DivisionRing ℍ[R] :=
       rw [coe_mul_eq_smul]
       ext <;> exact DivisionRing.qsmul_eq_mul' _ _ }
 
-/- warning: quaternion.rat_cast_re -> Quaternion.rat_cast_re is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align quaternion.rat_cast_re Quaternion.rat_cast_reₓ'. -/
 @[simp, norm_cast]
 theorem rat_cast_re (q : ℚ) : (q : ℍ[R]).re = q :=
   rfl
 #align quaternion.rat_cast_re Quaternion.rat_cast_re
 
-/- warning: quaternion.rat_cast_im_i -> Quaternion.rat_cast_imI is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align quaternion.rat_cast_im_i Quaternion.rat_cast_imIₓ'. -/
 @[simp, norm_cast]
 theorem rat_cast_imI (q : ℚ) : (q : ℍ[R]).imI = 0 :=
   rfl
 #align quaternion.rat_cast_im_i Quaternion.rat_cast_imI
 
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-Case conversion may be inaccurate. Consider using '#align quaternion.rat_cast_im_j Quaternion.rat_cast_imJₓ'. -/
 @[simp, norm_cast]
 theorem rat_cast_imJ (q : ℚ) : (q : ℍ[R]).imJ = 0 :=
   rfl
 #align quaternion.rat_cast_im_j Quaternion.rat_cast_imJ
 
-/- warning: quaternion.rat_cast_im_k -> Quaternion.rat_cast_imK is a dubious translation:
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 @[simp, norm_cast]
 theorem rat_cast_imK (q : ℚ) : (q : ℍ[R]).imK = 0 :=
   rfl
 #align quaternion.rat_cast_im_k Quaternion.rat_cast_imK
 
-/- warning: quaternion.rat_cast_im -> Quaternion.rat_cast_im is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.rat_cast_im Quaternion.rat_cast_imₓ'. -/
 @[simp, norm_cast]
 theorem rat_cast_im (q : ℚ) : (q : ℍ[R]).im = 0 :=
   rfl
 #align quaternion.rat_cast_im Quaternion.rat_cast_im
 
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 @[norm_cast]
 theorem coe_rat_cast (q : ℚ) : ↑(q : R) = (q : ℍ[R]) :=
   rfl
 #align quaternion.coe_rat_cast Quaternion.coe_rat_cast
 
-/- warning: quaternion.norm_sq_inv -> Quaternion.normSq_inv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_inv Quaternion.normSq_invₓ'. -/
 @[simp]
 theorem normSq_inv : normSq a⁻¹ = (normSq a)⁻¹ :=
   map_inv₀ normSq _
 #align quaternion.norm_sq_inv Quaternion.normSq_inv
 
-/- warning: quaternion.norm_sq_div -> Quaternion.normSq_div is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_div Quaternion.normSq_divₓ'. -/
 @[simp]
 theorem normSq_div : normSq (a / b) = normSq a / normSq b :=
   map_div₀ normSq a b
 #align quaternion.norm_sq_div Quaternion.normSq_div
 
-/- warning: quaternion.norm_sq_zpow -> Quaternion.normSq_zpow is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_zpow Quaternion.normSq_zpowₓ'. -/
 @[simp]
 theorem normSq_zpow (z : ℤ) : normSq (a ^ z) = normSq a ^ z :=
   map_zpow₀ normSq a z
 #align quaternion.norm_sq_zpow Quaternion.normSq_zpow
 
-/- warning: quaternion.norm_sq_rat_cast -> Quaternion.normSq_rat_cast is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_rat_cast Quaternion.normSq_rat_castₓ'. -/
 @[norm_cast]
 theorem normSq_rat_cast (q : ℚ) : normSq (q : ℍ[R]) = q ^ 2 := by rw [← coe_rat_cast, norm_sq_coe]
 #align quaternion.norm_sq_rat_cast Quaternion.normSq_rat_cast

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

@@ -814,10 +814,8 @@ lean 3 declaration is
 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align quaternion_algebra.rank_eq_four QuaternionAlgebra.rank_eq_fourₓ'. -/
-theorem rank_eq_four [StrongRankCondition R] : Module.rank R ℍ[R,c₁,c₂] = 4 :=
-  by
-  rw [rank_eq_card_basis (basis_one_i_j_k c₁ c₂), Fintype.card_fin]
-  norm_num
+theorem rank_eq_four [StrongRankCondition R] : Module.rank R ℍ[R,c₁,c₂] = 4 := by
+  rw [rank_eq_card_basis (basis_one_i_j_k c₁ c₂), Fintype.card_fin]; norm_num
 #align quaternion_algebra.rank_eq_four QuaternionAlgebra.rank_eq_four
 
 /- warning: quaternion_algebra.finrank_eq_four -> QuaternionAlgebra.finrank_eq_four is a dubious translation:
@@ -1134,9 +1132,7 @@ lean 3 declaration is
 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align quaternion_algebra.mul_star_eq_coe QuaternionAlgebra.mul_star_eq_coeₓ'. -/
-theorem mul_star_eq_coe : a * star a = (a * star a).re :=
-  by
-  rw [← star_comm_self']
+theorem mul_star_eq_coe : a * star a = (a * star a).re := by rw [← star_comm_self'];
   exact a.star_mul_eq_coe
 #align quaternion_algebra.mul_star_eq_coe QuaternionAlgebra.mul_star_eq_coe
 
@@ -2382,9 +2378,7 @@ theorem normSq_ne_zero : normSq a ≠ 0 ↔ a ≠ 0 :=
 <too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_nonneg Quaternion.normSq_nonnegₓ'. -/
 @[simp]
-theorem normSq_nonneg : 0 ≤ normSq a := by
-  rw [norm_sq_def']
-  apply_rules [sq_nonneg, add_nonneg]
+theorem normSq_nonneg : 0 ≤ normSq a := by rw [norm_sq_def']; apply_rules [sq_nonneg, add_nonneg]
 #align quaternion.norm_sq_nonneg Quaternion.normSq_nonneg
 
 /- warning: quaternion.norm_sq_le_zero -> Quaternion.normSq_le_zero is a dubious translation:
@@ -2596,11 +2590,8 @@ private theorem pow_four [Infinite R] : (#R) ^ 4 = (#R) :=
 
 #print Cardinal.mk_quaternionAlgebra /-
 /-- The cardinality of a quaternion algebra, as a type. -/
-theorem mk_quaternionAlgebra : (#ℍ[R,c₁,c₂]) = (#R) ^ 4 :=
-  by
-  rw [mk_congr (QuaternionAlgebra.equivProd c₁ c₂)]
-  simp only [mk_prod, lift_id]
-  ring
+theorem mk_quaternionAlgebra : (#ℍ[R,c₁,c₂]) = (#R) ^ 4 := by
+  rw [mk_congr (QuaternionAlgebra.equivProd c₁ c₂)]; simp only [mk_prod, lift_id]; ring
 #align cardinal.mk_quaternion_algebra Cardinal.mk_quaternionAlgebra
 -/
 

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

@@ -388,10 +388,7 @@ instance : Mul ℍ[R,c₁,c₂] :=
       a.1 * b.4 + a.2 * b.3 - a.3 * b.2 + a.4 * b.1⟩⟩
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion_algebra.mk_mul_mk QuaternionAlgebra.mk_mul_mkₓ'. -/
 @[simp]
 theorem mk_mul_mk (a₁ a₂ a₃ a₄ b₁ b₂ b₃ b₄ : R) :
@@ -770,10 +767,7 @@ def linearEquivTuple : ℍ[R,c₁,c₂] ≃ₗ[R] Fin 4 → R :=
 #align quaternion_algebra.linear_equiv_tuple QuaternionAlgebra.linearEquivTuple
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion_algebra.coe_linear_equiv_tuple QuaternionAlgebra.coe_linearEquivTupleₓ'. -/
 @[simp]
 theorem coe_linearEquivTuple : ⇑(linearEquivTuple c₁ c₂) = equivTuple c₁ c₂ :=
@@ -781,10 +775,7 @@ theorem coe_linearEquivTuple : ⇑(linearEquivTuple c₁ c₂) = equivTuple c₁
 #align quaternion_algebra.coe_linear_equiv_tuple QuaternionAlgebra.coe_linearEquivTuple
 
 /- warning: quaternion_algebra.coe_linear_equiv_tuple_symm -> QuaternionAlgebra.coe_linearEquivTuple_symm is a dubious translation:
-lean 3 declaration is
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(instOfNatNat 4))) -> R) (QuaternionAlgebra.{u1} R c₁ c₂) (SMulZeroClass.toSMul.{u1, u1} R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (AddMonoid.toZero.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (AddMonoid.toAddZeroClass.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (AddMonoid.toZero.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (AddMonoid.toAddZeroClass.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (Module.toDistribMulAction.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((Fin 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(a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (QuaternionAlgebra.{u1} R c₁ c₂) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (Module.toDistribMulAction.{u1, u1} R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u1, u1} R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (QuaternionAlgebra.{u1} R c₁ c₂) (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion_algebra.coe_linear_equiv_tuple_symm QuaternionAlgebra.coe_linearEquivTuple_symmₓ'. -/
 @[simp]
 theorem coe_linearEquivTuple_symm : ⇑(linearEquivTuple c₁ c₂).symm = (equivTuple c₁ c₂).symm :=
@@ -803,10 +794,7 @@ noncomputable def basisOneIJK : Basis (Fin 4) R ℍ[R,c₁,c₂] :=
 #align quaternion_algebra.basis_one_i_j_k QuaternionAlgebra.basisOneIJK
 
 /- warning: quaternion_algebra.coe_basis_one_i_j_k_repr -> QuaternionAlgebra.coe_basisOneIJK_repr is a dubious translation:
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_inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (QuaternionAlgebra.{u1} R c₁ c₂) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (AddMonoid.toZero.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (AddMonoid.toAddZeroClass.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (Module.toDistribMulAction.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u1} R (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddMonoid.toZero.{u1} (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (QuaternionAlgebra.{u1} R c₁ c₂) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (QuaternionAlgebra.{u1} R c₁ c₂) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (AddCommMonoid.toAddMonoid.{u1} (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Basis.repr.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (QuaternionAlgebra.{u1} R c₁ c₂) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (QuaternionAlgebra.basisOneIJK.{u1} R _inst_1 c₁ c₂)) q)) (Matrix.vecCons.{u1} R (Nat.succ (Nat.succ (Nat.succ (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (QuaternionAlgebra.re.{u1} R c₁ c₂ q) (Matrix.vecCons.{u1} R (Nat.succ (Nat.succ (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (QuaternionAlgebra.imI.{u1} R c₁ c₂ q) (Matrix.vecCons.{u1} R (Nat.succ (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (QuaternionAlgebra.imJ.{u1} R c₁ c₂ q) (Matrix.vecCons.{u1} R (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (QuaternionAlgebra.imK.{u1} R c₁ c₂ q) (Matrix.vecEmpty.{u1} R)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion_algebra.coe_basis_one_i_j_k_repr QuaternionAlgebra.coe_basisOneIJK_reprₓ'. -/
 @[simp]
 theorem coe_basisOneIJK_repr (q : ℍ[R,c₁,c₂]) :
@@ -1170,10 +1158,7 @@ def starAe : ℍ[R,c₁,c₂] ≃ₐ[R] ℍ[R,c₁,c₂]ᵐᵒᵖ :=
 #align quaternion_algebra.star_ae QuaternionAlgebra.starAe
 
 /- warning: quaternion_algebra.coe_star_ae -> QuaternionAlgebra.coe_starAe is a dubious translation:
-lean 3 declaration is
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u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Semiring.toNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (AddCommMonoid.toAddMonoid.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 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c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (Algebra.toModule.{u1, u1} R (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Semiring.toNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Module.toDistribMulAction.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Semiring.toNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (Algebra.toModule.{u1, u1} R (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AlgEquiv.{u1, u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))))) (QuaternionAlgebra.starAe.{u1} R _inst_1 c₁ c₂)) (Function.comp.{succ u1, succ u1, succ u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MulOpposite.op.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (Star.star.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instStarQuaternionAlgebra.{u1} R _inst_1 c₁ c₂)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion_algebra.coe_star_ae QuaternionAlgebra.coe_starAeₓ'. -/
 @[simp]
 theorem coe_starAe : ⇑(starAe : ℍ[R,c₁,c₂] ≃ₐ[R] _) = op ∘ star :=
@@ -1248,10 +1233,7 @@ instance : StarRing ℍ[R] :=
   QuaternionAlgebra.starRing
 
 /- warning: quaternion.ext -> Quaternion.ext is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.ext Quaternion.extₓ'. -/
 @[ext]
 theorem ext : a.re = b.re → a.imI = b.imI → a.imJ = b.imJ → a.imK = b.imK → a = b :=
@@ -1259,10 +1241,7 @@ theorem ext : a.re = b.re → a.imI = b.imI → a.imJ = b.imJ → a.imK = b.imK
 #align quaternion.ext Quaternion.ext
 
 /- warning: quaternion.ext_iff -> Quaternion.ext_iff is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.ext_iff Quaternion.ext_iffₓ'. -/
 theorem ext_iff {a b : ℍ[R]} :
     a = b ↔ a.re = b.re ∧ a.imI = b.imI ∧ a.imJ = b.imJ ∧ a.imK = b.imK :=
@@ -1464,10 +1443,7 @@ theorem zero_imK : (0 : ℍ[R]).imK = 0 :=
 #align quaternion.zero_im_k Quaternion.zero_imK
 
 /- warning: quaternion.zero_im -> Quaternion.zero_im is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.zero_im Quaternion.zero_imₓ'. -/
 @[simp]
 theorem zero_im : (0 : ℍ[R]).im = 0 :=
@@ -1552,10 +1528,7 @@ theorem coe_one : ((1 : R) : ℍ[R]) = 1 :=
 #align quaternion.coe_one Quaternion.coe_one
 
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 Case conversion may be inaccurate. Consider using '#align quaternion.add_re Quaternion.add_reₓ'. -/
 @[simp]
 theorem add_re : (a + b).re = a.re + b.re :=
@@ -1563,10 +1536,7 @@ theorem add_re : (a + b).re = a.re + b.re :=
 #align quaternion.add_re Quaternion.add_re
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.add_im_i Quaternion.add_imIₓ'. -/
 @[simp]
 theorem add_imI : (a + b).imI = a.imI + b.imI :=
@@ -1574,10 +1544,7 @@ theorem add_imI : (a + b).imI = a.imI + b.imI :=
 #align quaternion.add_im_i Quaternion.add_imI
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.add_im_j Quaternion.add_imJₓ'. -/
 @[simp]
 theorem add_imJ : (a + b).imJ = a.imJ + b.imJ :=
@@ -1585,10 +1552,7 @@ theorem add_imJ : (a + b).imJ = a.imJ + b.imJ :=
 #align quaternion.add_im_j Quaternion.add_imJ
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.add_im_k Quaternion.add_imKₓ'. -/
 @[simp]
 theorem add_imK : (a + b).imK = a.imK + b.imK :=
@@ -1596,10 +1560,7 @@ theorem add_imK : (a + b).imK = a.imK + b.imK :=
 #align quaternion.add_im_k Quaternion.add_imK
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.add_im Quaternion.add_imₓ'. -/
 @[simp]
 theorem add_im : (a + b).im = a.im + b.im :=
@@ -1607,10 +1568,7 @@ theorem add_im : (a + b).im = a.im + b.im :=
 #align quaternion.add_im Quaternion.add_im
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.coe_add Quaternion.coe_addₓ'. -/
 @[simp, norm_cast]
 theorem coe_add : ((x + y : R) : ℍ[R]) = x + y :=
@@ -1684,10 +1642,7 @@ theorem coe_neg : ((-x : R) : ℍ[R]) = -x :=
 #align quaternion.coe_neg Quaternion.coe_neg
 
 /- warning: quaternion.sub_re -> Quaternion.sub_re is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.sub_re Quaternion.sub_reₓ'. -/
 @[simp]
 theorem sub_re : (a - b).re = a.re - b.re :=
@@ -1695,10 +1650,7 @@ theorem sub_re : (a - b).re = a.re - b.re :=
 #align quaternion.sub_re Quaternion.sub_re
 
 /- warning: quaternion.sub_im_i -> Quaternion.sub_imI is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.sub_im_i Quaternion.sub_imIₓ'. -/
 @[simp]
 theorem sub_imI : (a - b).imI = a.imI - b.imI :=
@@ -1706,10 +1658,7 @@ theorem sub_imI : (a - b).imI = a.imI - b.imI :=
 #align quaternion.sub_im_i Quaternion.sub_imI
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.sub_im_j Quaternion.sub_imJₓ'. -/
 @[simp]
 theorem sub_imJ : (a - b).imJ = a.imJ - b.imJ :=
@@ -1717,10 +1666,7 @@ theorem sub_imJ : (a - b).imJ = a.imJ - b.imJ :=
 #align quaternion.sub_im_j Quaternion.sub_imJ
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.sub_im_k Quaternion.sub_imKₓ'. -/
 @[simp]
 theorem sub_imK : (a - b).imK = a.imK - b.imK :=
@@ -1728,10 +1674,7 @@ theorem sub_imK : (a - b).imK = a.imK - b.imK :=
 #align quaternion.sub_im_k Quaternion.sub_imK
 
 /- warning: quaternion.sub_im -> Quaternion.sub_im is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.sub_im Quaternion.sub_imₓ'. -/
 @[simp]
 theorem sub_im : (a - b).im = a.im - b.im :=
@@ -1739,10 +1682,7 @@ theorem sub_im : (a - b).im = a.im - b.im :=
 #align quaternion.sub_im Quaternion.sub_im
 
 /- warning: quaternion.coe_sub -> Quaternion.coe_sub is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.coe_sub Quaternion.coe_subₓ'. -/
 @[simp, norm_cast]
 theorem coe_sub : ((x - y : R) : ℍ[R]) = x - y :=
@@ -1750,10 +1690,7 @@ theorem coe_sub : ((x - y : R) : ℍ[R]) = x - y :=
 #align quaternion.coe_sub Quaternion.coe_sub
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.mul_re Quaternion.mul_reₓ'. -/
 @[simp]
 theorem mul_re : (a * b).re = a.re * b.re - a.imI * b.imI - a.imJ * b.imJ - a.imK * b.imK :=
@@ -1761,10 +1698,7 @@ theorem mul_re : (a * b).re = a.re * b.re - a.imI * b.imI - a.imJ * b.imJ - a.im
 #align quaternion.mul_re Quaternion.mul_re
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.mul_im_i Quaternion.mul_imIₓ'. -/
 @[simp]
 theorem mul_imI : (a * b).imI = a.re * b.imI + a.imI * b.re + a.imJ * b.imK - a.imK * b.imJ :=
@@ -1772,10 +1706,7 @@ theorem mul_imI : (a * b).imI = a.re * b.imI + a.imI * b.re + a.imJ * b.imK - a.
 #align quaternion.mul_im_i Quaternion.mul_imI
 
 /- warning: quaternion.mul_im_j -> Quaternion.mul_imJ is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.mul_im_j Quaternion.mul_imJₓ'. -/
 @[simp]
 theorem mul_imJ : (a * b).imJ = a.re * b.imJ - a.imI * b.imK + a.imJ * b.re + a.imK * b.imI :=
@@ -1783,10 +1714,7 @@ theorem mul_imJ : (a * b).imJ = a.re * b.imJ - a.imI * b.imK + a.imJ * b.re + a.
 #align quaternion.mul_im_j Quaternion.mul_imJ
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.mul_im_k Quaternion.mul_imKₓ'. -/
 @[simp]
 theorem mul_imK : (a * b).imK = a.re * b.imK + a.imI * b.imJ - a.imJ * b.imI + a.imK * b.re :=
@@ -2035,10 +1963,7 @@ theorem coe_smul [SMulZeroClass S R] (s : S) (r : R) : (↑(s • r) : ℍ[R]) =
 #align quaternion.coe_smul Quaternion.coe_smul
 
 /- warning: quaternion.coe_commutes -> Quaternion.coe_commutes is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.coe_commutes Quaternion.coe_commutesₓ'. -/
 theorem coe_commutes : ↑r * a = a * r :=
   QuaternionAlgebra.coe_commutes r a
@@ -2075,10 +2000,7 @@ theorem mul_coe_eq_smul : a * r = r • a :=
 #align quaternion.mul_coe_eq_smul Quaternion.mul_coe_eq_smul
 
 /- warning: quaternion.algebra_map_def -> Quaternion.algebraMap_def is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.algebra_map_def Quaternion.algebraMap_defₓ'. -/
 @[simp]
 theorem algebraMap_def : ⇑(algebraMap R ℍ[R]) = coe :=
@@ -2166,10 +2088,7 @@ theorem star_imK : (star a).imK = -a.imK :=
 #align quaternion.star_im_k Quaternion.star_imK
 
 /- warning: quaternion.star_im -> Quaternion.star_im is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.star_im Quaternion.star_imₓ'. -/
 @[simp]
 theorem star_im : (star a).im = -a.im :=
@@ -2177,50 +2096,35 @@ theorem star_im : (star a).im = -a.im :=
 #align quaternion.star_im Quaternion.star_im
 
 /- warning: quaternion.self_add_star' -> Quaternion.self_add_star' is a dubious translation:
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-but is expected to have type
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.self_add_star' Quaternion.self_add_star'ₓ'. -/
 theorem self_add_star' : a + star a = ↑(2 * a.re) :=
   a.self_add_star'
 #align quaternion.self_add_star' Quaternion.self_add_star'
 
 /- warning: quaternion.self_add_star -> Quaternion.self_add_star is a dubious translation:
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R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (instHAdd.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Distrib.toHasAdd.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toDistrib.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) a (Star.star.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (InvolutiveStar.toHasStar.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (StarAddMonoid.toHasInvolutiveStar.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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_inst_1))))))) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Quaternion.{u1} R 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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.self_add_star Quaternion.self_add_starₓ'. -/
 theorem self_add_star : a + star a = 2 * a.re :=
   a.self_add_star
 #align quaternion.self_add_star Quaternion.self_add_star
 
 /- warning: quaternion.star_add_self' -> Quaternion.star_add_self' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.star_add_self' Quaternion.star_add_self'ₓ'. -/
 theorem star_add_self' : star a + a = ↑(2 * a.re) :=
   a.star_add_self'
 #align quaternion.star_add_self' Quaternion.star_add_self'
 
 /- warning: quaternion.star_add_self -> Quaternion.star_add_self is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.star_add_self Quaternion.star_add_selfₓ'. -/
 theorem star_add_self : star a + a = 2 * a.re :=
   a.star_add_self
 #align quaternion.star_add_self Quaternion.star_add_self
 
 /- warning: quaternion.star_eq_two_re_sub -> Quaternion.star_eq_two_re_sub is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.star_eq_two_re_sub Quaternion.star_eq_two_re_subₓ'. -/
 theorem star_eq_two_re_sub : star a = ↑(2 * a.re) - a :=
   a.star_eq_two_re_sub
@@ -2238,10 +2142,7 @@ theorem star_coe : star (x : ℍ[R]) = x :=
 #align quaternion.star_coe Quaternion.star_coe
 
 /- warning: quaternion.im_star -> Quaternion.im_star is a dubious translation:
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(AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (InvolutiveStar.toHasStar.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (StarAddMonoid.toHasInvolutiveStar.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.starRing.{u1} R _inst_1)))) (Quaternion.im.{u1} R _inst_1 a)) (Neg.neg.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddGroup.toSubNegMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddGroupWithOne.toAddGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommGroupWithOne.toAddGroupWithOne.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toAddCommGroupWithOne.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))))) (Quaternion.im.{u1} R _inst_1 a))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Star.star.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instStarQuaternionToOneToSemiringToCommSemiringToNegToRing.{u1} R _inst_1) (Quaternion.im.{u1} R _inst_1 a)) (Neg.neg.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNeg.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.im.{u1} R _inst_1 a))
+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.im_star Quaternion.im_starₓ'. -/
 @[simp]
 theorem im_star : star a.im = -a.im :=
@@ -2249,10 +2150,7 @@ theorem im_star : star a.im = -a.im :=
 #align quaternion.im_star Quaternion.im_star
 
 /- warning: quaternion.star_smul -> Quaternion.star_smul is a dubious translation:
-lean 3 declaration is
-  forall {S : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] [_inst_2 : Monoid.{u1} S] [_inst_3 : DistribMulAction.{u1, u2} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1)))))] (s : S) (a : Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))), Eq.{succ u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (Star.star.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (InvolutiveStar.toHasStar.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (StarAddMonoid.toHasInvolutiveStar.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} 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(Quaternion.ring.{u2} R _inst_1)))))) (StarRing.toStarAddMonoid.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (Ring.toNonUnitalRing.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (Quaternion.ring.{u2} R _inst_1))) (Quaternion.starRing.{u2} R _inst_1)))) (SMul.smul.{u1, u2} S (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (Quaternion.hasSmul.{u1, u2} S R _inst_1 (SMulZeroClass.toHasSmul.{u1, u2} S R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (DistribSMul.toSmulZeroClass.{u1, u2} S R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, u2} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) _inst_3)))) s a)) (SMul.smul.{u1, u2} S (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (Quaternion.hasSmul.{u1, u2} S R _inst_1 (SMulZeroClass.toHasSmul.{u1, u2} S R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (DistribSMul.toSmulZeroClass.{u1, u2} S R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, u2} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) _inst_3)))) s (Star.star.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (InvolutiveStar.toHasStar.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (StarAddMonoid.toHasInvolutiveStar.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (Ring.toNonUnitalRing.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (Quaternion.ring.{u2} R _inst_1)))))) (StarRing.toStarAddMonoid.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (Ring.toNonUnitalRing.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (Quaternion.ring.{u2} R _inst_1))) (Quaternion.starRing.{u2} R _inst_1)))) a))
-but is expected to have type
-  forall {S : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Monoid.{u2} S] [_inst_3 : DistribMulAction.{u2, u1} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))] (s : S) (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Star.star.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instStarQuaternionToOneToSemiringToCommSemiringToNegToRing.{u1} R _inst_1) (HSMul.hSMul.{u2, u1, u1} S (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSMul.{u2, u1} S (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instSMulQuaternionToOneToSemiringToCommSemiringToNegToRing.{u2, u1} S R _inst_1 (SMulZeroClass.toSMul.{u2, u1} S R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (DistribSMul.toSMulZeroClass.{u2, u1} S R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (DistribMulAction.toDistribSMul.{u2, u1} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3))))) s a)) (HSMul.hSMul.{u2, u1, u1} S (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSMul.{u2, u1} S (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instSMulQuaternionToOneToSemiringToCommSemiringToNegToRing.{u2, u1} S R _inst_1 (SMulZeroClass.toSMul.{u2, u1} S R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (DistribSMul.toSMulZeroClass.{u2, u1} S R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (DistribMulAction.toDistribSMul.{u2, u1} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3))))) s (Star.star.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instStarQuaternionToOneToSemiringToCommSemiringToNegToRing.{u1} R _inst_1) a))
+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.star_smul Quaternion.star_smulₓ'. -/
 @[simp]
 theorem star_smul [Monoid S] [DistribMulAction S R] (s : S) (a : ℍ[R]) :
@@ -2285,10 +2183,7 @@ section CharZero
 variable [NoZeroDivisors R] [CharZero R]
 
 /- warning: quaternion.star_eq_self -> Quaternion.star_eq_self is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))] [_inst_3 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))] {a : Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))}, Iff (Eq.{succ u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Star.star.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (InvolutiveStar.toHasStar.{u1} (Quaternion.{u1} R 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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.star_eq_self Quaternion.star_eq_selfₓ'. -/
 @[simp]
 theorem star_eq_self {a : ℍ[R]} : star a = a ↔ a = a.re :=
@@ -2296,10 +2191,7 @@ theorem star_eq_self {a : ℍ[R]} : star a = a ↔ a = a.re :=
 #align quaternion.star_eq_self Quaternion.star_eq_self
 
 /- warning: quaternion.star_eq_neg -> Quaternion.star_eq_neg is a dubious translation:
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-but is expected to have type
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.star_eq_neg Quaternion.star_eq_negₓ'. -/
 @[simp]
 theorem star_eq_neg {a : ℍ[R]} : star a = -a ↔ a.re = 0 :=
@@ -2309,20 +2201,14 @@ theorem star_eq_neg {a : ℍ[R]} : star a = -a ↔ a.re = 0 :=
 end CharZero
 
 /- warning: quaternion.star_mul_eq_coe -> Quaternion.star_mul_eq_coe is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.star_mul_eq_coe Quaternion.star_mul_eq_coeₓ'. -/
 theorem star_mul_eq_coe : star a * a = (star a * a).re :=
   a.star_mul_eq_coe
 #align quaternion.star_mul_eq_coe Quaternion.star_mul_eq_coe
 
 /- warning: quaternion.mul_star_eq_coe -> Quaternion.mul_star_eq_coe is a dubious translation:
-lean 3 declaration is
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R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (instHMul.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Distrib.toHasMul.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toDistrib.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) a (Star.star.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (InvolutiveStar.toHasStar.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (StarAddMonoid.toHasInvolutiveStar.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.starRing.{u1} R _inst_1)))) a)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HasLiftT.mk.{succ u1, succ u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CoeTCₓ.coe.{succ u1, succ u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.hasCoeT.{u1} R _inst_1))) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (HMul.hMul.{u1, u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (instHMul.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Distrib.toHasMul.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toDistrib.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) a (Star.star.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (InvolutiveStar.toHasStar.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (StarAddMonoid.toHasInvolutiveStar.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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-but is expected to have type
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.mul_star_eq_coe Quaternion.mul_star_eq_coeₓ'. -/
 theorem mul_star_eq_coe : a * star a = (a * star a).re :=
   a.mul_star_eq_coe
@@ -2342,10 +2228,7 @@ def starAe : ℍ[R] ≃ₐ[R] ℍ[R]ᵐᵒᵖ :=
 #align quaternion.star_ae Quaternion.starAe
 
 /- warning: quaternion.coe_star_ae -> Quaternion.coe_starAe is a dubious translation:
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-but is expected to have type
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(CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (_x : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R 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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.coe_star_ae Quaternion.coe_starAeₓ'. -/
 @[simp]
 theorem coe_starAe : ⇑(starAe : ℍ[R] ≃ₐ[R] ℍ[R]ᵐᵒᵖ) = op ∘ star :=
@@ -2371,20 +2254,14 @@ def normSq : ℍ[R] →*₀ R where
 #align quaternion.norm_sq Quaternion.normSq
 
 /- warning: quaternion.norm_sq_def -> Quaternion.normSq_def is a dubious translation:
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-but is expected to have type
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R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instStarQuaternionToOneToSemiringToCommSemiringToNegToRing.{u1} R _inst_1) a)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_def Quaternion.normSq_defₓ'. -/
 theorem normSq_def : normSq a = (a * star a).re :=
   rfl
 #align quaternion.norm_sq_def Quaternion.normSq_def
 
 /- warning: quaternion.norm_sq_def' -> Quaternion.normSq_def' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_def' Quaternion.normSq_def'ₓ'. -/
 theorem normSq_def' : normSq a = a.1 ^ 2 + a.2 ^ 2 + a.3 ^ 2 + a.4 ^ 2 := by
   simp only [norm_sq_def, sq, mul_neg, sub_neg_eq_add, mul_re, star_re, star_im_i, star_im_j,
@@ -2392,108 +2269,75 @@ theorem normSq_def' : normSq a = a.1 ^ 2 + a.2 ^ 2 + a.3 ^ 2 + a.4 ^ 2 := by
 #align quaternion.norm_sq_def' Quaternion.normSq_def'
 
 /- warning: quaternion.norm_sq_coe -> Quaternion.normSq_coe is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_coe Quaternion.normSq_coeₓ'. -/
 theorem normSq_coe : normSq (x : ℍ[R]) = x ^ 2 := by
   rw [norm_sq_def, star_coe, ← coe_mul, coe_re, sq]
 #align quaternion.norm_sq_coe Quaternion.normSq_coe
 
 /- warning: quaternion.norm_sq_star -> Quaternion.normSq_star is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Quaternion.normSq.{u1} R _inst_1) (Star.star.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (InvolutiveStar.toHasStar.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} 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(StarRing.toStarAddMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.starRing.{u1} R _inst_1)))) a)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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-but is expected to have type
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_star Quaternion.normSq_starₓ'. -/
 @[simp]
 theorem normSq_star : normSq (star a) = normSq a := by simp [norm_sq_def']
 #align quaternion.norm_sq_star Quaternion.normSq_star
 
 /- warning: quaternion.norm_sq_nat_cast -> Quaternion.normSq_nat_cast is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_nat_cast Quaternion.normSq_nat_castₓ'. -/
 @[norm_cast]
 theorem normSq_nat_cast (n : ℕ) : normSq (n : ℍ[R]) = n ^ 2 := by rw [← coe_nat_cast, norm_sq_coe]
 #align quaternion.norm_sq_nat_cast Quaternion.normSq_nat_cast
 
 /- warning: quaternion.norm_sq_int_cast -> Quaternion.normSq_int_cast is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Quaternion.normSq.{u1} R _inst_1) (Int.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toIntCast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) z)) (HPow.hPow.{u1, 0, u1} R Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (Int.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toIntCast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) z)) (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Int.cast.{u1} R (Ring.toIntCast.{u1} R (CommRing.toRing.{u1} R _inst_1)) z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_int_cast Quaternion.normSq_int_castₓ'. -/
 @[norm_cast]
 theorem normSq_int_cast (z : ℤ) : normSq (z : ℍ[R]) = z ^ 2 := by rw [← coe_int_cast, norm_sq_coe]
 #align quaternion.norm_sq_int_cast Quaternion.normSq_int_cast
 
 /- warning: quaternion.norm_sq_neg -> Quaternion.normSq_neg is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_neg Quaternion.normSq_negₓ'. -/
 @[simp]
 theorem normSq_neg : normSq (-a) = normSq a := by simp only [norm_sq_def, star_neg, neg_mul_neg]
 #align quaternion.norm_sq_neg Quaternion.normSq_neg
 
 /- warning: quaternion.self_mul_star -> Quaternion.self_mul_star is a dubious translation:
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(AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R 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(NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Quaternion.normSq.{u1} R _inst_1) a))
-but is expected to have type
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.self_mul_star Quaternion.self_mul_starₓ'. -/
 theorem self_mul_star : a * star a = normSq a := by rw [mul_star_eq_coe, norm_sq_def]
 #align quaternion.self_mul_star Quaternion.self_mul_star
 
 /- warning: quaternion.star_mul_self -> Quaternion.star_mul_self is a dubious translation:
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(NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Quaternion.normSq.{u1} R _inst_1) a))
-but is expected to have type
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.star_mul_self Quaternion.star_mul_selfₓ'. -/
 theorem star_mul_self : star a * a = normSq a := by rw [star_comm_self', self_mul_star]
 #align quaternion.star_mul_self Quaternion.star_mul_self
 
 /- warning: quaternion.im_sq -> Quaternion.im_sq is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.im_sq Quaternion.im_sqₓ'. -/
 theorem im_sq : a.im ^ 2 = -normSq a.im := by
   simp_rw [sq, ← star_mul_self, im_star, neg_mul, neg_neg]
 #align quaternion.im_sq Quaternion.im_sq
 
 /- warning: quaternion.coe_norm_sq_add -> Quaternion.coe_normSq_add is a dubious translation:
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(AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> R) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Quaternion.normSq.{u1} R _inst_1) b)))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (b : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) _inst_1))) (Quaternion.coe.{u1} ((fun 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_inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (_x : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b))) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) b) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) b) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) b) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) b) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) b) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) b) _inst_1))) (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (instHAdd.{u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Quaternion.instRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (instHAdd.{u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Quaternion.instRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) 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(CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (instHAdd.{u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} 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R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun 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(NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R 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(CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Quaternion.normSq.{u1} R _inst_1) a)) (HMul.hMul.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) a (Star.star.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instStarQuaternionToOneToSemiringToCommSemiringToNegToRing.{u1} R _inst_1) b))) (HMul.hMul.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) b (Star.star.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instStarQuaternionToOneToSemiringToCommSemiringToNegToRing.{u1} R _inst_1) a))) (Quaternion.coe.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) b) _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (_x : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (MulOneClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Quaternion.normSq.{u1} R _inst_1) b)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.coe_norm_sq_add Quaternion.coe_normSq_addₓ'. -/
 theorem coe_normSq_add : (normSq (a + b) : ℍ[R]) = normSq a + a * star b + b * star a + normSq b :=
   by simp [← self_mul_star, mul_add, add_mul, add_assoc]
 #align quaternion.coe_norm_sq_add Quaternion.coe_normSq_add
 
 /- warning: quaternion.norm_sq_smul -> Quaternion.normSq_smul is a dubious translation:
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(CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Quaternion.normSq.{u1} R _inst_1) q))
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_smul Quaternion.normSq_smulₓ'. -/
 theorem normSq_smul (r : R) (q : ℍ[R]) : normSq (r • q) = r ^ 2 * normSq q := by
   simp_rw [norm_sq_def, star_smul, smul_mul_smul, smul_re, sq, smul_eq_mul]
 #align quaternion.norm_sq_smul Quaternion.normSq_smul
 
 /- warning: quaternion.norm_sq_add -> Quaternion.normSq_add is a dubious translation:
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(Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> R) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) R 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(AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (instHAdd.{u1} 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(AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R 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(AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R 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R _inst_1))))) (Quaternion.normSq.{u1} R _inst_1) b)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (OfNat.ofNat.{u1} R 2 (OfNat.mk.{u1} R 2 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.starRing.{u1} R _inst_1)))) b)))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (b : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (_x : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (MulOneClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Quaternion.normSq.{u1} R _inst_1) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Distrib.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (NonUnitalNonAssocSemiring.toDistrib.{u1} ((fun 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(CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) b) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R 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(Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (MulOneClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Quaternion.normSq.{u1} R _inst_1) b)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) _inst_1))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) 2 (instOfNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) 2 (Semiring.toNatCast.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} 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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_add Quaternion.normSq_addₓ'. -/
 theorem normSq_add (a b : ℍ[R]) : normSq (a + b) = normSq a + normSq b + 2 * (a * star b).re :=
   calc
@@ -2516,10 +2360,7 @@ section LinearOrderedCommRing
 variable [LinearOrderedCommRing R] {a : ℍ[R]}
 
 /- warning: quaternion.norm_sq_eq_zero -> Quaternion.normSq_eq_zero is a dubious translation:
-lean 3 declaration is
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(AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (Quaternion.ring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : LinearOrderedCommRing.{u1} R] {a : Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))}, Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (fun (_x : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R 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(Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (MulOneClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) 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(LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))))) (Quaternion.normSq.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))) a) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (IsDomain.toCancelCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (StrictOrderedCommSemiring.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1))) (LinearOrderedRing.isDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1)))))))) (Eq.{succ u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) a (OfNat.ofNat.{u1} (Quaternion.{u1} R 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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_eq_zero Quaternion.normSq_eq_zeroₓ'. -/
 @[simp]
 theorem normSq_eq_zero : normSq a = 0 ↔ a = 0 :=
@@ -2531,20 +2372,14 @@ theorem normSq_eq_zero : normSq a = 0 ↔ a = 0 :=
 #align quaternion.norm_sq_eq_zero Quaternion.normSq_eq_zero
 
 /- warning: quaternion.norm_sq_ne_zero -> Quaternion.normSq_ne_zero is a dubious translation:
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(AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (Quaternion.ring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : LinearOrderedCommRing.{u1} R] {a : Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))}, Iff (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (fun (_x : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R 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(Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (MulOneClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) 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(StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_ne_zero Quaternion.normSq_ne_zeroₓ'. -/
 theorem normSq_ne_zero : normSq a ≠ 0 ↔ a ≠ 0 :=
   not_congr normSq_eq_zero
 #align quaternion.norm_sq_ne_zero Quaternion.normSq_ne_zero
 
 /- warning: quaternion.norm_sq_nonneg -> Quaternion.normSq_nonneg is a dubious translation:
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-but is expected to have type
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(StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R 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(LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1))) (LinearOrderedRing.isDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (MulOneClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R 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R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R 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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_nonneg Quaternion.normSq_nonnegₓ'. -/
 @[simp]
 theorem normSq_nonneg : 0 ≤ normSq a := by
@@ -2553,10 +2388,7 @@ theorem normSq_nonneg : 0 ≤ normSq a := by
 #align quaternion.norm_sq_nonneg Quaternion.normSq_nonneg
 
 /- warning: quaternion.norm_sq_le_zero -> Quaternion.normSq_le_zero is a dubious translation:
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(AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (Quaternion.ring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : LinearOrderedCommRing.{u1} R] {a : Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))}, Iff (LE.le.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (StrictOrderedRing.toPartialOrder.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R 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(LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R 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_inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))))) (Quaternion.normSq.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))) a) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (IsDomain.toCancelCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (StrictOrderedCommSemiring.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1))) (LinearOrderedRing.isDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1)))))))) (Eq.{succ u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) a (OfNat.ofNat.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) 0 (Zero.toOfNat0.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_le_zero Quaternion.normSq_le_zeroₓ'. -/
 @[simp]
 theorem normSq_le_zero : normSq a ≤ 0 ↔ a = 0 := by
@@ -2575,10 +2407,7 @@ instance : IsDomain ℍ[R] :=
   NoZeroDivisors.to_isDomain _
 
 /- warning: quaternion.sq_eq_norm_sq -> Quaternion.sq_eq_normSq is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : LinearOrderedCommRing.{u1} R] {a : Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))}, Iff (Eq.{succ u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (HPow.hPow.{u1, 0, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) Nat (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (instHPow.{u1, 0} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) Nat (Monoid.Pow.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (Ring.toMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (Quaternion.ring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) a (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (HasLiftT.mk.{succ u1, succ u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (CoeTCₓ.coe.{succ u1, succ u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (Quaternion.hasCoeT.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (Quaternion.ring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (Quaternion.ring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) => (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) -> R) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (Quaternion.ring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Quaternion.normSq.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))) a))) (Eq.{succ u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) a ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (HasLiftT.mk.{succ u1, succ u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) 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-but is expected to have type
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R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R 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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.sq_eq_norm_sq Quaternion.sq_eq_normSqₓ'. -/
 theorem sq_eq_normSq : a ^ 2 = normSq a ↔ a = a.re :=
   by
@@ -2589,10 +2418,7 @@ theorem sq_eq_normSq : a ^ 2 = normSq a ↔ a = a.re :=
 #align quaternion.sq_eq_norm_sq Quaternion.sq_eq_normSq
 
 /- warning: quaternion.sq_eq_neg_norm_sq -> Quaternion.sq_eq_neg_normSq is a dubious translation:
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-but is expected to have type
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(x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R 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(StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1))))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (StrictOrderedCommRing.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1))))) (HPow.hPow.{u1, 0, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) Nat (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (StrictOrderedCommRing.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1))))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (StrictOrderedCommRing.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1))))) (instHPow.{u1, 0} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) Nat (Monoid.Pow.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) a (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Neg.neg.{u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (StrictOrderedCommRing.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1))))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (StrictOrderedCommRing.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1))))) (Ring.toNeg.{u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (StrictOrderedCommRing.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1))))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R 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((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (StrictOrderedCommRing.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1)))) (Quaternion.coe.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (StrictOrderedCommRing.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.sq_eq_neg_norm_sq Quaternion.sq_eq_neg_normSqₓ'. -/
 theorem sq_eq_neg_normSq : a ^ 2 = -normSq a ↔ a.re = 0 :=
   by
@@ -2634,10 +2460,7 @@ theorem coe_inv (x : R) : ((x⁻¹ : R) : ℍ[R]) = x⁻¹ :=
 #align quaternion.coe_inv Quaternion.coe_inv
 
 /- warning: quaternion.coe_div -> Quaternion.coe_div is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.coe_div Quaternion.coe_divₓ'. -/
 @[norm_cast, simp]
 theorem coe_div (x y : R) : ((x / y : R) : ℍ[R]) = x / y :=
@@ -2645,10 +2468,7 @@ theorem coe_div (x y : R) : ((x / y : R) : ℍ[R]) = x / y :=
 #align quaternion.coe_div Quaternion.coe_div
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.coe_zpow Quaternion.coe_zpowₓ'. -/
 @[norm_cast, simp]
 theorem coe_zpow (x : R) (z : ℤ) : ((x ^ z : R) : ℍ[R]) = x ^ z :=
@@ -2710,10 +2530,7 @@ theorem rat_cast_imK (q : ℚ) : (q : ℍ[R]).imK = 0 :=
 #align quaternion.rat_cast_im_k Quaternion.rat_cast_imK
 
 /- warning: quaternion.rat_cast_im -> Quaternion.rat_cast_im is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.rat_cast_im Quaternion.rat_cast_imₓ'. -/
 @[simp, norm_cast]
 theorem rat_cast_im (q : ℚ) : (q : ℍ[R]).im = 0 :=
@@ -2732,10 +2549,7 @@ theorem coe_rat_cast (q : ℚ) : ↑(q : R) = (q : ℍ[R]) :=
 #align quaternion.coe_rat_cast Quaternion.coe_rat_cast
 
 /- warning: quaternion.norm_sq_inv -> Quaternion.normSq_inv is a dubious translation:
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(Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) => (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) -> R) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.normSq.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Inv.inv.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.hasInv.{u1} R _inst_1) a)) (Inv.inv.{u1} R (DivInvMonoid.toHasInv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) => (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) -> R) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.normSq.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) a))
-but is expected to have type
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(LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Inv.inv.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instInv.{u1} R _inst_1) a)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} 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(LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (fun (_x : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))))) (Quaternion.normSq.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Inv.inv.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instInv.{u1} R _inst_1) a)) (Inv.inv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) a) (LinearOrderedField.toInv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) a) _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (fun (_x : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (MulOneClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R 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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_inv Quaternion.normSq_invₓ'. -/
 @[simp]
 theorem normSq_inv : normSq a⁻¹ = (normSq a)⁻¹ :=
@@ -2743,10 +2557,7 @@ theorem normSq_inv : normSq a⁻¹ = (normSq a)⁻¹ :=
 #align quaternion.norm_sq_inv Quaternion.normSq_inv
 
 /- warning: quaternion.norm_sq_div -> Quaternion.normSq_div is a dubious translation:
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(EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) => (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) -> R) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.normSq.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (HDiv.hDiv.{u1, u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (instHDiv.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (DivInvMonoid.toHasDiv.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (DivisionRing.toDivInvMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.divisionRing.{u1} R _inst_1)))) a b)) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) => (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) -> R) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.normSq.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) a) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R 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(LinearOrderedField.toField.{u1} R _inst_1)))))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} 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(CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) => (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) -> R) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} 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(LinearOrderedField.toField.{u1} R _inst_1)))) b))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (b : Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (HDiv.hDiv.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (instHDiv.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (DivisionRing.toDiv.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) 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(LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))))) (Quaternion.normSq.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (HDiv.hDiv.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (instHDiv.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (DivisionRing.toDiv.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instDivisionRingQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1))) a b)) (HDiv.hDiv.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) b) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) a) (instHDiv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) a) (LinearOrderedField.toDiv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) a) _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (fun (_x : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (MulOneClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))))) (Quaternion.normSq.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (fun (_x : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R 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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_div Quaternion.normSq_divₓ'. -/
 @[simp]
 theorem normSq_div : normSq (a / b) = normSq a / normSq b :=
@@ -2754,10 +2565,7 @@ theorem normSq_div : normSq (a / b) = normSq a / normSq b :=
 #align quaternion.norm_sq_div Quaternion.normSq_div
 
 /- warning: quaternion.norm_sq_zpow -> Quaternion.normSq_zpow is a dubious translation:
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(LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) => (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) -> R) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.normSq.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (HPow.hPow.{u1, 0, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) Int (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (instHPow.{u1, 0} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) Int (DivInvMonoid.Pow.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (DivisionRing.toDivInvMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.divisionRing.{u1} R _inst_1)))) a z)) (HPow.hPow.{u1, 0, u1} R Int R (instHPow.{u1, 0} R Int (DivInvMonoid.Pow.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) => (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} 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(Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.normSq.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) a) z)
-but is expected to have type
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(StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (instHPow.{u1, 0} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) Int (DivInvMonoid.Pow.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R 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(Quaternion.instDivisionRingQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1)))) a z)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R 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(EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (fun (_x : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (MulOneClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))))) (Quaternion.normSq.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (HPow.hPow.{u1, 0, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) Int (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (instHPow.{u1, 0} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) Int (DivInvMonoid.Pow.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (DivisionRing.toDivInvMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instDivisionRingQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1)))) a z)) (HPow.hPow.{u1, 0, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) a) Int ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) a) (instHPow.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) a) Int (DivInvMonoid.Pow.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) a) (DivisionRing.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) a) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) a) (LinearOrderedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) a) _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (fun (_x : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (MulOneClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} 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(NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_zpow Quaternion.normSq_zpowₓ'. -/
 @[simp]
 theorem normSq_zpow (z : ℤ) : normSq (a ^ z) = normSq a ^ z :=
@@ -2765,10 +2573,7 @@ theorem normSq_zpow (z : ℤ) : normSq (a ^ z) = normSq a ^ z :=
 #align quaternion.norm_sq_zpow Quaternion.normSq_zpow
 
 /- warning: quaternion.norm_sq_rat_cast -> Quaternion.normSq_rat_cast is a dubious translation:
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-but is expected to have type
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(Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (LinearOrderedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) _inst_1)))))) (Quaternion.coe.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (LinearOrderedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (fun (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) 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(CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))))) (Quaternion.normSq.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q))) (HPow.hPow.{u1, 0, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) Nat (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (LinearOrderedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) _inst_1)))))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (LinearOrderedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) _inst_1)))))) (instHPow.{u1, 0} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) Nat (Monoid.Pow.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (DivisionSemiring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (DivisionRing.toDivisionSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instDivisionRingQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1))))))) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_rat_cast Quaternion.normSq_rat_castₓ'. -/
 @[norm_cast]
 theorem normSq_rat_cast (q : ℚ) : normSq (q : ℍ[R]) = q ^ 2 := by rw [← coe_rat_cast, norm_sq_coe]
@@ -2788,7 +2593,6 @@ variable {R : Type _} (c₁ c₂ : R)
 
 private theorem pow_four [Infinite R] : (#R) ^ 4 = (#R) :=
   power_nat_eq (aleph0_le_mk R) <| by simp
-#align cardinal.pow_four cardinal.pow_four
 
 #print Cardinal.mk_quaternionAlgebra /-
 /-- The cardinality of a quaternion algebra, as a type. -/

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

@@ -773,7 +773,7 @@ def linearEquivTuple : ℍ[R,c₁,c₂] ≃ₗ[R] Fin 4 → R :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (c₁ : R) (c₂ : R), Eq.{succ u1} ((QuaternionAlgebra.{u1} R c₁ c₂) -> (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> R) (coeFn.{succ u1, succ u1} (LinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (QuaternionAlgebra.linearEquivTuple._proof_1.{u1} R _inst_1) (QuaternionAlgebra.linearEquivTuple._proof_2.{u1} R _inst_1) (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> R) (AddCommGroup.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.addCommGroup.{u1} R _inst_1 c₁ c₂)) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) => AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.ring.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.algebra.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.Function.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (QuaternionAlgebra.linearEquivTuple._proof_1.{u1} R _inst_1) (QuaternionAlgebra.linearEquivTuple._proof_2.{u1} R _inst_1) (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> R) (AddCommGroup.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.addCommGroup.{u1} R _inst_1 c₁ c₂)) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) => AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.ring.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.algebra.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.Function.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (QuaternionAlgebra.{u1} R c₁ c₂) -> (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> R) (LinearEquiv.hasCoeToFun.{u1, u1, u1, u1} R R (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> R) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.addCommGroup.{u1} R _inst_1 c₁ c₂)) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) => AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.ring.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.algebra.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.Function.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (QuaternionAlgebra.linearEquivTuple._proof_1.{u1} R _inst_1) (QuaternionAlgebra.linearEquivTuple._proof_2.{u1} R _inst_1)) (QuaternionAlgebra.linearEquivTuple.{u1} R _inst_1 c₁ c₂)) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> R)) (fun (_x : Equiv.{succ u1, succ u1} (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> R)) => (QuaternionAlgebra.{u1} R c₁ c₂) -> (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> R) (Equiv.hasCoeToFun.{succ u1, succ u1} (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> R)) (QuaternionAlgebra.equivTuple.{u1} R c₁ c₂))
 but is expected to have type
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(QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (QuaternionAlgebra.{u1} R c₁ c₂) (fun (_x : QuaternionAlgebra.{u1} R c₁ c₂) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : QuaternionAlgebra.{u1} R c₁ c₂) => (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (SMulZeroClass.toSMul.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (AddMonoid.toZero.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (AddMonoid.toAddZeroClass.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (Module.toDistribMulAction.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u1} R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (AddMonoid.toZero.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (AddMonoid.toAddZeroClass.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R ((Fin 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(NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (AddCommMonoid.toAddMonoid.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u1, u1, u1} R R (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u1, u1} R R (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (QuaternionAlgebra.linearEquivTuple.{u1} R _inst_1 c₁ c₂)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R)) (QuaternionAlgebra.{u1} R c₁ c₂) (fun (_x : QuaternionAlgebra.{u1} R c₁ c₂) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : QuaternionAlgebra.{u1} R c₁ c₂) => (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R)) (QuaternionAlgebra.equivTuple.{u1} R c₁ c₂))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (c₁ : R) (c₂ : R), Eq.{succ u1} (forall (ᾰ : QuaternionAlgebra.{u1} R c₁ c₂), (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : QuaternionAlgebra.{u1} R c₁ c₂) => (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) ᾰ) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (QuaternionAlgebra.{u1} R c₁ c₂) (fun (_x : QuaternionAlgebra.{u1} R c₁ c₂) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : QuaternionAlgebra.{u1} R c₁ c₂) => (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (SMulZeroClass.toSMul.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (AddMonoid.toZero.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (AddMonoid.toAddZeroClass.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (Module.toDistribMulAction.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u1} R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (AddMonoid.toZero.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (AddMonoid.toAddZeroClass.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (AddCommMonoid.toAddMonoid.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u1, u1, u1} R R (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u1, u1} R R (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (QuaternionAlgebra.linearEquivTuple.{u1} R _inst_1 c₁ c₂)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R)) (QuaternionAlgebra.{u1} R c₁ c₂) (fun (_x : QuaternionAlgebra.{u1} R c₁ c₂) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : QuaternionAlgebra.{u1} R c₁ c₂) => (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R)) (QuaternionAlgebra.equivTuple.{u1} R c₁ c₂))
 Case conversion may be inaccurate. Consider using '#align quaternion_algebra.coe_linear_equiv_tuple QuaternionAlgebra.coe_linearEquivTupleₓ'. -/
 @[simp]
 theorem coe_linearEquivTuple : ⇑(linearEquivTuple c₁ c₂) = equivTuple c₁ c₂ :=
@@ -784,7 +784,7 @@ theorem coe_linearEquivTuple : ⇑(linearEquivTuple c₁ c₂) = equivTuple c₁
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (c₁ : R) (c₂ : R), Eq.{succ u1} (((Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> R) -> (QuaternionAlgebra.{u1} R c₁ c₂)) (coeFn.{succ u1, succ u1} (LinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (QuaternionAlgebra.linearEquivTuple._proof_2.{u1} R _inst_1) (QuaternionAlgebra.linearEquivTuple._proof_1.{u1} R _inst_1) ((Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> R) (QuaternionAlgebra.{u1} R c₁ c₂) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) => AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.addCommGroup.{u1} R _inst_1 c₁ c₂)) (Pi.Function.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.ring.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.algebra.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (_x : LinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (QuaternionAlgebra.linearEquivTuple._proof_2.{u1} R _inst_1) (QuaternionAlgebra.linearEquivTuple._proof_1.{u1} R _inst_1) ((Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> R) (QuaternionAlgebra.{u1} R c₁ c₂) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) => AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.addCommGroup.{u1} R _inst_1 c₁ c₂)) (Pi.Function.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.ring.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.algebra.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => ((Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> R) -> (QuaternionAlgebra.{u1} R c₁ c₂)) (LinearEquiv.hasCoeToFun.{u1, u1, u1, u1} R R ((Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> R) (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) => AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.addCommGroup.{u1} R _inst_1 c₁ c₂)) (Pi.Function.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.ring.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.algebra.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (QuaternionAlgebra.linearEquivTuple._proof_2.{u1} R _inst_1) (QuaternionAlgebra.linearEquivTuple._proof_1.{u1} R _inst_1)) (LinearEquiv.symm.{u1, u1, u1, u1} R R (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> R) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.addCommGroup.{u1} R _inst_1 c₁ c₂)) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) => AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.ring.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.algebra.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.Function.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (QuaternionAlgebra.linearEquivTuple._proof_1.{u1} R _inst_1) (QuaternionAlgebra.linearEquivTuple._proof_2.{u1} R _inst_1) (QuaternionAlgebra.linearEquivTuple.{u1} R _inst_1 c₁ c₂))) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} ((Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> R) (QuaternionAlgebra.{u1} R c₁ c₂)) (fun (_x : Equiv.{succ u1, succ u1} ((Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> R) (QuaternionAlgebra.{u1} R c₁ c₂)) => ((Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> R) -> (QuaternionAlgebra.{u1} R c₁ c₂)) (Equiv.hasCoeToFun.{succ u1, succ u1} ((Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> R) (QuaternionAlgebra.{u1} R c₁ c₂)) (Equiv.symm.{succ u1, succ u1} (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> R) (QuaternionAlgebra.equivTuple.{u1} R c₁ c₂)))
 but is expected to have type
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R _inst_1))))) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (fun (_x : (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) => QuaternionAlgebra.{u1} R c₁ c₂) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((Fin (OfNat.ofNat.{0} Nat 4 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(instOfNatNat 4))) -> R) (QuaternionAlgebra.{u1} R c₁ c₂) (SMulZeroClass.toSMul.{u1, u1} R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (AddMonoid.toZero.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (AddMonoid.toAddZeroClass.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin (OfNat.ofNat.{0} Nat 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(OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (AddMonoid.toZero.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (AddMonoid.toAddZeroClass.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (Module.toDistribMulAction.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((Fin 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R _inst_1))))) R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (QuaternionAlgebra.{u1} R c₁ c₂) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (Module.toDistribMulAction.{u1, u1} R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u1, u1} R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (QuaternionAlgebra.{u1} R c₁ c₂) (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (QuaternionAlgebra.{u1} R c₁ c₂) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u1, u1, u1} R R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (QuaternionAlgebra.{u1} R c₁ c₂) (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u1, u1} R R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (QuaternionAlgebra.{u1} R c₁ c₂) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (LinearEquiv.symm.{u1, u1, u1, u1} R R (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (QuaternionAlgebra.linearEquivTuple.{u1} R _inst_1 c₁ c₂))) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (QuaternionAlgebra.{u1} R c₁ c₂)) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (fun (_x : (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) => QuaternionAlgebra.{u1} R c₁ c₂) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (QuaternionAlgebra.{u1} R c₁ c₂)) (Equiv.symm.{succ u1, succ u1} (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (QuaternionAlgebra.equivTuple.{u1} R c₁ c₂)))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (c₁ : R) (c₂ : R), Eq.{succ u1} (forall (ᾰ : (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R), (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) => QuaternionAlgebra.{u1} R c₁ c₂) ᾰ) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (QuaternionAlgebra.{u1} R c₁ c₂) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (fun (_x : (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) => QuaternionAlgebra.{u1} R c₁ c₂) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((Fin (OfNat.ofNat.{0} Nat 4 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c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (AddMonoid.toAddZeroClass.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) 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(QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((Fin 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R _inst_1))))) R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (QuaternionAlgebra.{u1} R c₁ c₂) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 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(QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u1, u1} R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (QuaternionAlgebra.{u1} R c₁ c₂) (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (QuaternionAlgebra.{u1} R c₁ c₂) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u1, u1, u1} R R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (QuaternionAlgebra.{u1} R c₁ c₂) (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (QuaternionAlgebra.{u1} R c₁ c₂) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u1, u1} R R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (QuaternionAlgebra.{u1} R c₁ c₂) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (LinearEquiv.symm.{u1, u1, u1, u1} R R (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (QuaternionAlgebra.linearEquivTuple.{u1} R _inst_1 c₁ c₂))) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (QuaternionAlgebra.{u1} R c₁ c₂)) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (fun (_x : (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) => QuaternionAlgebra.{u1} R c₁ c₂) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (QuaternionAlgebra.{u1} R c₁ c₂)) (Equiv.symm.{succ u1, succ u1} (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (QuaternionAlgebra.equivTuple.{u1} R c₁ c₂)))
 Case conversion may be inaccurate. Consider using '#align quaternion_algebra.coe_linear_equiv_tuple_symm QuaternionAlgebra.coe_linearEquivTuple_symmₓ'. -/
 @[simp]
 theorem coe_linearEquivTuple_symm : ⇑(linearEquivTuple c₁ c₂).symm = (equivTuple c₁ c₂).symm :=
@@ -806,7 +806,7 @@ noncomputable def basisOneIJK : Basis (Fin 4) R ℍ[R,c₁,c₂] :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (c₁ : R) (c₂ : R) (q : QuaternionAlgebra.{u1} R c₁ c₂), Eq.{succ u1} ((Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> R) (coeFn.{succ u1, succ u1} (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (fun (_x : Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) => (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> R) (Finsupp.coeFun.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (coeFn.{succ u1, succ u1} (LinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (QuaternionAlgebra.{u1} R c₁ c₂) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.addCommGroup.{u1} R _inst_1 c₁ c₂)) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.ring.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.algebra.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (QuaternionAlgebra.{u1} R c₁ c₂) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.addCommGroup.{u1} R _inst_1 c₁ c₂)) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.ring.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.algebra.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (QuaternionAlgebra.{u1} R c₁ c₂) -> (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (LinearEquiv.hasCoeToFun.{u1, u1, u1, u1} R R (QuaternionAlgebra.{u1} R c₁ c₂) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.addCommGroup.{u1} R _inst_1 c₁ c₂)) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.ring.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.algebra.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Basis.repr.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) R (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.addCommGroup.{u1} R _inst_1 c₁ c₂)) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.ring.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.algebra.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (QuaternionAlgebra.basisOneIJK.{u1} R _inst_1 c₁ c₂)) q)) (Matrix.vecCons.{u1} R (Nat.succ (Nat.succ (Nat.succ (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))))) (QuaternionAlgebra.re.{u1} R c₁ c₂ q) (Matrix.vecCons.{u1} R (Nat.succ (Nat.succ (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (QuaternionAlgebra.imI.{u1} R c₁ c₂ q) (Matrix.vecCons.{u1} R (Nat.succ (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (QuaternionAlgebra.imJ.{u1} R c₁ c₂ q) (Matrix.vecCons.{u1} R (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) (QuaternionAlgebra.imK.{u1} R c₁ c₂ q) (Matrix.vecEmpty.{u1} R)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (c₁ : R) (c₂ : R) (q : QuaternionAlgebra.{u1} R c₁ c₂), Eq.{succ u1} (forall (ᾰ : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))), (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) ᾰ) (FunLike.coe.{succ u1, 1, succ u1} (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (_x : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) _x) (Finsupp.funLike.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (QuaternionAlgebra.{u1} R c₁ c₂) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (QuaternionAlgebra.{u1} R c₁ c₂) (fun (_x : QuaternionAlgebra.{u1} R c₁ c₂) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : QuaternionAlgebra.{u1} R c₁ c₂) => Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (QuaternionAlgebra.{u1} R c₁ c₂) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (QuaternionAlgebra.{u1} R c₁ c₂) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (AddMonoid.toZero.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (AddMonoid.toAddZeroClass.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (Module.toDistribMulAction.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u1} R (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddMonoid.toZero.{u1} (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (QuaternionAlgebra.{u1} R c₁ c₂) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (QuaternionAlgebra.{u1} R c₁ c₂) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (AddCommMonoid.toAddMonoid.{u1} (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (QuaternionAlgebra.{u1} R c₁ c₂) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u1, u1, u1} R R (QuaternionAlgebra.{u1} R c₁ c₂) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (QuaternionAlgebra.{u1} R c₁ c₂) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u1, u1} R R (QuaternionAlgebra.{u1} R c₁ c₂) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Basis.repr.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (QuaternionAlgebra.{u1} R c₁ c₂) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (QuaternionAlgebra.basisOneIJK.{u1} R _inst_1 c₁ c₂)) q)) (Matrix.vecCons.{u1} R (Nat.succ (Nat.succ (Nat.succ (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (QuaternionAlgebra.re.{u1} R c₁ c₂ q) (Matrix.vecCons.{u1} R (Nat.succ (Nat.succ (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (QuaternionAlgebra.imI.{u1} R c₁ c₂ q) (Matrix.vecCons.{u1} R (Nat.succ (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (QuaternionAlgebra.imJ.{u1} R c₁ c₂ q) (Matrix.vecCons.{u1} R (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (QuaternionAlgebra.imK.{u1} R c₁ c₂ q) (Matrix.vecEmpty.{u1} R)))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (c₁ : R) (c₂ : R) (q : QuaternionAlgebra.{u1} R c₁ c₂), Eq.{succ u1} (forall (ᾰ : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))), (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) ᾰ) (FunLike.coe.{succ u1, 1, succ u1} (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (_x : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) _x) (Finsupp.funLike.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (QuaternionAlgebra.{u1} R c₁ c₂) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Finsupp.module.{0, 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(QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (AddMonoid.toAddZeroClass.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) 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(QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u1} R (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddMonoid.toZero.{u1} (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (AddCommMonoid.toAddMonoid.{u1} (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (QuaternionAlgebra.{u1} R c₁ c₂) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u1, u1, u1} R R (QuaternionAlgebra.{u1} R c₁ c₂) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (QuaternionAlgebra.{u1} R c₁ c₂) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u1, u1} R R (QuaternionAlgebra.{u1} R c₁ c₂) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Basis.repr.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (QuaternionAlgebra.{u1} R c₁ c₂) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (QuaternionAlgebra.basisOneIJK.{u1} R _inst_1 c₁ c₂)) q)) (Matrix.vecCons.{u1} R (Nat.succ (Nat.succ (Nat.succ (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (QuaternionAlgebra.re.{u1} R c₁ c₂ q) (Matrix.vecCons.{u1} R (Nat.succ (Nat.succ (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (QuaternionAlgebra.imI.{u1} R c₁ c₂ q) (Matrix.vecCons.{u1} R (Nat.succ (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (QuaternionAlgebra.imJ.{u1} R c₁ c₂ q) (Matrix.vecCons.{u1} R (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (QuaternionAlgebra.imK.{u1} R c₁ c₂ q) (Matrix.vecEmpty.{u1} R)))))
 Case conversion may be inaccurate. Consider using '#align quaternion_algebra.coe_basis_one_i_j_k_repr QuaternionAlgebra.coe_basisOneIJK_reprₓ'. -/
 @[simp]
 theorem coe_basisOneIJK_repr (q : ℍ[R,c₁,c₂]) :
@@ -1173,7 +1173,7 @@ def starAe : ℍ[R,c₁,c₂] ≃ₐ[R] ℍ[R,c₁,c₂]ᵐᵒᵖ :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {c₁ : R} {c₂ : R}, Eq.{succ u1} ((QuaternionAlgebra.{u1} R c₁ c₂) -> (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂))) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.ring.{u1} R _inst_1 c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.ring.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.algebra.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.algebra.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.ring.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.algebra.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (_x : AlgEquiv.{u1, u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.ring.{u1} R _inst_1 c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.ring.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.algebra.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.algebra.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.ring.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.algebra.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => (QuaternionAlgebra.{u1} R c₁ c₂) -> (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.ring.{u1} R _inst_1 c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.ring.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.algebra.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.algebra.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.ring.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.algebra.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (QuaternionAlgebra.starAe.{u1} R _inst_1 c₁ c₂)) (Function.comp.{succ u1, succ u1, succ u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MulOpposite.op.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (Star.star.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.hasStar.{u1} R _inst_1 c₁ c₂)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {c₁ : R} {c₂ : R}, Eq.{succ u1} (forall (ᾰ : QuaternionAlgebra.{u1} R c₁ c₂), (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : QuaternionAlgebra.{u1} R c₁ c₂) => MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) ᾰ) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (QuaternionAlgebra.{u1} R c₁ c₂) (fun (_x : QuaternionAlgebra.{u1} R c₁ c₂) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : QuaternionAlgebra.{u1} R c₁ c₂) => MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (SMulZeroClass.toSMul.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (AddMonoid.toZero.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Semiring.toNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (AddMonoid.toAddZeroClass.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Semiring.toNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Semiring.toNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (Module.toDistribMulAction.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Semiring.toNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u1} R (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (AddMonoid.toZero.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (AddCommMonoid.toAddMonoid.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (AddMonoid.toAddZeroClass.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (AddCommMonoid.toAddMonoid.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))))) (Module.toDistribMulAction.{u1, u1} R (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (Algebra.toModule.{u1, u1} R (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Semiring.toNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (AddCommMonoid.toAddMonoid.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))))) (Module.toDistribMulAction.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Semiring.toNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (Algebra.toModule.{u1, u1} R (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Semiring.toNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Module.toDistribMulAction.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Semiring.toNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (Algebra.toModule.{u1, u1} R (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AlgEquiv.{u1, u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))))) (QuaternionAlgebra.starAe.{u1} R _inst_1 c₁ c₂)) (Function.comp.{succ u1, succ u1, succ u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MulOpposite.op.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (Star.star.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instStarQuaternionAlgebra.{u1} R _inst_1 c₁ c₂)))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {c₁ : R} {c₂ : R}, Eq.{succ u1} (forall (ᾰ : QuaternionAlgebra.{u1} R c₁ c₂), (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : QuaternionAlgebra.{u1} R c₁ c₂) => MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) ᾰ) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (QuaternionAlgebra.{u1} R c₁ c₂) (fun (_x : QuaternionAlgebra.{u1} R c₁ c₂) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : QuaternionAlgebra.{u1} R c₁ c₂) => MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (SMulZeroClass.toSMul.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (AddMonoid.toZero.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Semiring.toNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (AddMonoid.toAddZeroClass.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Semiring.toNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Semiring.toNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (Module.toDistribMulAction.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Semiring.toNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u1} R (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (AddMonoid.toZero.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (AddCommMonoid.toAddMonoid.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (AddMonoid.toAddZeroClass.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (AddCommMonoid.toAddMonoid.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))))) (Module.toDistribMulAction.{u1, u1} R (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (Algebra.toModule.{u1, u1} R (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Semiring.toNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (AddCommMonoid.toAddMonoid.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))))) (Module.toDistribMulAction.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Semiring.toNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (Algebra.toModule.{u1, u1} R (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Semiring.toNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Module.toDistribMulAction.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Semiring.toNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (Algebra.toModule.{u1, u1} R (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AlgEquiv.{u1, u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))))) (QuaternionAlgebra.starAe.{u1} R _inst_1 c₁ c₂)) (Function.comp.{succ u1, succ u1, succ u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MulOpposite.op.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (Star.star.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instStarQuaternionAlgebra.{u1} R _inst_1 c₁ c₂)))
 Case conversion may be inaccurate. Consider using '#align quaternion_algebra.coe_star_ae QuaternionAlgebra.coe_starAeₓ'. -/
 @[simp]
 theorem coe_starAe : ⇑(starAe : ℍ[R,c₁,c₂] ≃ₐ[R] _) = op ∘ star :=
@@ -2345,7 +2345,7 @@ def starAe : ℍ[R] ≃ₐ[R] ℍ[R]ᵐᵒᵖ :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R], Eq.{succ u1} ((Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (MulOpposite.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (MulOpposite.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.algebra.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (_x : AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (MulOpposite.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.algebra.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (MulOpposite.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (MulOpposite.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.algebra.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.starAe.{u1} R _inst_1)) (Function.comp.{succ u1, succ u1, succ u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (MulOpposite.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (MulOpposite.op.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Star.star.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (InvolutiveStar.toHasStar.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (StarAddMonoid.toHasInvolutiveStar.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.starRing.{u1} R _inst_1))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R], Eq.{succ u1} (forall (ᾰ : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))), (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) ᾰ) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (_x : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))))) (Quaternion.starAe.{u1} R _inst_1)) (Function.comp.{succ u1, succ u1, succ u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulOpposite.op.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Star.star.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instStarQuaternionToOneToSemiringToCommSemiringToNegToRing.{u1} R _inst_1)))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R], Eq.{succ u1} (forall (ᾰ : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))), (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) ᾰ) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (_x : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))))) (Quaternion.starAe.{u1} R _inst_1)) (Function.comp.{succ u1, succ u1, succ u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulOpposite.op.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Star.star.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instStarQuaternionToOneToSemiringToCommSemiringToNegToRing.{u1} R _inst_1)))
 Case conversion may be inaccurate. Consider using '#align quaternion.coe_star_ae Quaternion.coe_starAeₓ'. -/
 @[simp]
 theorem coe_starAe : ⇑(starAe : ℍ[R] ≃ₐ[R] ℍ[R]ᵐᵒᵖ) = op ∘ star :=

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 
 ! This file was ported from Lean 3 source module algebra.quaternion
-! leanprover-community/mathlib commit cf7a7252c1989efe5800e0b3cdfeb4228ac6b40e
+! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -18,6 +18,9 @@ import Mathbin.Tactic.RingExp
 /-!
 # Quaternions
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we define quaternions `ℍ[R]` over a commutative ring `R`, and define some
 algebraic structures on `ℍ[R]`.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/1b0a28e1c93409dbf6d69526863cd9984ef652ce

@@ -55,6 +55,7 @@ quaternion
 -/
 
 
+#print QuaternionAlgebra /-
 /- ./././Mathport/Syntax/Translate/Command.lean:429:34: infer kinds are unsupported in Lean 4: mk {} -/
 /-- Quaternion algebra over a type with fixed coefficients $a=i^2$ and $b=j^2$.
 Implemented as a structure with four fields: `re`, `im_i`, `im_j`, and `im_k`. -/
@@ -65,12 +66,14 @@ structure QuaternionAlgebra (R : Type _) (a b : R) where mk ::
   imJ : R
   imK : R
 #align quaternion_algebra QuaternionAlgebra
+-/
 
 -- mathport name: quaternion_algebra
 scoped[Quaternion] notation "ℍ[" R "," a "," b "]" => QuaternionAlgebra R a b
 
 namespace QuaternionAlgebra
 
+#print QuaternionAlgebra.equivProd /-
 /-- The equivalence between a quaternion algebra over R and R × R × R × R. -/
 @[simps]
 def equivProd {R : Type _} (c₁ c₂ : R) : ℍ[R,c₁,c₂] ≃ R × R × R × R
@@ -80,7 +83,9 @@ def equivProd {R : Type _} (c₁ c₂ : R) : ℍ[R,c₁,c₂] ≃ R × R × R ×
   left_inv := fun ⟨a₁, a₂, a₃, a₄⟩ => rfl
   right_inv := fun ⟨a₁, a₂, a₃, a₄⟩ => rfl
 #align quaternion_algebra.equiv_prod QuaternionAlgebra.equivProd
+-/
 
+#print QuaternionAlgebra.equivTuple /-
 /-- The equivalence between a quaternion algebra over `R` and `fin 4 → R`. -/
 @[simps symm_apply]
 def equivTuple {R : Type _} (c₁ c₂ : R) : ℍ[R,c₁,c₂] ≃ (Fin 4 → R)
@@ -90,76 +95,129 @@ def equivTuple {R : Type _} (c₁ c₂ : R) : ℍ[R,c₁,c₂] ≃ (Fin 4 → R)
   left_inv := fun ⟨a₁, a₂, a₃, a₄⟩ => rfl
   right_inv f := by ext ⟨_, _ | _ | _ | _ | _ | ⟨⟩⟩ <;> rfl
 #align quaternion_algebra.equiv_tuple QuaternionAlgebra.equivTuple
+-/
 
+#print QuaternionAlgebra.equivTuple_apply /-
 @[simp]
 theorem equivTuple_apply {R : Type _} (c₁ c₂ : R) (x : ℍ[R,c₁,c₂]) :
     equivTuple c₁ c₂ x = ![x.re, x.imI, x.imJ, x.imK] :=
   rfl
 #align quaternion_algebra.equiv_tuple_apply QuaternionAlgebra.equivTuple_apply
+-/
 
+#print QuaternionAlgebra.mk.eta /-
 @[simp]
 theorem mk.eta {R : Type _} {c₁ c₂} : ∀ a : ℍ[R,c₁,c₂], mk a.1 a.2 a.3 a.4 = a
   | ⟨a₁, a₂, a₃, a₄⟩ => rfl
 #align quaternion_algebra.mk.eta QuaternionAlgebra.mk.eta
+-/
 
 variable {S T R : Type _} [CommRing R] {c₁ c₂ : R} (r x y z : R) (a b c : ℍ[R,c₁,c₂])
 
+#print QuaternionAlgebra.im /-
 /-- The imaginary part of a quaternion. -/
 def im (x : ℍ[R,c₁,c₂]) : ℍ[R,c₁,c₂] :=
   ⟨0, x.imI, x.imJ, x.imK⟩
 #align quaternion_algebra.im QuaternionAlgebra.im
+-/
 
+/- warning: quaternion_algebra.im_re -> QuaternionAlgebra.im_re is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {c₁ : R} {c₂ : R} (a : QuaternionAlgebra.{u1} R c₁ c₂), Eq.{succ u1} R (QuaternionAlgebra.re.{u1} R c₁ c₂ (QuaternionAlgebra.im.{u1} R _inst_1 c₁ c₂ a)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {c₁ : R} {c₂ : R} (a : QuaternionAlgebra.{u1} R c₁ c₂), Eq.{succ u1} R (QuaternionAlgebra.re.{u1} R c₁ c₂ (QuaternionAlgebra.im.{u1} R _inst_1 c₁ c₂ a)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.im_re QuaternionAlgebra.im_reₓ'. -/
 @[simp]
 theorem im_re : a.im.re = 0 :=
   rfl
 #align quaternion_algebra.im_re QuaternionAlgebra.im_re
 
+#print QuaternionAlgebra.im_imI /-
 @[simp]
 theorem im_imI : a.im.imI = a.imI :=
   rfl
 #align quaternion_algebra.im_im_i QuaternionAlgebra.im_imI
+-/
 
+#print QuaternionAlgebra.im_imJ /-
 @[simp]
 theorem im_imJ : a.im.imJ = a.imJ :=
   rfl
 #align quaternion_algebra.im_im_j QuaternionAlgebra.im_imJ
+-/
 
+#print QuaternionAlgebra.im_imK /-
 @[simp]
 theorem im_imK : a.im.imK = a.imK :=
   rfl
 #align quaternion_algebra.im_im_k QuaternionAlgebra.im_imK
+-/
 
+#print QuaternionAlgebra.im_idem /-
 @[simp]
 theorem im_idem : a.im.im = a.im :=
   rfl
 #align quaternion_algebra.im_idem QuaternionAlgebra.im_idem
+-/
 
 instance : CoeTC R ℍ[R,c₁,c₂] :=
   ⟨fun x => ⟨x, 0, 0, 0⟩⟩
 
+#print QuaternionAlgebra.coe_re /-
 @[simp, norm_cast]
 theorem coe_re : (x : ℍ[R,c₁,c₂]).re = x :=
   rfl
 #align quaternion_algebra.coe_re QuaternionAlgebra.coe_re
+-/
 
+/- warning: quaternion_algebra.coe_im_i -> QuaternionAlgebra.coe_imI is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.coe_im_i QuaternionAlgebra.coe_imIₓ'. -/
 @[simp, norm_cast]
 theorem coe_imI : (x : ℍ[R,c₁,c₂]).imI = 0 :=
   rfl
 #align quaternion_algebra.coe_im_i QuaternionAlgebra.coe_imI
 
+/- warning: quaternion_algebra.coe_im_j -> QuaternionAlgebra.coe_imJ is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.coe_im_j QuaternionAlgebra.coe_imJₓ'. -/
 @[simp, norm_cast]
 theorem coe_imJ : (x : ℍ[R,c₁,c₂]).imJ = 0 :=
   rfl
 #align quaternion_algebra.coe_im_j QuaternionAlgebra.coe_imJ
 
+/- warning: quaternion_algebra.coe_im_k -> QuaternionAlgebra.coe_imK is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.coe_im_k QuaternionAlgebra.coe_imKₓ'. -/
 @[simp, norm_cast]
 theorem coe_imK : (x : ℍ[R,c₁,c₂]).imK = 0 :=
   rfl
 #align quaternion_algebra.coe_im_k QuaternionAlgebra.coe_imK
 
+/- warning: quaternion_algebra.coe_injective -> QuaternionAlgebra.coe_injective is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.coe_injective QuaternionAlgebra.coe_injectiveₓ'. -/
 theorem coe_injective : Function.Injective (coe : R → ℍ[R,c₁,c₂]) := fun x y h => congr_arg re h
 #align quaternion_algebra.coe_injective QuaternionAlgebra.coe_injective
 
+/- warning: quaternion_algebra.coe_inj -> QuaternionAlgebra.coe_inj is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.coe_inj QuaternionAlgebra.coe_injₓ'. -/
 @[simp]
 theorem coe_inj {x y : R} : (x : ℍ[R,c₁,c₂]) = y ↔ x = y :=
   coe_injective.eq_iff
@@ -169,6 +227,12 @@ theorem coe_inj {x y : R} : (x : ℍ[R,c₁,c₂]) = y ↔ x = y :=
 instance : Zero ℍ[R,c₁,c₂] :=
   ⟨⟨0, 0, 0, 0⟩⟩
 
+/- warning: quaternion_algebra.coe_zero -> QuaternionAlgebra.coe_zero is a dubious translation:
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 @[simp, norm_cast]
 theorem coe_zero : ((0 : R) : ℍ[R,c₁,c₂]) = 0 :=
   rfl
@@ -181,6 +245,12 @@ instance : Inhabited ℍ[R,c₁,c₂] :=
 instance : One ℍ[R,c₁,c₂] :=
   ⟨⟨1, 0, 0, 0⟩⟩
 
+/- warning: quaternion_algebra.coe_one -> QuaternionAlgebra.coe_one is a dubious translation:
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 @[simp, norm_cast]
 theorem coe_one : ((1 : R) : ℍ[R,c₁,c₂]) = 1 :=
   rfl
@@ -190,12 +260,24 @@ theorem coe_one : ((1 : R) : ℍ[R,c₁,c₂]) = 1 :=
 instance : Add ℍ[R,c₁,c₂] :=
   ⟨fun a b => ⟨a.1 + b.1, a.2 + b.2, a.3 + b.3, a.4 + b.4⟩⟩
 
+/- warning: quaternion_algebra.mk_add_mk -> QuaternionAlgebra.mk_add_mk is a dubious translation:
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 @[simp]
 theorem mk_add_mk (a₁ a₂ a₃ a₄ b₁ b₂ b₃ b₄ : R) :
     (mk a₁ a₂ a₃ a₄ : ℍ[R,c₁,c₂]) + mk b₁ b₂ b₃ b₄ = mk (a₁ + b₁) (a₂ + b₂) (a₃ + b₃) (a₄ + b₄) :=
   rfl
 #align quaternion_algebra.mk_add_mk QuaternionAlgebra.mk_add_mk
 
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.coe_add QuaternionAlgebra.coe_addₓ'. -/
 @[norm_cast, simp]
 theorem coe_add : ((x + y : R) : ℍ[R,c₁,c₂]) = x + y := by ext <;> simp
 #align quaternion_algebra.coe_add QuaternionAlgebra.coe_add
@@ -204,11 +286,23 @@ theorem coe_add : ((x + y : R) : ℍ[R,c₁,c₂]) = x + y := by ext <;> simp
 instance : Neg ℍ[R,c₁,c₂] :=
   ⟨fun a => ⟨-a.1, -a.2, -a.3, -a.4⟩⟩
 
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 @[simp]
 theorem neg_mk (a₁ a₂ a₃ a₄ : R) : -(mk a₁ a₂ a₃ a₄ : ℍ[R,c₁,c₂]) = ⟨-a₁, -a₂, -a₃, -a₄⟩ :=
   rfl
 #align quaternion_algebra.neg_mk QuaternionAlgebra.neg_mk
 
+/- warning: quaternion_algebra.coe_neg -> QuaternionAlgebra.coe_neg is a dubious translation:
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 @[norm_cast, simp]
 theorem coe_neg : ((-x : R) : ℍ[R,c₁,c₂]) = -x := by ext <;> simp
 #align quaternion_algebra.coe_neg QuaternionAlgebra.coe_neg
@@ -217,27 +311,57 @@ theorem coe_neg : ((-x : R) : ℍ[R,c₁,c₂]) = -x := by ext <;> simp
 instance : Sub ℍ[R,c₁,c₂] :=
   ⟨fun a b => ⟨a.1 - b.1, a.2 - b.2, a.3 - b.3, a.4 - b.4⟩⟩
 
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 @[simp]
 theorem mk_sub_mk (a₁ a₂ a₃ a₄ b₁ b₂ b₃ b₄ : R) :
     (mk a₁ a₂ a₃ a₄ : ℍ[R,c₁,c₂]) - mk b₁ b₂ b₃ b₄ = mk (a₁ - b₁) (a₂ - b₂) (a₃ - b₃) (a₄ - b₄) :=
   rfl
 #align quaternion_algebra.mk_sub_mk QuaternionAlgebra.mk_sub_mk
 
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 @[simp, norm_cast]
 theorem coe_im : (x : ℍ[R,c₁,c₂]).im = 0 :=
   rfl
 #align quaternion_algebra.coe_im QuaternionAlgebra.coe_im
 
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 @[simp]
 theorem re_add_im : ↑a.re + a.im = a :=
   ext _ _ (add_zero _) (zero_add _) (zero_add _) (zero_add _)
 #align quaternion_algebra.re_add_im QuaternionAlgebra.re_add_im
 
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 @[simp]
 theorem sub_self_im : a - a.im = a.re :=
   ext _ _ (sub_zero _) (sub_self _) (sub_self _) (sub_self _)
 #align quaternion_algebra.sub_self_im QuaternionAlgebra.sub_self_im
 
+/- warning: quaternion_algebra.sub_self_re -> QuaternionAlgebra.sub_self_re is a dubious translation:
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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {c₁ : R} {c₂ : R} (a : QuaternionAlgebra.{u1} R c₁ c₂), Eq.{succ u1} (QuaternionAlgebra.{u1} R c₁ c₂) (HSub.hSub.{u1, u1, u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.{u1} R c₁ c₂) (instHSub.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instSubQuaternionAlgebra.{u1} R _inst_1 c₁ c₂)) a (QuaternionAlgebra.coe.{u1} R _inst_1 c₁ c₂ (QuaternionAlgebra.re.{u1} R c₁ c₂ a))) (QuaternionAlgebra.im.{u1} R _inst_1 c₁ c₂ a)
+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.sub_self_re QuaternionAlgebra.sub_self_reₓ'. -/
 @[simp]
 theorem sub_self_re : a - a.re = a.im :=
   ext _ _ (sub_self _) (sub_zero _) (sub_zero _) (sub_zero _)
@@ -260,6 +384,12 @@ instance : Mul ℍ[R,c₁,c₂] :=
       a.1 * b.3 + c₁ * a.2 * b.4 + a.3 * b.1 - c₁ * a.4 * b.2,
       a.1 * b.4 + a.2 * b.3 - a.3 * b.2 + a.4 * b.1⟩⟩
 
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R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) a₄ b₁)))
+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.mk_mul_mk QuaternionAlgebra.mk_mul_mkₓ'. -/
 @[simp]
 theorem mk_mul_mk (a₁ a₂ a₃ a₄ b₁ b₂ b₃ b₄ : R) :
     (mk a₁ a₂ a₃ a₄ : ℍ[R,c₁,c₂]) * mk b₁ b₂ b₃ b₄ =
@@ -287,26 +417,56 @@ instance [SMul S T] [IsScalarTower S T R] : IsScalarTower S T ℍ[R,c₁,c₂]
 instance [SMulCommClass S T R] : SMulCommClass S T ℍ[R,c₁,c₂]
     where smul_comm s t x := by ext <;> exact smul_comm _ _ _
 
+/- warning: quaternion_algebra.smul_re -> QuaternionAlgebra.smul_re is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.smul_re QuaternionAlgebra.smul_reₓ'. -/
 @[simp]
 theorem smul_re : (s • a).re = s • a.re :=
   rfl
 #align quaternion_algebra.smul_re QuaternionAlgebra.smul_re
 
+/- warning: quaternion_algebra.smul_im_i -> QuaternionAlgebra.smul_imI is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.smul_im_i QuaternionAlgebra.smul_imIₓ'. -/
 @[simp]
 theorem smul_imI : (s • a).imI = s • a.imI :=
   rfl
 #align quaternion_algebra.smul_im_i QuaternionAlgebra.smul_imI
 
+/- warning: quaternion_algebra.smul_im_j -> QuaternionAlgebra.smul_imJ is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.smul_im_j QuaternionAlgebra.smul_imJₓ'. -/
 @[simp]
 theorem smul_imJ : (s • a).imJ = s • a.imJ :=
   rfl
 #align quaternion_algebra.smul_im_j QuaternionAlgebra.smul_imJ
 
+/- warning: quaternion_algebra.smul_im_k -> QuaternionAlgebra.smul_imK is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.smul_im_k QuaternionAlgebra.smul_imKₓ'. -/
 @[simp]
 theorem smul_imK : (s • a).imK = s • a.imK :=
   rfl
 #align quaternion_algebra.smul_im_k QuaternionAlgebra.smul_imK
 
+/- warning: quaternion_algebra.smul_mk -> QuaternionAlgebra.smul_mk is a dubious translation:
+lean 3 declaration is
+  forall {S : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {c₁ : R} {c₂ : R} [_inst_2 : SMul.{u1, u2} S R] (s : S) (re : R) (im_i : R) (im_j : R) (im_k : R), Eq.{succ u2} (QuaternionAlgebra.{u2} R c₁ c₂) (SMul.smul.{u1, u2} S (QuaternionAlgebra.{u2} R c₁ c₂) (QuaternionAlgebra.hasSmul.{u1, u2} S R _inst_1 c₁ c₂ _inst_2) s (QuaternionAlgebra.mk.{u2} R c₁ c₂ re im_i im_j im_k)) (QuaternionAlgebra.mk.{u2} R c₁ c₂ (SMul.smul.{u1, u2} S R _inst_2 s re) (SMul.smul.{u1, u2} S R _inst_2 s im_i) (SMul.smul.{u1, u2} S R _inst_2 s im_j) (SMul.smul.{u1, u2} S R _inst_2 s im_k))
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.smul_mk QuaternionAlgebra.smul_mkₓ'. -/
 @[simp]
 theorem smul_mk (re im_i im_j im_k : R) :
     s • (⟨re, im_i, im_j, im_k⟩ : ℍ[R,c₁,c₂]) = ⟨s • re, s • im_i, s • im_j, s • im_k⟩ :=
@@ -315,6 +475,12 @@ theorem smul_mk (re im_i im_j im_k : R) :
 
 end
 
+/- warning: quaternion_algebra.coe_smul -> QuaternionAlgebra.coe_smul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.coe_smul QuaternionAlgebra.coe_smulₓ'. -/
 @[simp, norm_cast]
 theorem coe_smul [SMulZeroClass S R] (s : S) (r : R) : (↑(s • r) : ℍ[R,c₁,c₂]) = s • ↑r :=
   ext _ _ rfl (smul_zero s).symm (smul_zero s).symm (smul_zero s).symm
@@ -345,61 +511,133 @@ instance : AddGroupWithOne ℍ[R,c₁,c₂] :=
     intCast_negSucc := fun n => show ↑↑_ = -↑↑_ by rw [Int.cast_neg, Int.cast_ofNat, coe_neg]
     one := 1 }
 
+/- warning: quaternion_algebra.nat_cast_re -> QuaternionAlgebra.nat_cast_re is a dubious translation:
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+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {c₁ : R} {c₂ : R} (n : Nat), Eq.{succ u1} R (QuaternionAlgebra.re.{u1} R c₁ c₂ (Nat.cast.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (AddCommGroupWithOne.toNatCast.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instAddCommGroupWithOneQuaternionAlgebra.{u1} R _inst_1 c₁ c₂)) n)) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n)
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 @[simp, norm_cast]
 theorem nat_cast_re (n : ℕ) : (n : ℍ[R,c₁,c₂]).re = n :=
   rfl
 #align quaternion_algebra.nat_cast_re QuaternionAlgebra.nat_cast_re
 
+/- warning: quaternion_algebra.nat_cast_im_i -> QuaternionAlgebra.nat_cast_imI is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.nat_cast_im_i QuaternionAlgebra.nat_cast_imIₓ'. -/
 @[simp, norm_cast]
 theorem nat_cast_imI (n : ℕ) : (n : ℍ[R,c₁,c₂]).imI = 0 :=
   rfl
 #align quaternion_algebra.nat_cast_im_i QuaternionAlgebra.nat_cast_imI
 
+/- warning: quaternion_algebra.nat_cast_im_j -> QuaternionAlgebra.nat_cast_imJ is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.nat_cast_im_j QuaternionAlgebra.nat_cast_imJₓ'. -/
 @[simp, norm_cast]
 theorem nat_cast_imJ (n : ℕ) : (n : ℍ[R,c₁,c₂]).imJ = 0 :=
   rfl
 #align quaternion_algebra.nat_cast_im_j QuaternionAlgebra.nat_cast_imJ
 
+/- warning: quaternion_algebra.nat_cast_im_k -> QuaternionAlgebra.nat_cast_imK is a dubious translation:
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 @[simp, norm_cast]
 theorem nat_cast_imK (n : ℕ) : (n : ℍ[R,c₁,c₂]).imK = 0 :=
   rfl
 #align quaternion_algebra.nat_cast_im_k QuaternionAlgebra.nat_cast_imK
 
+/- warning: quaternion_algebra.nat_cast_im -> QuaternionAlgebra.nat_cast_im is a dubious translation:
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 @[simp, norm_cast]
 theorem nat_cast_im (n : ℕ) : (n : ℍ[R,c₁,c₂]).im = 0 :=
   rfl
 #align quaternion_algebra.nat_cast_im QuaternionAlgebra.nat_cast_im
 
+/- warning: quaternion_algebra.coe_nat_cast -> QuaternionAlgebra.coe_nat_cast is a dubious translation:
+lean 3 declaration is
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 @[norm_cast]
 theorem coe_nat_cast (n : ℕ) : ↑(n : R) = (n : ℍ[R,c₁,c₂]) :=
   rfl
 #align quaternion_algebra.coe_nat_cast QuaternionAlgebra.coe_nat_cast
 
+/- warning: quaternion_algebra.int_cast_re -> QuaternionAlgebra.int_cast_re is a dubious translation:
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 @[simp, norm_cast]
 theorem int_cast_re (z : ℤ) : (z : ℍ[R,c₁,c₂]).re = z :=
   rfl
 #align quaternion_algebra.int_cast_re QuaternionAlgebra.int_cast_re
 
+/- warning: quaternion_algebra.int_cast_im_i -> QuaternionAlgebra.int_cast_imI is a dubious translation:
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 @[simp, norm_cast]
 theorem int_cast_imI (z : ℤ) : (z : ℍ[R,c₁,c₂]).imI = 0 :=
   rfl
 #align quaternion_algebra.int_cast_im_i QuaternionAlgebra.int_cast_imI
 
+/- warning: quaternion_algebra.int_cast_im_j -> QuaternionAlgebra.int_cast_imJ is a dubious translation:
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 @[simp, norm_cast]
 theorem int_cast_imJ (z : ℤ) : (z : ℍ[R,c₁,c₂]).imJ = 0 :=
   rfl
 #align quaternion_algebra.int_cast_im_j QuaternionAlgebra.int_cast_imJ
 
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 @[simp, norm_cast]
 theorem int_cast_imK (z : ℤ) : (z : ℍ[R,c₁,c₂]).imK = 0 :=
   rfl
 #align quaternion_algebra.int_cast_im_k QuaternionAlgebra.int_cast_imK
 
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.int_cast_im QuaternionAlgebra.int_cast_imₓ'. -/
 @[simp, norm_cast]
 theorem int_cast_im (z : ℤ) : (z : ℍ[R,c₁,c₂]).im = 0 :=
   rfl
 #align quaternion_algebra.int_cast_im QuaternionAlgebra.int_cast_im
 
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.coe_int_cast QuaternionAlgebra.coe_int_castₓ'. -/
 @[norm_cast]
 theorem coe_int_cast (z : ℤ) : ↑(z : R) = (z : ℍ[R,c₁,c₂]) :=
   rfl
@@ -419,6 +657,12 @@ instance : Ring ℍ[R,c₁,c₂] := by
       simp <;>
     ring
 
+/- warning: quaternion_algebra.coe_mul -> QuaternionAlgebra.coe_mul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.coe_mul QuaternionAlgebra.coe_mulₓ'. -/
 @[norm_cast, simp]
 theorem coe_mul : ((x * y : R) : ℍ[R,c₁,c₂]) = x * y := by ext <;> simp
 #align quaternion_algebra.coe_mul QuaternionAlgebra.coe_mul
@@ -436,6 +680,12 @@ instance [CommSemiring S] [Algebra S R] : Algebra S ℍ[R,c₁,c₂]
   smul_def' s x := by ext <;> simp [Algebra.smul_def]
   commutes' s x := by ext <;> simp [Algebra.commutes]
 
+/- warning: quaternion_algebra.algebra_map_eq -> QuaternionAlgebra.algebraMap_eq is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.algebra_map_eq QuaternionAlgebra.algebraMap_eqₓ'. -/
 theorem algebraMap_eq (r : R) : algebraMap R ℍ[R,c₁,c₂] r = ⟨r, 0, 0, 0⟩ :=
   rfl
 #align quaternion_algebra.algebra_map_eq QuaternionAlgebra.algebraMap_eq
@@ -444,38 +694,68 @@ section
 
 variable (c₁ c₂)
 
+/- warning: quaternion_algebra.re_lm -> QuaternionAlgebra.reₗ is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (c₁ : R) (c₂ : R), LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (QuaternionAlgebra.{u1} R c₁ c₂) R (AddCommGroup.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.addCommGroup.{u1} R _inst_1 c₁ c₂)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.ring.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.algebra.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (c₁ : R) (c₂ : R), LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (QuaternionAlgebra.{u1} R c₁ c₂) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))
+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.re_lm QuaternionAlgebra.reₗₓ'. -/
 /-- `quaternion_algebra.re` as a `linear_map`-/
 @[simps]
-def reLm : ℍ[R,c₁,c₂] →ₗ[R] R where
+def reₗ : ℍ[R,c₁,c₂] →ₗ[R] R where
   toFun := re
   map_add' x y := rfl
   map_smul' r x := rfl
-#align quaternion_algebra.re_lm QuaternionAlgebra.reLm
-
+#align quaternion_algebra.re_lm QuaternionAlgebra.reₗ
+
+/- warning: quaternion_algebra.im_i_lm -> QuaternionAlgebra.imIₗ is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (c₁ : R) (c₂ : R), LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (QuaternionAlgebra.{u1} R c₁ c₂) R (AddCommGroup.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.addCommGroup.{u1} R _inst_1 c₁ c₂)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.ring.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.algebra.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (c₁ : R) (c₂ : R), LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (QuaternionAlgebra.{u1} R c₁ c₂) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))
+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.im_i_lm QuaternionAlgebra.imIₗₓ'. -/
 /-- `quaternion_algebra.im_i` as a `linear_map`-/
 @[simps]
-def imILm : ℍ[R,c₁,c₂] →ₗ[R] R where
+def imIₗ : ℍ[R,c₁,c₂] →ₗ[R] R where
   toFun := imI
   map_add' x y := rfl
   map_smul' r x := rfl
-#align quaternion_algebra.im_i_lm QuaternionAlgebra.imILm
-
+#align quaternion_algebra.im_i_lm QuaternionAlgebra.imIₗ
+
+/- warning: quaternion_algebra.im_j_lm -> QuaternionAlgebra.imJₗ is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (c₁ : R) (c₂ : R), LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (QuaternionAlgebra.{u1} R c₁ c₂) R (AddCommGroup.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.addCommGroup.{u1} R _inst_1 c₁ c₂)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.ring.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.algebra.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (c₁ : R) (c₂ : R), LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (QuaternionAlgebra.{u1} R c₁ c₂) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))
+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.im_j_lm QuaternionAlgebra.imJₗₓ'. -/
 /-- `quaternion_algebra.im_j` as a `linear_map`-/
 @[simps]
-def imJLm : ℍ[R,c₁,c₂] →ₗ[R] R where
+def imJₗ : ℍ[R,c₁,c₂] →ₗ[R] R where
   toFun := imJ
   map_add' x y := rfl
   map_smul' r x := rfl
-#align quaternion_algebra.im_j_lm QuaternionAlgebra.imJLm
-
+#align quaternion_algebra.im_j_lm QuaternionAlgebra.imJₗ
+
+/- warning: quaternion_algebra.im_k_lm -> QuaternionAlgebra.imKₗ is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (c₁ : R) (c₂ : R), LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (QuaternionAlgebra.{u1} R c₁ c₂) R (AddCommGroup.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.addCommGroup.{u1} R _inst_1 c₁ c₂)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.ring.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.algebra.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (c₁ : R) (c₂ : R), LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (QuaternionAlgebra.{u1} R c₁ c₂) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))
+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.im_k_lm QuaternionAlgebra.imKₗₓ'. -/
 /-- `quaternion_algebra.im_k` as a `linear_map`-/
 @[simps]
-def imKLm : ℍ[R,c₁,c₂] →ₗ[R] R where
+def imKₗ : ℍ[R,c₁,c₂] →ₗ[R] R where
   toFun := imK
   map_add' x y := rfl
   map_smul' r x := rfl
-#align quaternion_algebra.im_k_lm QuaternionAlgebra.imKLm
-
+#align quaternion_algebra.im_k_lm QuaternionAlgebra.imKₗ
+
+/- warning: quaternion_algebra.linear_equiv_tuple -> QuaternionAlgebra.linearEquivTuple is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (c₁ : R) (c₂ : R), LinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (QuaternionAlgebra.linearEquivTuple._proof_1.{u1} R _inst_1) (QuaternionAlgebra.linearEquivTuple._proof_2.{u1} R _inst_1) (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> R) (AddCommGroup.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.addCommGroup.{u1} R _inst_1 c₁ c₂)) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) => AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.ring.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.algebra.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.Function.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.linear_equiv_tuple QuaternionAlgebra.linearEquivTupleₓ'. -/
 /-- `quaternion_algebra.equiv_tuple` as a linear equivalence. -/
 def linearEquivTuple : ℍ[R,c₁,c₂] ≃ₗ[R] Fin 4 → R :=
   LinearEquiv.symm-- proofs are not `rfl` in the forward direction
@@ -486,21 +766,45 @@ def linearEquivTuple : ℍ[R,c₁,c₂] ≃ₗ[R] Fin 4 → R :=
       map_smul' := fun v₁ v₂ => rfl }
 #align quaternion_algebra.linear_equiv_tuple QuaternionAlgebra.linearEquivTuple
 
+/- warning: quaternion_algebra.coe_linear_equiv_tuple -> QuaternionAlgebra.coe_linearEquivTuple is a dubious translation:
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(fun (_x : QuaternionAlgebra.{u1} R c₁ c₂) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : QuaternionAlgebra.{u1} R c₁ c₂) => (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (SMulZeroClass.toSMul.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (AddMonoid.toZero.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (AddMonoid.toAddZeroClass.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (Module.toDistribMulAction.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u1} R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (AddMonoid.toZero.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (AddMonoid.toAddZeroClass.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R ((Fin 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(NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (AddCommMonoid.toAddMonoid.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => 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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.coe_linear_equiv_tuple QuaternionAlgebra.coe_linearEquivTupleₓ'. -/
 @[simp]
 theorem coe_linearEquivTuple : ⇑(linearEquivTuple c₁ c₂) = equivTuple c₁ c₂ :=
   rfl
 #align quaternion_algebra.coe_linear_equiv_tuple QuaternionAlgebra.coe_linearEquivTuple
 
+/- warning: quaternion_algebra.coe_linear_equiv_tuple_symm -> QuaternionAlgebra.coe_linearEquivTuple_symm is a dubious translation:
+lean 3 declaration is
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(NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.ring.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.algebra.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (_x : LinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) 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c₂) (QuaternionAlgebra.addCommGroup.{u1} R _inst_1 c₁ c₂)) (Pi.Function.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.ring.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.algebra.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => ((Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat 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(NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.addCommGroup.{u1} R _inst_1 c₁ c₂)) (Pi.Function.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.ring.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.algebra.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (QuaternionAlgebra.linearEquivTuple._proof_2.{u1} R _inst_1) (QuaternionAlgebra.linearEquivTuple._proof_1.{u1} R _inst_1)) (LinearEquiv.symm.{u1, u1, u1, u1} R R (QuaternionAlgebra.{u1} R c₁ c₂) ((Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> R) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.addCommGroup.{u1} R _inst_1 c₁ c₂)) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat 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(bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (QuaternionAlgebra.linearEquivTuple._proof_1.{u1} R _inst_1) (QuaternionAlgebra.linearEquivTuple._proof_2.{u1} R _inst_1) (QuaternionAlgebra.linearEquivTuple.{u1} R _inst_1 c₁ c₂))) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} ((Fin (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} 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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (c₁ : R) (c₂ : R), Eq.{succ u1} (forall (ᾰ : (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R), (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) => QuaternionAlgebra.{u1} R c₁ c₂) ᾰ) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((Fin 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(instOfNatNat 4))) -> R) (QuaternionAlgebra.{u1} R c₁ c₂) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin 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(instOfNatNat 4))) -> R) (QuaternionAlgebra.{u1} R c₁ c₂) (SMulZeroClass.toSMul.{u1, u1} R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (AddMonoid.toZero.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (AddMonoid.toAddZeroClass.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (AddMonoid.toZero.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (AddMonoid.toAddZeroClass.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (Module.toDistribMulAction.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((Fin 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(a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (QuaternionAlgebra.{u1} R c₁ c₂) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (Module.toDistribMulAction.{u1, u1} R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Pi.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (fun (a._@.Mathlib.Algebra.Quaternion._hyg.7342 : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u1, u1} R ((Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) -> R) (QuaternionAlgebra.{u1} R c₁ c₂) (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.coe_linear_equiv_tuple_symm QuaternionAlgebra.coe_linearEquivTuple_symmₓ'. -/
 @[simp]
 theorem coe_linearEquivTuple_symm : ⇑(linearEquivTuple c₁ c₂).symm = (equivTuple c₁ c₂).symm :=
   rfl
 #align quaternion_algebra.coe_linear_equiv_tuple_symm QuaternionAlgebra.coe_linearEquivTuple_symm
 
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+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.basis_one_i_j_k QuaternionAlgebra.basisOneIJKₓ'. -/
 /-- `ℍ[R, c₁, c₂]` has a basis over `R` given by `1`, `i`, `j`, and `k`. -/
 noncomputable def basisOneIJK : Basis (Fin 4) R ℍ[R,c₁,c₂] :=
   Basis.ofEquivFun <| linearEquivTuple c₁ c₂
 #align quaternion_algebra.basis_one_i_j_k QuaternionAlgebra.basisOneIJK
 
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(QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (QuaternionAlgebra.{u1} R c₁ c₂) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (AddMonoid.toZero.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (AddMonoid.toAddZeroClass.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (Module.toDistribMulAction.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u1} R (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddMonoid.toZero.{u1} (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (LinearEquiv.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (QuaternionAlgebra.{u1} R c₁ c₂) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (QuaternionAlgebra.{u1} R c₁ c₂) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toNonAssocRing.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (AddCommMonoid.toAddMonoid.{u1} (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} 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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.coe_basis_one_i_j_k_repr QuaternionAlgebra.coe_basisOneIJK_reprₓ'. -/
 @[simp]
 theorem coe_basisOneIJK_repr (q : ℍ[R,c₁,c₂]) :
     ⇑((basisOneIJK c₁ c₂).repr q) = ![q.re, q.imI, q.imJ, q.imK] :=
@@ -513,12 +817,24 @@ instance : Module.Finite R ℍ[R,c₁,c₂] :=
 instance : Module.Free R ℍ[R,c₁,c₂] :=
   Module.Free.of_basis (basisOneIJK c₁ c₂)
 
+/- warning: quaternion_algebra.rank_eq_four -> QuaternionAlgebra.rank_eq_four is a dubious translation:
+lean 3 declaration is
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 theorem rank_eq_four [StrongRankCondition R] : Module.rank R ℍ[R,c₁,c₂] = 4 :=
   by
   rw [rank_eq_card_basis (basis_one_i_j_k c₁ c₂), Fintype.card_fin]
   norm_num
 #align quaternion_algebra.rank_eq_four QuaternionAlgebra.rank_eq_four
 
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 theorem finrank_eq_four [StrongRankCondition R] : FiniteDimensional.finrank R ℍ[R,c₁,c₂] = 4 :=
   by
   have : Cardinal.toNat 4 = 4 := by
@@ -528,67 +844,147 @@ theorem finrank_eq_four [StrongRankCondition R] : FiniteDimensional.finrank R 
 
 end
 
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 @[norm_cast, simp]
 theorem coe_sub : ((x - y : R) : ℍ[R,c₁,c₂]) = x - y :=
   (algebraMap R ℍ[R,c₁,c₂]).map_sub x y
 #align quaternion_algebra.coe_sub QuaternionAlgebra.coe_sub
 
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 @[norm_cast, simp]
 theorem coe_pow (n : ℕ) : (↑(x ^ n) : ℍ[R,c₁,c₂]) = ↑x ^ n :=
   (algebraMap R ℍ[R,c₁,c₂]).map_pow x n
 #align quaternion_algebra.coe_pow QuaternionAlgebra.coe_pow
 
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 theorem coe_commutes : ↑r * a = a * r :=
   Algebra.commutes r a
 #align quaternion_algebra.coe_commutes QuaternionAlgebra.coe_commutes
 
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 theorem coe_commute : Commute (↑r) a :=
   coe_commutes r a
 #align quaternion_algebra.coe_commute QuaternionAlgebra.coe_commute
 
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 theorem coe_mul_eq_smul : ↑r * a = r • a :=
   (Algebra.smul_def r a).symm
 #align quaternion_algebra.coe_mul_eq_smul QuaternionAlgebra.coe_mul_eq_smul
 
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.mul_coe_eq_smul QuaternionAlgebra.mul_coe_eq_smulₓ'. -/
 theorem mul_coe_eq_smul : a * r = r • a := by rw [← coe_commutes, coe_mul_eq_smul]
 #align quaternion_algebra.mul_coe_eq_smul QuaternionAlgebra.mul_coe_eq_smul
 
+/- warning: quaternion_algebra.coe_algebra_map -> QuaternionAlgebra.coe_algebraMap is a dubious translation:
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 @[norm_cast, simp]
 theorem coe_algebraMap : ⇑(algebraMap R ℍ[R,c₁,c₂]) = coe :=
   rfl
 #align quaternion_algebra.coe_algebra_map QuaternionAlgebra.coe_algebraMap
 
+/- warning: quaternion_algebra.smul_coe -> QuaternionAlgebra.smul_coe is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.smul_coe QuaternionAlgebra.smul_coeₓ'. -/
 theorem smul_coe : x • (y : ℍ[R,c₁,c₂]) = ↑(x * y) := by rw [coe_mul, coe_mul_eq_smul]
 #align quaternion_algebra.smul_coe QuaternionAlgebra.smul_coe
 
 /-- Quaternion conjugate. -/
 instance : Star ℍ[R,c₁,c₂] where unit a := ⟨a.1, -a.2, -a.3, -a.4⟩
 
+#print QuaternionAlgebra.re_star /-
 @[simp]
 theorem re_star : (star a).re = a.re :=
   rfl
 #align quaternion_algebra.re_star QuaternionAlgebra.re_star
+-/
 
+/- warning: quaternion_algebra.im_i_star -> QuaternionAlgebra.imI_star is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.im_i_star QuaternionAlgebra.imI_starₓ'. -/
 @[simp]
 theorem imI_star : (star a).imI = -a.imI :=
   rfl
 #align quaternion_algebra.im_i_star QuaternionAlgebra.imI_star
 
+/- warning: quaternion_algebra.im_j_star -> QuaternionAlgebra.imJ_star is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.im_j_star QuaternionAlgebra.imJ_starₓ'. -/
 @[simp]
 theorem imJ_star : (star a).imJ = -a.imJ :=
   rfl
 #align quaternion_algebra.im_j_star QuaternionAlgebra.imJ_star
 
+/- warning: quaternion_algebra.im_k_star -> QuaternionAlgebra.imK_star is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.im_k_star QuaternionAlgebra.imK_starₓ'. -/
 @[simp]
 theorem imK_star : (star a).imK = -a.imK :=
   rfl
 #align quaternion_algebra.im_k_star QuaternionAlgebra.imK_star
 
+/- warning: quaternion_algebra.im_star -> QuaternionAlgebra.im_star is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.im_star QuaternionAlgebra.im_starₓ'. -/
 @[simp]
 theorem im_star : (star a).im = -a.im :=
   ext _ _ neg_zero.symm rfl rfl rfl
 #align quaternion_algebra.im_star QuaternionAlgebra.im_star
 
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 @[simp]
 theorem star_mk (a₁ a₂ a₃ a₄ : R) : star (mk a₁ a₂ a₃ a₄ : ℍ[R,c₁,c₂]) = ⟨a₁, -a₂, -a₃, -a₄⟩ :=
   rfl
@@ -600,18 +996,48 @@ instance : StarRing ℍ[R,c₁,c₂]
   star_add a b := by ext <;> simp [neg_add]
   star_mul a b := by ext <;> simp <;> ring
 
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 theorem self_add_star' : a + star a = ↑(2 * a.re) := by ext <;> simp [two_mul]
 #align quaternion_algebra.self_add_star' QuaternionAlgebra.self_add_star'
 
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 theorem self_add_star : a + star a = 2 * a.re := by simp only [self_add_star', two_mul, coe_add]
 #align quaternion_algebra.self_add_star QuaternionAlgebra.self_add_star
 
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 theorem star_add_self' : star a + a = ↑(2 * a.re) := by rw [add_comm, self_add_star']
 #align quaternion_algebra.star_add_self' QuaternionAlgebra.star_add_self'
 
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 theorem star_add_self : star a + a = 2 * a.re := by rw [add_comm, self_add_star]
 #align quaternion_algebra.star_add_self QuaternionAlgebra.star_add_self
 
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.star_eq_two_re_sub QuaternionAlgebra.star_eq_two_re_subₓ'. -/
 theorem star_eq_two_re_sub : star a = ↑(2 * a.re) - a :=
   eq_sub_iff_add_eq.2 a.star_add_self'
 #align quaternion_algebra.star_eq_two_re_sub QuaternionAlgebra.star_eq_two_re_sub
@@ -621,24 +1047,54 @@ instance : IsStarNormal a :=
     rw [a.star_eq_two_re_sub]
     exact (coe_commute (2 * a.re) a).sub_left (Commute.refl a)⟩
 
+/- warning: quaternion_algebra.star_coe -> QuaternionAlgebra.star_coe is a dubious translation:
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 @[simp, norm_cast]
 theorem star_coe : star (x : ℍ[R,c₁,c₂]) = x := by ext <;> simp
 #align quaternion_algebra.star_coe QuaternionAlgebra.star_coe
 
+/- warning: quaternion_algebra.star_im -> QuaternionAlgebra.star_im is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.star_im QuaternionAlgebra.star_imₓ'. -/
 @[simp]
 theorem star_im : star a.im = -a.im :=
   im_star _
 #align quaternion_algebra.star_im QuaternionAlgebra.star_im
 
+/- warning: quaternion_algebra.star_smul -> QuaternionAlgebra.star_smul is a dubious translation:
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 @[simp]
 theorem star_smul [Monoid S] [DistribMulAction S R] (s : S) (a : ℍ[R,c₁,c₂]) :
     star (s • a) = s • star a :=
   ext _ _ rfl (smul_neg _ _).symm (smul_neg _ _).symm (smul_neg _ _).symm
 #align quaternion_algebra.star_smul QuaternionAlgebra.star_smul
 
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 theorem eq_re_of_eq_coe {a : ℍ[R,c₁,c₂]} {x : R} (h : a = x) : a = a.re := by rw [h, coe_re]
 #align quaternion_algebra.eq_re_of_eq_coe QuaternionAlgebra.eq_re_of_eq_coe
 
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.eq_re_iff_mem_range_coe QuaternionAlgebra.eq_re_iff_mem_range_coeₓ'. -/
 theorem eq_re_iff_mem_range_coe {a : ℍ[R,c₁,c₂]} :
     a = a.re ↔ a ∈ Set.range (coe : R → ℍ[R,c₁,c₂]) :=
   ⟨fun h => ⟨a.re, h.symm⟩, fun ⟨x, h⟩ => eq_re_of_eq_coe h.symm⟩
@@ -648,21 +1104,45 @@ section CharZero
 
 variable [NoZeroDivisors R] [CharZero R]
 
+/- warning: quaternion_algebra.star_eq_self -> QuaternionAlgebra.star_eq_self is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))] [_inst_3 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))] {c₁ : R} {c₂ : R} {a : QuaternionAlgebra.{u1} R c₁ c₂}, Iff (Eq.{succ u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Star.star.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.hasStar.{u1} R _inst_1 c₁ c₂) a) a) (Eq.{succ u1} (QuaternionAlgebra.{u1} R c₁ c₂) a ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) R (QuaternionAlgebra.{u1} R c₁ c₂) (HasLiftT.mk.{succ u1, succ u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CoeTCₓ.coe.{succ u1, succ u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.hasCoeT.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.re.{u1} R c₁ c₂ a)))
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.star_eq_self QuaternionAlgebra.star_eq_selfₓ'. -/
 @[simp]
 theorem star_eq_self {c₁ c₂ : R} {a : ℍ[R,c₁,c₂]} : star a = a ↔ a = a.re := by
   simp [ext_iff, neg_eq_iff_add_eq_zero, add_self_eq_zero]
 #align quaternion_algebra.star_eq_self QuaternionAlgebra.star_eq_self
 
+/- warning: quaternion_algebra.star_eq_neg -> QuaternionAlgebra.star_eq_neg is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.star_eq_neg QuaternionAlgebra.star_eq_negₓ'. -/
 theorem star_eq_neg {c₁ c₂ : R} {a : ℍ[R,c₁,c₂]} : star a = -a ↔ a.re = 0 := by
   simp [ext_iff, eq_neg_iff_add_eq_zero]
 #align quaternion_algebra.star_eq_neg QuaternionAlgebra.star_eq_neg
 
 end CharZero
 
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.star_mul_eq_coe QuaternionAlgebra.star_mul_eq_coeₓ'. -/
 -- Can't use `rw ← star_eq_self` in the proof without additional assumptions
 theorem star_mul_eq_coe : star a * a = (star a * a).re := by ext <;> simp <;> ring
 #align quaternion_algebra.star_mul_eq_coe QuaternionAlgebra.star_mul_eq_coe
 
+/- warning: quaternion_algebra.mul_star_eq_coe -> QuaternionAlgebra.mul_star_eq_coe is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.mul_star_eq_coe QuaternionAlgebra.mul_star_eq_coeₓ'. -/
 theorem mul_star_eq_coe : a * star a = (a * star a).re :=
   by
   rw [← star_comm_self']
@@ -671,6 +1151,12 @@ theorem mul_star_eq_coe : a * star a = (a * star a).re :=
 
 open MulOpposite
 
+/- warning: quaternion_algebra.star_ae -> QuaternionAlgebra.starAe is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.star_ae QuaternionAlgebra.starAeₓ'. -/
 /-- Quaternion conjugate as an `alg_equiv` to the opposite ring. -/
 def starAe : ℍ[R,c₁,c₂] ≃ₐ[R] ℍ[R,c₁,c₂]ᵐᵒᵖ :=
   { starAddEquiv.trans opAddEquiv with
@@ -680,6 +1166,12 @@ def starAe : ℍ[R,c₁,c₂] ≃ₐ[R] ℍ[R,c₁,c₂]ᵐᵒᵖ :=
     commutes' := fun r => by simp }
 #align quaternion_algebra.star_ae QuaternionAlgebra.starAe
 
+/- warning: quaternion_algebra.coe_star_ae -> QuaternionAlgebra.coe_starAe is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Semiring.toNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (AddCommMonoid.toAddMonoid.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))))) (Module.toDistribMulAction.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Semiring.toNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (Algebra.toModule.{u1, u1} R (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Semiring.toNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Module.toDistribMulAction.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Semiring.toNonAssocSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))))) (Algebra.toModule.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)))))) (Algebra.toModule.{u1, u1} R (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AlgEquiv.{u1, u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (MulOpposite.semiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂))) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))))) (QuaternionAlgebra.starAe.{u1} R _inst_1 c₁ c₂)) (Function.comp.{succ u1, succ u1, succ u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.{u1} R c₁ c₂) (MulOpposite.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (MulOpposite.op.{u1} (QuaternionAlgebra.{u1} R c₁ c₂)) (Star.star.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instStarQuaternionAlgebra.{u1} R _inst_1 c₁ c₂)))
+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.coe_star_ae QuaternionAlgebra.coe_starAeₓ'. -/
 @[simp]
 theorem coe_starAe : ⇑(starAe : ℍ[R,c₁,c₂] ≃ₐ[R] _) = op ∘ star :=
   rfl
@@ -687,32 +1179,40 @@ theorem coe_starAe : ⇑(starAe : ℍ[R,c₁,c₂] ≃ₐ[R] _) = op ∘ star :=
 
 end QuaternionAlgebra
 
+#print Quaternion /-
 /-- Space of quaternions over a type. Implemented as a structure with four fields:
 `re`, `im_i`, `im_j`, and `im_k`. -/
 def Quaternion (R : Type _) [One R] [Neg R] :=
   QuaternionAlgebra R (-1) (-1)
 #align quaternion Quaternion
+-/
 
 -- mathport name: quaternion
 scoped[Quaternion] notation "ℍ[" R "]" => Quaternion R
 
+#print Quaternion.equivProd /-
 /-- The equivalence between the quaternions over `R` and `R × R × R × R`. -/
 @[simps]
 def Quaternion.equivProd (R : Type _) [One R] [Neg R] : ℍ[R] ≃ R × R × R × R :=
   QuaternionAlgebra.equivProd _ _
 #align quaternion.equiv_prod Quaternion.equivProd
+-/
 
+#print Quaternion.equivTuple /-
 /-- The equivalence between the quaternions over `R` and `fin 4 → R`. -/
 @[simps symm_apply]
 def Quaternion.equivTuple (R : Type _) [One R] [Neg R] : ℍ[R] ≃ (Fin 4 → R) :=
   QuaternionAlgebra.equivTuple _ _
 #align quaternion.equiv_tuple Quaternion.equivTuple
+-/
 
+#print Quaternion.equivTuple_apply /-
 @[simp]
 theorem Quaternion.equivTuple_apply (R : Type _) [One R] [Neg R] (x : ℍ[R]) :
     Quaternion.equivTuple R x = ![x.re, x.imI, x.imJ, x.imK] :=
   rfl
 #align quaternion.equiv_tuple_apply Quaternion.equivTuple_apply
+-/
 
 namespace Quaternion
 
@@ -744,390 +1244,850 @@ instance [CommSemiring S] [Algebra S R] : Algebra S ℍ[R] :=
 instance : StarRing ℍ[R] :=
   QuaternionAlgebra.starRing
 
+/- warning: quaternion.ext -> Quaternion.ext is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (b : Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))), (Eq.{succ u1} R (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) a) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) b)) -> (Eq.{succ u1} R (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) 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_inst_1))))))))) b)) -> (Eq.{succ u1} R (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R 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(Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) a) (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) b)) -> (Eq.{succ u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) a b)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (b : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))), (Eq.{succ u1} R (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) a) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) b)) -> (Eq.{succ u1} R (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) a) (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) b)) -> (Eq.{succ u1} R (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) a) (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) b)) -> (Eq.{succ u1} R (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) a) (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) b)) -> (Eq.{succ u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) a b)
+Case conversion may be inaccurate. Consider using '#align quaternion.ext Quaternion.extₓ'. -/
 @[ext]
 theorem ext : a.re = b.re → a.imI = b.imI → a.imJ = b.imJ → a.imK = b.imK → a = b :=
   QuaternionAlgebra.ext a b
 #align quaternion.ext Quaternion.ext
 
+/- warning: quaternion.ext_iff -> Quaternion.ext_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {a : Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))} {b : Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))}, Iff (Eq.{succ u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R 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+Case conversion may be inaccurate. Consider using '#align quaternion.ext_iff Quaternion.ext_iffₓ'. -/
 theorem ext_iff {a b : ℍ[R]} :
     a = b ↔ a.re = b.re ∧ a.imI = b.imI ∧ a.imJ = b.imJ ∧ a.imK = b.imK :=
   QuaternionAlgebra.ext_iff a b
 #align quaternion.ext_iff Quaternion.ext_iff
 
+/- warning: quaternion.im -> Quaternion.im is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R], (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R], (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) -> (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))
+Case conversion may be inaccurate. Consider using '#align quaternion.im Quaternion.imₓ'. -/
 /-- The imaginary part of a quaternion. -/
 def im (x : ℍ[R]) : ℍ[R] :=
   x.im
 #align quaternion.im Quaternion.im
 
+/- warning: quaternion.im_re -> Quaternion.im_re is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align quaternion.im_re Quaternion.im_reₓ'. -/
 @[simp]
 theorem im_re : a.im.re = 0 :=
   rfl
 #align quaternion.im_re Quaternion.im_re
 
+/- warning: quaternion.im_im_i -> Quaternion.im_imI is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align quaternion.im_im_i Quaternion.im_imIₓ'. -/
 @[simp]
 theorem im_imI : a.im.imI = a.imI :=
   rfl
 #align quaternion.im_im_i Quaternion.im_imI
 
+/- warning: quaternion.im_im_j -> Quaternion.im_imJ is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align quaternion.im_im_j Quaternion.im_imJₓ'. -/
 @[simp]
 theorem im_imJ : a.im.imJ = a.imJ :=
   rfl
 #align quaternion.im_im_j Quaternion.im_imJ
 
+/- warning: quaternion.im_im_k -> Quaternion.im_imK is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align quaternion.im_im_k Quaternion.im_imKₓ'. -/
 @[simp]
 theorem im_imK : a.im.imK = a.imK :=
   rfl
 #align quaternion.im_im_k Quaternion.im_imK
 
+/- warning: quaternion.im_idem -> Quaternion.im_idem is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion.im_idem Quaternion.im_idemₓ'. -/
 @[simp]
 theorem im_idem : a.im.im = a.im :=
   rfl
 #align quaternion.im_idem Quaternion.im_idem
 
+/- warning: quaternion.re_add_im -> Quaternion.re_add_im is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align quaternion.re_add_im Quaternion.re_add_imₓ'. -/
 @[simp]
 theorem re_add_im : ↑a.re + a.im = a :=
   a.re_add_im
 #align quaternion.re_add_im Quaternion.re_add_im
 
+/- warning: quaternion.sub_self_im -> Quaternion.sub_self_im is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align quaternion.sub_self_im Quaternion.sub_self_imₓ'. -/
 @[simp]
 theorem sub_self_im : a - a.im = a.re :=
   a.sub_self_im
 #align quaternion.sub_self_im Quaternion.sub_self_im
 
+/- warning: quaternion.sub_self_re -> Quaternion.sub_self_re is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion.sub_self_re Quaternion.sub_self_reₓ'. -/
 @[simp]
 theorem sub_self_re : a - a.re = a.im :=
   a.sub_self_re
 #align quaternion.sub_self_re Quaternion.sub_self_re
 
+#print Quaternion.coe_re /-
 @[simp, norm_cast]
 theorem coe_re : (x : ℍ[R]).re = x :=
   rfl
 #align quaternion.coe_re Quaternion.coe_re
+-/
 
+/- warning: quaternion.coe_im_i -> Quaternion.coe_imI is a dubious translation:
+lean 3 declaration is
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+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (x : R), Eq.{succ u1} R (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.coe.{u1} R _inst_1 x)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align quaternion.coe_im_i Quaternion.coe_imIₓ'. -/
 @[simp, norm_cast]
 theorem coe_imI : (x : ℍ[R]).imI = 0 :=
   rfl
 #align quaternion.coe_im_i Quaternion.coe_imI
 
+/- warning: quaternion.coe_im_j -> Quaternion.coe_imJ is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align quaternion.coe_im_j Quaternion.coe_imJₓ'. -/
 @[simp, norm_cast]
 theorem coe_imJ : (x : ℍ[R]).imJ = 0 :=
   rfl
 #align quaternion.coe_im_j Quaternion.coe_imJ
 
+/- warning: quaternion.coe_im_k -> Quaternion.coe_imK is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion.coe_im_k Quaternion.coe_imKₓ'. -/
 @[simp, norm_cast]
 theorem coe_imK : (x : ℍ[R]).imK = 0 :=
   rfl
 #align quaternion.coe_im_k Quaternion.coe_imK
 
+/- warning: quaternion.coe_im -> Quaternion.coe_im is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion.coe_im Quaternion.coe_imₓ'. -/
 @[simp, norm_cast]
 theorem coe_im : (x : ℍ[R]).im = 0 :=
   rfl
 #align quaternion.coe_im Quaternion.coe_im
 
+/- warning: quaternion.zero_re -> Quaternion.zero_re is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion.zero_re Quaternion.zero_reₓ'. -/
 @[simp]
 theorem zero_re : (0 : ℍ[R]).re = 0 :=
   rfl
 #align quaternion.zero_re Quaternion.zero_re
 
+/- warning: quaternion.zero_im_i -> Quaternion.zero_imI is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion.zero_im_i Quaternion.zero_imIₓ'. -/
 @[simp]
 theorem zero_imI : (0 : ℍ[R]).imI = 0 :=
   rfl
 #align quaternion.zero_im_i Quaternion.zero_imI
 
+/- warning: quaternion.zero_im_j -> Quaternion.zero_imJ is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion.zero_im_j Quaternion.zero_imJₓ'. -/
 @[simp]
 theorem zero_imJ : (0 : ℍ[R]).imJ = 0 :=
   rfl
 #align quaternion.zero_im_j Quaternion.zero_imJ
 
+/- warning: quaternion.zero_im_k -> Quaternion.zero_imK is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion.zero_im_k Quaternion.zero_imKₓ'. -/
 @[simp]
 theorem zero_imK : (0 : ℍ[R]).imK = 0 :=
   rfl
 #align quaternion.zero_im_k Quaternion.zero_imK
 
+/- warning: quaternion.zero_im -> Quaternion.zero_im is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align quaternion.zero_im Quaternion.zero_imₓ'. -/
 @[simp]
 theorem zero_im : (0 : ℍ[R]).im = 0 :=
   rfl
 #align quaternion.zero_im Quaternion.zero_im
 
+/- warning: quaternion.coe_zero -> Quaternion.coe_zero is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align quaternion.coe_zero Quaternion.coe_zeroₓ'. -/
 @[simp, norm_cast]
 theorem coe_zero : ((0 : R) : ℍ[R]) = 0 :=
   rfl
 #align quaternion.coe_zero Quaternion.coe_zero
 
+/- warning: quaternion.one_re -> Quaternion.one_re is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align quaternion.one_re Quaternion.one_reₓ'. -/
 @[simp]
 theorem one_re : (1 : ℍ[R]).re = 1 :=
   rfl
 #align quaternion.one_re Quaternion.one_re
 
+/- warning: quaternion.one_im_i -> Quaternion.one_imI is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R], Eq.{succ u1} R (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (OfNat.ofNat.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) 1 (OfNat.mk.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) 1 (One.one.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddMonoidWithOne.toOne.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddGroupWithOne.toAddMonoidWithOne.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommGroupWithOne.toAddGroupWithOne.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toAddCommGroupWithOne.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))))))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))
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+Case conversion may be inaccurate. Consider using '#align quaternion.one_im_i Quaternion.one_imIₓ'. -/
 @[simp]
 theorem one_imI : (1 : ℍ[R]).imI = 0 :=
   rfl
 #align quaternion.one_im_i Quaternion.one_imI
 
+/- warning: quaternion.one_im_j -> Quaternion.one_imJ is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align quaternion.one_im_j Quaternion.one_imJₓ'. -/
 @[simp]
 theorem one_imJ : (1 : ℍ[R]).imJ = 0 :=
   rfl
 #align quaternion.one_im_j Quaternion.one_imJ
 
+/- warning: quaternion.one_im_k -> Quaternion.one_imK is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align quaternion.one_im_k Quaternion.one_imKₓ'. -/
 @[simp]
 theorem one_imK : (1 : ℍ[R]).imK = 0 :=
   rfl
 #align quaternion.one_im_k Quaternion.one_imK
 
+/- warning: quaternion.one_im -> Quaternion.one_im is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align quaternion.one_im Quaternion.one_imₓ'. -/
 @[simp]
 theorem one_im : (1 : ℍ[R]).im = 0 :=
   rfl
 #align quaternion.one_im Quaternion.one_im
 
+/- warning: quaternion.coe_one -> Quaternion.coe_one is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion.coe_one Quaternion.coe_oneₓ'. -/
 @[simp, norm_cast]
 theorem coe_one : ((1 : R) : ℍ[R]) = 1 :=
   rfl
 #align quaternion.coe_one Quaternion.coe_one
 
+/- warning: quaternion.add_re -> Quaternion.add_re is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align quaternion.add_re Quaternion.add_reₓ'. -/
 @[simp]
 theorem add_re : (a + b).re = a.re + b.re :=
   rfl
 #align quaternion.add_re Quaternion.add_re
 
+/- warning: quaternion.add_im_i -> Quaternion.add_imI is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion.add_im_i Quaternion.add_imIₓ'. -/
 @[simp]
 theorem add_imI : (a + b).imI = a.imI + b.imI :=
   rfl
 #align quaternion.add_im_i Quaternion.add_imI
 
+/- warning: quaternion.add_im_j -> Quaternion.add_imJ is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion.add_im_j Quaternion.add_imJₓ'. -/
 @[simp]
 theorem add_imJ : (a + b).imJ = a.imJ + b.imJ :=
   rfl
 #align quaternion.add_im_j Quaternion.add_imJ
 
+/- warning: quaternion.add_im_k -> Quaternion.add_imK is a dubious translation:
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(AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toDistrib.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) a b)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (b : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u1} R (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) a) (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) b))
+Case conversion may be inaccurate. Consider using '#align quaternion.add_im_k Quaternion.add_imKₓ'. -/
 @[simp]
 theorem add_imK : (a + b).imK = a.imK + b.imK :=
   rfl
 #align quaternion.add_im_k Quaternion.add_imK
 
+/- warning: quaternion.add_im -> Quaternion.add_im is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align quaternion.add_im Quaternion.add_imₓ'. -/
 @[simp]
 theorem add_im : (a + b).im = a.im + b.im :=
   ext _ _ (add_zero _).symm rfl rfl rfl
 #align quaternion.add_im Quaternion.add_im
 
+/- warning: quaternion.coe_add -> Quaternion.coe_add is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion.coe_add Quaternion.coe_addₓ'. -/
 @[simp, norm_cast]
 theorem coe_add : ((x + y : R) : ℍ[R]) = x + y :=
   QuaternionAlgebra.coe_add x y
 #align quaternion.coe_add Quaternion.coe_add
 
+/- warning: quaternion.neg_re -> Quaternion.neg_re is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion.neg_re Quaternion.neg_reₓ'. -/
 @[simp]
 theorem neg_re : (-a).re = -a.re :=
   rfl
 #align quaternion.neg_re Quaternion.neg_re
 
+/- warning: quaternion.neg_im_i -> Quaternion.neg_imI is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion.neg_im_i Quaternion.neg_imIₓ'. -/
 @[simp]
 theorem neg_imI : (-a).imI = -a.imI :=
   rfl
 #align quaternion.neg_im_i Quaternion.neg_imI
 
+/- warning: quaternion.neg_im_j -> Quaternion.neg_imJ is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion.neg_im_j Quaternion.neg_imJₓ'. -/
 @[simp]
 theorem neg_imJ : (-a).imJ = -a.imJ :=
   rfl
 #align quaternion.neg_im_j Quaternion.neg_imJ
 
+/- warning: quaternion.neg_im_k -> Quaternion.neg_imK is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align quaternion.neg_im_k Quaternion.neg_imKₓ'. -/
 @[simp]
 theorem neg_imK : (-a).imK = -a.imK :=
   rfl
 #align quaternion.neg_im_k Quaternion.neg_imK
 
+/- warning: quaternion.neg_im -> Quaternion.neg_im is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align quaternion.neg_im Quaternion.neg_imₓ'. -/
 @[simp]
 theorem neg_im : (-a).im = -a.im :=
   ext _ _ neg_zero.symm rfl rfl rfl
 #align quaternion.neg_im Quaternion.neg_im
 
+/- warning: quaternion.coe_neg -> Quaternion.coe_neg is a dubious translation:
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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (x : R), Eq.{succ u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.coe.{u1} R _inst_1 (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) x)) (Neg.neg.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNeg.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.coe.{u1} R _inst_1 x))
+Case conversion may be inaccurate. Consider using '#align quaternion.coe_neg Quaternion.coe_negₓ'. -/
 @[simp, norm_cast]
 theorem coe_neg : ((-x : R) : ℍ[R]) = -x :=
   QuaternionAlgebra.coe_neg x
 #align quaternion.coe_neg Quaternion.coe_neg
 
+/- warning: quaternion.sub_re -> Quaternion.sub_re is a dubious translation:
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(AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) b))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (b : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u1} R (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (HSub.hSub.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSub.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) a b)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) a) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) b))
+Case conversion may be inaccurate. Consider using '#align quaternion.sub_re Quaternion.sub_reₓ'. -/
 @[simp]
 theorem sub_re : (a - b).re = a.re - b.re :=
   rfl
 #align quaternion.sub_re Quaternion.sub_re
 
+/- warning: quaternion.sub_im_i -> Quaternion.sub_imI is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align quaternion.sub_im_i Quaternion.sub_imIₓ'. -/
 @[simp]
 theorem sub_imI : (a - b).imI = a.imI - b.imI :=
   rfl
 #align quaternion.sub_im_i Quaternion.sub_imI
 
+/- warning: quaternion.sub_im_j -> Quaternion.sub_imJ is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align quaternion.sub_im_j Quaternion.sub_imJₓ'. -/
 @[simp]
 theorem sub_imJ : (a - b).imJ = a.imJ - b.imJ :=
   rfl
 #align quaternion.sub_im_j Quaternion.sub_imJ
 
+/- warning: quaternion.sub_im_k -> Quaternion.sub_imK is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion.sub_im_k Quaternion.sub_imKₓ'. -/
 @[simp]
 theorem sub_imK : (a - b).imK = a.imK - b.imK :=
   rfl
 #align quaternion.sub_im_k Quaternion.sub_imK
 
+/- warning: quaternion.sub_im -> Quaternion.sub_im is a dubious translation:
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(AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasSub.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddGroup.toSubNegMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R 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(AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toAddCommGroupWithOne.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))))) (Quaternion.im.{u1} R _inst_1 a) (Quaternion.im.{u1} R _inst_1 b))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (b : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.im.{u1} R _inst_1 (HSub.hSub.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSub.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) a b)) (HSub.hSub.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSub.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Quaternion.im.{u1} R _inst_1 a) (Quaternion.im.{u1} R _inst_1 b))
+Case conversion may be inaccurate. Consider using '#align quaternion.sub_im Quaternion.sub_imₓ'. -/
 @[simp]
 theorem sub_im : (a - b).im = a.im - b.im :=
   ext _ _ (sub_zero _).symm rfl rfl rfl
 #align quaternion.sub_im Quaternion.sub_im
 
+/- warning: quaternion.coe_sub -> Quaternion.coe_sub is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align quaternion.coe_sub Quaternion.coe_subₓ'. -/
 @[simp, norm_cast]
 theorem coe_sub : ((x - y : R) : ℍ[R]) = x - y :=
   QuaternionAlgebra.coe_sub x y
 #align quaternion.coe_sub Quaternion.coe_sub
 
+/- warning: quaternion.mul_re -> Quaternion.mul_re is a dubious translation:
+lean 3 declaration is
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(instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R 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+but is expected to have type
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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) a b)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) a) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) b)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) a) (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) b))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) a) (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) b))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) a) (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) b)))
+Case conversion may be inaccurate. Consider using '#align quaternion.mul_re Quaternion.mul_reₓ'. -/
 @[simp]
 theorem mul_re : (a * b).re = a.re * b.re - a.imI * b.imI - a.imJ * b.imJ - a.imK * b.imK :=
-  (QuaternionAlgebra.hasMul_mul_re a b).trans <| by
-    simp only [one_mul, neg_mul, sub_eq_add_neg, neg_neg]
+  (QuaternionAlgebra.mul_re a b).trans <| by simp only [one_mul, neg_mul, sub_eq_add_neg, neg_neg]
 #align quaternion.mul_re Quaternion.mul_re
 
+/- warning: quaternion.mul_im_i -> Quaternion.mul_imI is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (b : Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))), Eq.{succ u1} R (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (HMul.hMul.{u1, u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (instHMul.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Distrib.toHasMul.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toDistrib.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) a b)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) a) (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) b)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) a) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) b))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) a) (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) b))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) a) (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) b)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (b : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u1} R (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (HMul.hMul.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) a b)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HMul.hMul.{u1, u1, u1} R R R 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+Case conversion may be inaccurate. Consider using '#align quaternion.mul_im_i Quaternion.mul_imIₓ'. -/
 @[simp]
 theorem mul_imI : (a * b).imI = a.re * b.imI + a.imI * b.re + a.imJ * b.imK - a.imK * b.imJ :=
-  (QuaternionAlgebra.hasMul_mul_imI a b).trans <| by
-    simp only [one_mul, neg_mul, sub_eq_add_neg, neg_neg]
+  (QuaternionAlgebra.mul_imI a b).trans <| by simp only [one_mul, neg_mul, sub_eq_add_neg, neg_neg]
 #align quaternion.mul_im_i Quaternion.mul_imI
 
+/- warning: quaternion.mul_im_j -> Quaternion.mul_imJ is a dubious translation:
+lean 3 declaration is
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(AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) a) (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} 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+but is expected to have type
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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) a b)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) a) (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) b)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) a) (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) b))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) a) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) b))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) a) (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) b)))
+Case conversion may be inaccurate. Consider using '#align quaternion.mul_im_j Quaternion.mul_imJₓ'. -/
 @[simp]
 theorem mul_imJ : (a * b).imJ = a.re * b.imJ - a.imI * b.imK + a.imJ * b.re + a.imK * b.imI :=
-  (QuaternionAlgebra.hasMul_mul_imJ a b).trans <| by
-    simp only [one_mul, neg_mul, sub_eq_add_neg, neg_neg]
+  (QuaternionAlgebra.mul_imJ a b).trans <| by simp only [one_mul, neg_mul, sub_eq_add_neg, neg_neg]
 #align quaternion.mul_im_j Quaternion.mul_imJ
 
+/- warning: quaternion.mul_im_k -> Quaternion.mul_imK is a dubious translation:
+lean 3 declaration is
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(SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (HMul.hMul.{u1, u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toDistrib.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) a b)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) a) (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} 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(CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) a) (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) b))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) a) (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) b))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) a) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) b)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (b : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u1} R (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (HMul.hMul.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) a b)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) a) (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R 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+Case conversion may be inaccurate. Consider using '#align quaternion.mul_im_k Quaternion.mul_imKₓ'. -/
 @[simp]
 theorem mul_imK : (a * b).imK = a.re * b.imK + a.imI * b.imJ - a.imJ * b.imI + a.imK * b.re :=
-  (QuaternionAlgebra.hasMul_mul_imK a b).trans <| by
-    simp only [one_mul, neg_mul, sub_eq_add_neg, neg_neg]
+  (QuaternionAlgebra.mul_imK a b).trans <| by simp only [one_mul, neg_mul, sub_eq_add_neg, neg_neg]
 #align quaternion.mul_im_k Quaternion.mul_imK
 
+/- warning: quaternion.coe_mul -> Quaternion.coe_mul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion.coe_mul Quaternion.coe_mulₓ'. -/
 @[simp, norm_cast]
 theorem coe_mul : ((x * y : R) : ℍ[R]) = x * y :=
   QuaternionAlgebra.coe_mul x y
 #align quaternion.coe_mul Quaternion.coe_mul
 
+/- warning: quaternion.coe_pow -> Quaternion.coe_pow is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align quaternion.coe_pow Quaternion.coe_powₓ'. -/
 @[norm_cast, simp]
 theorem coe_pow (n : ℕ) : (↑(x ^ n) : ℍ[R]) = ↑x ^ n :=
   QuaternionAlgebra.coe_pow x n
 #align quaternion.coe_pow Quaternion.coe_pow
 
+/- warning: quaternion.nat_cast_re -> Quaternion.nat_cast_re is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion.nat_cast_re Quaternion.nat_cast_reₓ'. -/
 @[simp, norm_cast]
 theorem nat_cast_re (n : ℕ) : (n : ℍ[R]).re = n :=
   rfl
 #align quaternion.nat_cast_re Quaternion.nat_cast_re
 
+/- warning: quaternion.nat_cast_im_i -> Quaternion.nat_cast_imI is a dubious translation:
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(AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CoeTCₓ.coe.{1, succ u1} Nat (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Nat.castCoe.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddMonoidWithOne.toNatCast.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddGroupWithOne.toAddMonoidWithOne.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommGroupWithOne.toAddGroupWithOne.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toAddCommGroupWithOne.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))))))) n)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align quaternion.nat_cast_im_i Quaternion.nat_cast_imIₓ'. -/
 @[simp, norm_cast]
 theorem nat_cast_imI (n : ℕ) : (n : ℍ[R]).imI = 0 :=
   rfl
 #align quaternion.nat_cast_im_i Quaternion.nat_cast_imI
 
+/- warning: quaternion.nat_cast_im_j -> Quaternion.nat_cast_imJ is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align quaternion.nat_cast_im_j Quaternion.nat_cast_imJₓ'. -/
 @[simp, norm_cast]
 theorem nat_cast_imJ (n : ℕ) : (n : ℍ[R]).imJ = 0 :=
   rfl
 #align quaternion.nat_cast_im_j Quaternion.nat_cast_imJ
 
+/- warning: quaternion.nat_cast_im_k -> Quaternion.nat_cast_imK is a dubious translation:
+lean 3 declaration is
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(AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CoeTCₓ.coe.{1, succ u1} Nat (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Nat.castCoe.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R 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(OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} R (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Nat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNatCast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) n)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align quaternion.nat_cast_im_k Quaternion.nat_cast_imKₓ'. -/
 @[simp, norm_cast]
 theorem nat_cast_imK (n : ℕ) : (n : ℍ[R]).imK = 0 :=
   rfl
 #align quaternion.nat_cast_im_k Quaternion.nat_cast_imK
 
+/- warning: quaternion.nat_cast_im -> Quaternion.nat_cast_im is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align quaternion.nat_cast_im Quaternion.nat_cast_imₓ'. -/
 @[simp, norm_cast]
 theorem nat_cast_im (n : ℕ) : (n : ℍ[R]).im = 0 :=
   rfl
 #align quaternion.nat_cast_im Quaternion.nat_cast_im
 
+/- warning: quaternion.coe_nat_cast -> Quaternion.coe_nat_cast is a dubious translation:
+lean 3 declaration is
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((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) n)) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HasLiftT.mk.{1, succ u1} Nat (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CoeTCₓ.coe.{1, succ u1} Nat (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Nat.castCoe.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))))))) n)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.coe.{u1} R _inst_1 (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n)) (Nat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNatCast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) n)
+Case conversion may be inaccurate. Consider using '#align quaternion.coe_nat_cast Quaternion.coe_nat_castₓ'. -/
 @[norm_cast]
 theorem coe_nat_cast (n : ℕ) : ↑(n : R) = (n : ℍ[R]) :=
   rfl
 #align quaternion.coe_nat_cast Quaternion.coe_nat_cast
 
+/- warning: quaternion.int_cast_re -> Quaternion.int_cast_re is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align quaternion.int_cast_re Quaternion.int_cast_reₓ'. -/
 @[simp, norm_cast]
 theorem int_cast_re (z : ℤ) : (z : ℍ[R]).re = z :=
   rfl
 #align quaternion.int_cast_re Quaternion.int_cast_re
 
+/- warning: quaternion.int_cast_im_i -> Quaternion.int_cast_imI is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (z : Int), Eq.{succ u1} R (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HasLiftT.mk.{1, succ u1} Int (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CoeTCₓ.coe.{1, succ u1} Int (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Int.castCoe.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddGroupWithOne.toHasIntCast.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommGroupWithOne.toAddGroupWithOne.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toAddCommGroupWithOne.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))))) z)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (z : Int), Eq.{succ u1} R (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Int.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toIntCast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) z)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align quaternion.int_cast_im_i Quaternion.int_cast_imIₓ'. -/
 @[simp, norm_cast]
 theorem int_cast_imI (z : ℤ) : (z : ℍ[R]).imI = 0 :=
   rfl
 #align quaternion.int_cast_im_i Quaternion.int_cast_imI
 
+/- warning: quaternion.int_cast_im_j -> Quaternion.int_cast_imJ is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (z : Int), Eq.{succ u1} R (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HasLiftT.mk.{1, succ u1} Int (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CoeTCₓ.coe.{1, succ u1} Int (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Int.castCoe.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddGroupWithOne.toHasIntCast.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommGroupWithOne.toAddGroupWithOne.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toAddCommGroupWithOne.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))))) z)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (z : Int), Eq.{succ u1} R (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Int.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toIntCast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) z)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align quaternion.int_cast_im_j Quaternion.int_cast_imJₓ'. -/
 @[simp, norm_cast]
 theorem int_cast_imJ (z : ℤ) : (z : ℍ[R]).imJ = 0 :=
   rfl
 #align quaternion.int_cast_im_j Quaternion.int_cast_imJ
 
+/- warning: quaternion.int_cast_im_k -> Quaternion.int_cast_imK is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (z : Int), Eq.{succ u1} R (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HasLiftT.mk.{1, succ u1} Int (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CoeTCₓ.coe.{1, succ u1} Int (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Int.castCoe.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddGroupWithOne.toHasIntCast.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommGroupWithOne.toAddGroupWithOne.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toAddCommGroupWithOne.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))))) z)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align quaternion.int_cast_im_k Quaternion.int_cast_imKₓ'. -/
 @[simp, norm_cast]
 theorem int_cast_imK (z : ℤ) : (z : ℍ[R]).imK = 0 :=
   rfl
 #align quaternion.int_cast_im_k Quaternion.int_cast_imK
 
+/- warning: quaternion.int_cast_im -> Quaternion.int_cast_im is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align quaternion.int_cast_im Quaternion.int_cast_imₓ'. -/
 @[simp, norm_cast]
 theorem int_cast_im (z : ℤ) : (z : ℍ[R]).im = 0 :=
   rfl
 #align quaternion.int_cast_im Quaternion.int_cast_im
 
+/- warning: quaternion.coe_int_cast -> Quaternion.coe_int_cast is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align quaternion.coe_int_cast Quaternion.coe_int_castₓ'. -/
 @[norm_cast]
 theorem coe_int_cast (z : ℤ) : ↑(z : R) = (z : ℍ[R]) :=
   rfl
 #align quaternion.coe_int_cast Quaternion.coe_int_cast
 
+/- warning: quaternion.coe_injective -> Quaternion.coe_injective is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion.coe_injective Quaternion.coe_injectiveₓ'. -/
 theorem coe_injective : Function.Injective (coe : R → ℍ[R]) :=
   QuaternionAlgebra.coe_injective
 #align quaternion.coe_injective Quaternion.coe_injective
 
+/- warning: quaternion.coe_inj -> Quaternion.coe_inj is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion.coe_inj Quaternion.coe_injₓ'. -/
 @[simp]
 theorem coe_inj {x y : R} : (x : ℍ[R]) = y ↔ x = y :=
   coe_injective.eq_iff
 #align quaternion.coe_inj Quaternion.coe_inj
 
+/- warning: quaternion.smul_re -> Quaternion.smul_re is a dubious translation:
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+  forall {S : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (a : Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) [_inst_2 : SMul.{u1, u2} S R] (s : S), Eq.{succ u2} R (QuaternionAlgebra.re.{u2} R (Neg.neg.{u2} R (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))))) (Neg.neg.{u2} R (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))))) (SMul.smul.{u1, u2} S (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (Quaternion.hasSmul.{u1, u2} S R _inst_1 _inst_2) s a)) (SMul.smul.{u1, u2} S R _inst_2 s (QuaternionAlgebra.re.{u2} R (Neg.neg.{u2} R (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))))) (Neg.neg.{u2} R (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))))) a))
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+  forall {S : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) [_inst_2 : SMul.{u2, u1} S R] (s : S), Eq.{succ u1} R (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (HSMul.hSMul.{u2, u1, u1} S (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSMul.{u2, u1} S (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instSMulQuaternionToOneToSemiringToCommSemiringToNegToRing.{u2, u1} S R _inst_1 _inst_2)) s a)) (HSMul.hSMul.{u2, u1, u1} S R R (instHSMul.{u2, u1} S R _inst_2) s (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) a))
+Case conversion may be inaccurate. Consider using '#align quaternion.smul_re Quaternion.smul_reₓ'. -/
 @[simp]
 theorem smul_re [SMul S R] (s : S) : (s • a).re = s • a.re :=
   rfl
 #align quaternion.smul_re Quaternion.smul_re
 
+/- warning: quaternion.smul_im_i -> Quaternion.smul_imI is a dubious translation:
+lean 3 declaration is
+  forall {S : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (a : Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) [_inst_2 : SMul.{u1, u2} S R] (s : S), Eq.{succ u2} R (QuaternionAlgebra.imI.{u2} R (Neg.neg.{u2} R (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))))) (Neg.neg.{u2} R (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))))) (SMul.smul.{u1, u2} S (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (Quaternion.hasSmul.{u1, u2} S R _inst_1 _inst_2) s a)) (SMul.smul.{u1, u2} S R _inst_2 s (QuaternionAlgebra.imI.{u2} R (Neg.neg.{u2} R (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))))) (Neg.neg.{u2} R (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))))) a))
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+Case conversion may be inaccurate. Consider using '#align quaternion.smul_im_i Quaternion.smul_imIₓ'. -/
 @[simp]
 theorem smul_imI [SMul S R] (s : S) : (s • a).imI = s • a.imI :=
   rfl
 #align quaternion.smul_im_i Quaternion.smul_imI
 
+/- warning: quaternion.smul_im_j -> Quaternion.smul_imJ is a dubious translation:
+lean 3 declaration is
+  forall {S : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (a : Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) [_inst_2 : SMul.{u1, u2} S R] (s : S), Eq.{succ u2} R (QuaternionAlgebra.imJ.{u2} R (Neg.neg.{u2} R (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))))) (Neg.neg.{u2} R (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))))) (SMul.smul.{u1, u2} S (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (Quaternion.hasSmul.{u1, u2} S R _inst_1 _inst_2) s a)) (SMul.smul.{u1, u2} S R _inst_2 s (QuaternionAlgebra.imJ.{u2} R (Neg.neg.{u2} R (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))))) (Neg.neg.{u2} R (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))))) a))
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+Case conversion may be inaccurate. Consider using '#align quaternion.smul_im_j Quaternion.smul_imJₓ'. -/
 @[simp]
 theorem smul_imJ [SMul S R] (s : S) : (s • a).imJ = s • a.imJ :=
   rfl
 #align quaternion.smul_im_j Quaternion.smul_imJ
 
+/- warning: quaternion.smul_im_k -> Quaternion.smul_imK is a dubious translation:
+lean 3 declaration is
+  forall {S : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (a : Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) [_inst_2 : SMul.{u1, u2} S R] (s : S), Eq.{succ u2} R (QuaternionAlgebra.imK.{u2} R (Neg.neg.{u2} R (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))))) (Neg.neg.{u2} R (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))))) (SMul.smul.{u1, u2} S (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (Quaternion.hasSmul.{u1, u2} S R _inst_1 _inst_2) s a)) (SMul.smul.{u1, u2} S R _inst_2 s (QuaternionAlgebra.imK.{u2} R (Neg.neg.{u2} R (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))))) (Neg.neg.{u2} R (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))))) a))
+but is expected to have type
+  forall {S : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) [_inst_2 : SMul.{u2, u1} S R] (s : S), Eq.{succ u1} R (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (HSMul.hSMul.{u2, u1, u1} S (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSMul.{u2, u1} S (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instSMulQuaternionToOneToSemiringToCommSemiringToNegToRing.{u2, u1} S R _inst_1 _inst_2)) s a)) (HSMul.hSMul.{u2, u1, u1} S R R (instHSMul.{u2, u1} S R _inst_2) s (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) a))
+Case conversion may be inaccurate. Consider using '#align quaternion.smul_im_k Quaternion.smul_imKₓ'. -/
 @[simp]
 theorem smul_imK [SMul S R] (s : S) : (s • a).imK = s • a.imK :=
   rfl
 #align quaternion.smul_im_k Quaternion.smul_imK
 
+/- warning: quaternion.smul_im -> Quaternion.smul_im is a dubious translation:
+lean 3 declaration is
+  forall {S : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (a : Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) [_inst_2 : SMulZeroClass.{u1, u2} S R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))))] (s : S), Eq.{succ u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (Quaternion.im.{u2} R _inst_1 (SMul.smul.{u1, u2} S (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (Quaternion.hasSmul.{u1, u2} S R _inst_1 (SMulZeroClass.toHasSmul.{u1, u2} S R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) _inst_2)) s a)) (SMul.smul.{u1, u2} S (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (Quaternion.hasSmul.{u1, u2} S R _inst_1 (SMulZeroClass.toHasSmul.{u1, u2} S R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) _inst_2)) s (Quaternion.im.{u2} R _inst_1 a))
+but is expected to have type
+  forall {S : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) [_inst_2 : SMulZeroClass.{u2, u1} S R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))] (s : S), Eq.{succ u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.im.{u1} R _inst_1 (HSMul.hSMul.{u2, u1, u1} S (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSMul.{u2, u1} S (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instSMulQuaternionToOneToSemiringToCommSemiringToNegToRing.{u2, u1} S R _inst_1 (SMulZeroClass.toSMul.{u2, u1} S R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_2))) s a)) (HSMul.hSMul.{u2, u1, u1} S (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSMul.{u2, u1} S (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instSMulQuaternionToOneToSemiringToCommSemiringToNegToRing.{u2, u1} S R _inst_1 (SMulZeroClass.toSMul.{u2, u1} S R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_2))) s (Quaternion.im.{u1} R _inst_1 a))
+Case conversion may be inaccurate. Consider using '#align quaternion.smul_im Quaternion.smul_imₓ'. -/
 @[simp]
 theorem smul_im [SMulZeroClass S R] (s : S) : (s • a).im = s • a.im :=
   ext _ _ (smul_zero _).symm rfl rfl rfl
 #align quaternion.smul_im Quaternion.smul_im
 
+/- warning: quaternion.coe_smul -> Quaternion.coe_smul is a dubious translation:
+lean 3 declaration is
+  forall {S : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] [_inst_2 : SMulZeroClass.{u1, u2} S R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))))] (s : S) (r : R), Eq.{succ u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) R (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (HasLiftT.mk.{succ u2, succ u2} R (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (CoeTCₓ.coe.{succ u2, succ u2} R (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (Quaternion.hasCoeT.{u2} R _inst_1))) (SMul.smul.{u1, u2} S R (SMulZeroClass.toHasSmul.{u1, u2} S R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) _inst_2) s r)) (SMul.smul.{u1, u2} S (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (Quaternion.hasSmul.{u1, u2} S R _inst_1 (SMulZeroClass.toHasSmul.{u1, u2} S R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) _inst_2)) s ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) R (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (HasLiftT.mk.{succ u2, succ u2} R (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (CoeTCₓ.coe.{succ u2, succ u2} R (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (Quaternion.hasCoeT.{u2} R _inst_1))) r))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align quaternion.coe_smul Quaternion.coe_smulₓ'. -/
 @[simp, norm_cast]
 theorem coe_smul [SMulZeroClass S R] (s : S) (r : R) : (↑(s • r) : ℍ[R]) = s • ↑r :=
   QuaternionAlgebra.coe_smul _ _
 #align quaternion.coe_smul Quaternion.coe_smul
 
+/- warning: quaternion.coe_commutes -> Quaternion.coe_commutes is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align quaternion.coe_commutes Quaternion.coe_commutesₓ'. -/
 theorem coe_commutes : ↑r * a = a * r :=
   QuaternionAlgebra.coe_commutes r a
 #align quaternion.coe_commutes Quaternion.coe_commutes
 
+/- warning: quaternion.coe_commute -> Quaternion.coe_commute is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion.coe_commute Quaternion.coe_commuteₓ'. -/
 theorem coe_commute : Commute (↑r) a :=
   QuaternionAlgebra.coe_commute r a
 #align quaternion.coe_commute Quaternion.coe_commute
 
+/- warning: quaternion.coe_mul_eq_smul -> Quaternion.coe_mul_eq_smul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion.coe_mul_eq_smul Quaternion.coe_mul_eq_smulₓ'. -/
 theorem coe_mul_eq_smul : ↑r * a = r • a :=
   QuaternionAlgebra.coe_mul_eq_smul r a
 #align quaternion.coe_mul_eq_smul Quaternion.coe_mul_eq_smul
 
+/- warning: quaternion.mul_coe_eq_smul -> Quaternion.mul_coe_eq_smul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion.mul_coe_eq_smul Quaternion.mul_coe_eq_smulₓ'. -/
 theorem mul_coe_eq_smul : a * r = r • a :=
   QuaternionAlgebra.mul_coe_eq_smul r a
 #align quaternion.mul_coe_eq_smul Quaternion.mul_coe_eq_smul
 
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+Case conversion may be inaccurate. Consider using '#align quaternion.algebra_map_def Quaternion.algebraMap_defₓ'. -/
 @[simp]
 theorem algebraMap_def : ⇑(algebraMap R ℍ[R]) = coe :=
   rfl
 #align quaternion.algebra_map_def Quaternion.algebraMap_def
 
+/- warning: quaternion.smul_coe -> Quaternion.smul_coe is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion.smul_coe Quaternion.smul_coeₓ'. -/
 theorem smul_coe : x • (y : ℍ[R]) = ↑(x * y) :=
   QuaternionAlgebra.smul_coe x y
 #align quaternion.smul_coe Quaternion.smul_coe
@@ -1138,79 +2098,181 @@ instance : Module.Finite R ℍ[R] :=
 instance : Module.Free R ℍ[R] :=
   QuaternionAlgebra.Module.free _ _
 
+/- warning: quaternion.rank_eq_four -> Quaternion.rank_eq_four is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align quaternion.rank_eq_four Quaternion.rank_eq_fourₓ'. -/
 theorem rank_eq_four [StrongRankCondition R] : Module.rank R ℍ[R] = 4 :=
   QuaternionAlgebra.rank_eq_four _ _
 #align quaternion.rank_eq_four Quaternion.rank_eq_four
 
+/- warning: quaternion.finrank_eq_four -> Quaternion.finrank_eq_four is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align quaternion.finrank_eq_four Quaternion.finrank_eq_fourₓ'. -/
 theorem finrank_eq_four [StrongRankCondition R] : FiniteDimensional.finrank R ℍ[R] = 4 :=
   QuaternionAlgebra.finrank_eq_four _ _
 #align quaternion.finrank_eq_four Quaternion.finrank_eq_four
 
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(Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) a)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u1} R (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Star.star.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instStarQuaternionToOneToSemiringToCommSemiringToNegToRing.{u1} R _inst_1) a)) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) a)
+Case conversion may be inaccurate. Consider using '#align quaternion.star_re Quaternion.star_reₓ'. -/
 @[simp]
 theorem star_re : (star a).re = a.re :=
   rfl
 #align quaternion.star_re Quaternion.star_re
 
+/- warning: quaternion.star_im_i -> Quaternion.star_imI is a dubious translation:
+lean 3 declaration is
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(CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.starRing.{u1} R _inst_1)))) a)) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) a))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u1} R (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Star.star.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instStarQuaternionToOneToSemiringToCommSemiringToNegToRing.{u1} R _inst_1) a)) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) a))
+Case conversion may be inaccurate. Consider using '#align quaternion.star_im_i Quaternion.star_imIₓ'. -/
 @[simp]
 theorem star_imI : (star a).imI = -a.imI :=
   rfl
 #align quaternion.star_im_i Quaternion.star_imI
 
+/- warning: quaternion.star_im_j -> Quaternion.star_imJ is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))), Eq.{succ u1} R (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Star.star.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (InvolutiveStar.toHasStar.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (StarAddMonoid.toHasInvolutiveStar.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.starRing.{u1} R _inst_1)))) a)) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) a))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u1} R (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Star.star.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instStarQuaternionToOneToSemiringToCommSemiringToNegToRing.{u1} R _inst_1) a)) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) a))
+Case conversion may be inaccurate. Consider using '#align quaternion.star_im_j Quaternion.star_imJₓ'. -/
 @[simp]
 theorem star_imJ : (star a).imJ = -a.imJ :=
   rfl
 #align quaternion.star_im_j Quaternion.star_imJ
 
+/- warning: quaternion.star_im_k -> Quaternion.star_imK is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))), Eq.{succ u1} R (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Star.star.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (InvolutiveStar.toHasStar.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (StarAddMonoid.toHasInvolutiveStar.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.starRing.{u1} R _inst_1)))) a)) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) a))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u1} R (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Star.star.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instStarQuaternionToOneToSemiringToCommSemiringToNegToRing.{u1} R _inst_1) a)) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) a))
+Case conversion may be inaccurate. Consider using '#align quaternion.star_im_k Quaternion.star_imKₓ'. -/
 @[simp]
 theorem star_imK : (star a).imK = -a.imK :=
   rfl
 #align quaternion.star_im_k Quaternion.star_imK
 
+/- warning: quaternion.star_im -> Quaternion.star_im is a dubious translation:
+lean 3 declaration is
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(AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddGroup.toSubNegMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddGroupWithOne.toAddGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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_inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))))) (Quaternion.im.{u1} R _inst_1 a))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.im.{u1} R _inst_1 (Star.star.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instStarQuaternionToOneToSemiringToCommSemiringToNegToRing.{u1} R _inst_1) a)) (Neg.neg.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNeg.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.im.{u1} R _inst_1 a))
+Case conversion may be inaccurate. Consider using '#align quaternion.star_im Quaternion.star_imₓ'. -/
 @[simp]
 theorem star_im : (star a).im = -a.im :=
   a.im_star
 #align quaternion.star_im Quaternion.star_im
 
+/- warning: quaternion.self_add_star' -> Quaternion.self_add_star' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))), Eq.{succ u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} 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(AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.starRing.{u1} R _inst_1)))) a)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HasLiftT.mk.{succ u1, succ u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CoeTCₓ.coe.{succ u1, succ u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.hasCoeT.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (OfNat.ofNat.{u1} R 2 (OfNat.mk.{u1} R 2 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) a)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a (Star.star.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instStarQuaternionToOneToSemiringToCommSemiringToNegToRing.{u1} R _inst_1) a)) (Quaternion.coe.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (OfNat.ofNat.{u1} R 2 (instOfNat.{u1} R 2 (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) a)))
+Case conversion may be inaccurate. Consider using '#align quaternion.self_add_star' Quaternion.self_add_star'ₓ'. -/
 theorem self_add_star' : a + star a = ↑(2 * a.re) :=
   a.self_add_star'
 #align quaternion.self_add_star' Quaternion.self_add_star'
 
+/- warning: quaternion.self_add_star -> Quaternion.self_add_star is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))), Eq.{succ u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} 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(CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (instHAdd.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Distrib.toHasAdd.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toDistrib.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) a (Star.star.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (InvolutiveStar.toHasStar.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (StarAddMonoid.toHasInvolutiveStar.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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_inst_1))))))) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Quaternion.{u1} R 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(AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) 2 (OfNat.mk.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) 2 (bit0.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R 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(Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HasLiftT.mk.{succ u1, succ u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CoeTCₓ.coe.{succ u1, succ u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.hasCoeT.{u1} R _inst_1))) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) a)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a (Star.star.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instStarQuaternionToOneToSemiringToCommSemiringToNegToRing.{u1} R _inst_1) a)) (HMul.hMul.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 2 (instOfNat.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 2 (Semiring.toNatCast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Quaternion.coe.{u1} R _inst_1 (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) a)))
+Case conversion may be inaccurate. Consider using '#align quaternion.self_add_star Quaternion.self_add_starₓ'. -/
 theorem self_add_star : a + star a = 2 * a.re :=
   a.self_add_star
 #align quaternion.self_add_star Quaternion.self_add_star
 
+/- warning: quaternion.star_add_self' -> Quaternion.star_add_self' is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Star.star.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instStarQuaternionToOneToSemiringToCommSemiringToNegToRing.{u1} R _inst_1) a) a) (Quaternion.coe.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (OfNat.ofNat.{u1} R 2 (instOfNat.{u1} R 2 (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) a)))
+Case conversion may be inaccurate. Consider using '#align quaternion.star_add_self' Quaternion.star_add_self'ₓ'. -/
 theorem star_add_self' : star a + a = ↑(2 * a.re) :=
   a.star_add_self'
 #align quaternion.star_add_self' Quaternion.star_add_self'
 
+/- warning: quaternion.star_add_self -> Quaternion.star_add_self is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) a)))
+Case conversion may be inaccurate. Consider using '#align quaternion.star_add_self Quaternion.star_add_selfₓ'. -/
 theorem star_add_self : star a + a = 2 * a.re :=
   a.star_add_self
 #align quaternion.star_add_self Quaternion.star_add_self
 
+/- warning: quaternion.star_eq_two_re_sub -> Quaternion.star_eq_two_re_sub is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align quaternion.star_eq_two_re_sub Quaternion.star_eq_two_re_subₓ'. -/
 theorem star_eq_two_re_sub : star a = ↑(2 * a.re) - a :=
   a.star_eq_two_re_sub
 #align quaternion.star_eq_two_re_sub Quaternion.star_eq_two_re_sub
 
+/- warning: quaternion.star_coe -> Quaternion.star_coe is a dubious translation:
+lean 3 declaration is
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(AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.starRing.{u1} R _inst_1)))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HasLiftT.mk.{succ u1, succ u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CoeTCₓ.coe.{succ u1, succ u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.hasCoeT.{u1} R _inst_1))) x)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HasLiftT.mk.{succ u1, succ u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CoeTCₓ.coe.{succ u1, succ u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.hasCoeT.{u1} R _inst_1))) x)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (x : R), Eq.{succ u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Star.star.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instStarQuaternionToOneToSemiringToCommSemiringToNegToRing.{u1} R _inst_1) (Quaternion.coe.{u1} R _inst_1 x)) (Quaternion.coe.{u1} R _inst_1 x)
+Case conversion may be inaccurate. Consider using '#align quaternion.star_coe Quaternion.star_coeₓ'. -/
 @[simp, norm_cast]
 theorem star_coe : star (x : ℍ[R]) = x :=
   QuaternionAlgebra.star_coe x
 #align quaternion.star_coe Quaternion.star_coe
 
+/- warning: quaternion.im_star -> Quaternion.im_star is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))), Eq.{succ u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Star.star.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (InvolutiveStar.toHasStar.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (StarAddMonoid.toHasInvolutiveStar.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.starRing.{u1} R _inst_1)))) (Quaternion.im.{u1} R _inst_1 a)) (Neg.neg.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R 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(AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommGroupWithOne.toAddGroupWithOne.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toAddCommGroupWithOne.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))))) (Quaternion.im.{u1} R _inst_1 a))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Star.star.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instStarQuaternionToOneToSemiringToCommSemiringToNegToRing.{u1} R _inst_1) (Quaternion.im.{u1} R _inst_1 a)) (Neg.neg.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNeg.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.im.{u1} R _inst_1 a))
+Case conversion may be inaccurate. Consider using '#align quaternion.im_star Quaternion.im_starₓ'. -/
 @[simp]
 theorem im_star : star a.im = -a.im :=
   QuaternionAlgebra.im_star _
 #align quaternion.im_star Quaternion.im_star
 
+/- warning: quaternion.star_smul -> Quaternion.star_smul is a dubious translation:
+lean 3 declaration is
+  forall {S : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] [_inst_2 : Monoid.{u1} S] [_inst_3 : DistribMulAction.{u1, u2} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1)))))] (s : S) (a : Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))), Eq.{succ u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (Star.star.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (InvolutiveStar.toHasStar.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (StarAddMonoid.toHasInvolutiveStar.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (Ring.toNonUnitalRing.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (Quaternion.ring.{u2} R _inst_1)))))) (StarRing.toStarAddMonoid.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (Ring.toNonUnitalRing.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (Quaternion.ring.{u2} R _inst_1))) (Quaternion.starRing.{u2} R _inst_1)))) (SMul.smul.{u1, u2} S (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (Quaternion.hasSmul.{u1, u2} S R _inst_1 (SMulZeroClass.toHasSmul.{u1, u2} S R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (DistribSMul.toSmulZeroClass.{u1, u2} S R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, u2} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) _inst_3)))) s a)) (SMul.smul.{u1, u2} S (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (Quaternion.hasSmul.{u1, u2} S R _inst_1 (SMulZeroClass.toHasSmul.{u1, u2} S R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (DistribSMul.toSmulZeroClass.{u1, u2} S R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, u2} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) _inst_3)))) s (Star.star.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (InvolutiveStar.toHasStar.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (StarAddMonoid.toHasInvolutiveStar.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (Ring.toNonUnitalRing.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (Quaternion.ring.{u2} R _inst_1)))))) (StarRing.toStarAddMonoid.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (Ring.toNonUnitalRing.{u2} (Quaternion.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) (Quaternion.ring.{u2} R _inst_1))) (Quaternion.starRing.{u2} R _inst_1)))) a))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align quaternion.star_smul Quaternion.star_smulₓ'. -/
 @[simp]
 theorem star_smul [Monoid S] [DistribMulAction S R] (s : S) (a : ℍ[R]) :
     star (s • a) = s • star a :=
   QuaternionAlgebra.star_smul _ _
 #align quaternion.star_smul Quaternion.star_smul
 
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+Case conversion may be inaccurate. Consider using '#align quaternion.eq_re_of_eq_coe Quaternion.eq_re_of_eq_coeₓ'. -/
 theorem eq_re_of_eq_coe {a : ℍ[R]} {x : R} (h : a = x) : a = a.re :=
   QuaternionAlgebra.eq_re_of_eq_coe h
 #align quaternion.eq_re_of_eq_coe Quaternion.eq_re_of_eq_coe
 
+/- warning: quaternion.eq_re_iff_mem_range_coe -> Quaternion.eq_re_iff_mem_range_coe is a dubious translation:
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(CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CoeTCₓ.coe.{succ u1, succ u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.hasCoeT.{u1} R _inst_1))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))}, Iff (Eq.{succ u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) a (Quaternion.coe.{u1} R _inst_1 (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) a))) (Membership.mem.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Set.instMembershipSet.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) a (Set.range.{u1, succ u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Quaternion.coe.{u1} R _inst_1)))
+Case conversion may be inaccurate. Consider using '#align quaternion.eq_re_iff_mem_range_coe Quaternion.eq_re_iff_mem_range_coeₓ'. -/
 theorem eq_re_iff_mem_range_coe {a : ℍ[R]} : a = a.re ↔ a ∈ Set.range (coe : R → ℍ[R]) :=
   QuaternionAlgebra.eq_re_iff_mem_range_coe
 #align quaternion.eq_re_iff_mem_range_coe Quaternion.eq_re_iff_mem_range_coe
@@ -1219,11 +2281,23 @@ section CharZero
 
 variable [NoZeroDivisors R] [CharZero R]
 
+/- warning: quaternion.star_eq_self -> Quaternion.star_eq_self is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))] [_inst_3 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))] {a : Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))}, Iff (Eq.{succ u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Star.star.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (InvolutiveStar.toHasStar.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (StarAddMonoid.toHasInvolutiveStar.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.starRing.{u1} R _inst_1)))) a) a) (Eq.{succ u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) a ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HasLiftT.mk.{succ u1, succ u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CoeTCₓ.coe.{succ u1, succ u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.hasCoeT.{u1} R _inst_1))) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) a)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))] [_inst_3 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))] {a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))}, Iff (Eq.{succ u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Star.star.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instStarQuaternionToOneToSemiringToCommSemiringToNegToRing.{u1} R _inst_1) a) a) (Eq.{succ u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) a (Quaternion.coe.{u1} R _inst_1 (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) a)))
+Case conversion may be inaccurate. Consider using '#align quaternion.star_eq_self Quaternion.star_eq_selfₓ'. -/
 @[simp]
 theorem star_eq_self {a : ℍ[R]} : star a = a ↔ a = a.re :=
   QuaternionAlgebra.star_eq_self
 #align quaternion.star_eq_self Quaternion.star_eq_self
 
+/- warning: quaternion.star_eq_neg -> Quaternion.star_eq_neg is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))] [_inst_3 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))] {a : Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))}, Iff (Eq.{succ u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Star.star.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (InvolutiveStar.toHasStar.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (StarAddMonoid.toHasInvolutiveStar.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.starRing.{u1} R _inst_1)))) a) (Neg.neg.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddGroup.toSubNegMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddGroupWithOne.toAddGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommGroupWithOne.toAddGroupWithOne.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toAddCommGroupWithOne.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))))) a)) (Eq.{succ u1} R (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) a) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))] [_inst_3 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))] {a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))}, Iff (Eq.{succ u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Star.star.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instStarQuaternionToOneToSemiringToCommSemiringToNegToRing.{u1} R _inst_1) a) (Neg.neg.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNeg.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) a)) (Eq.{succ u1} R (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) a) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align quaternion.star_eq_neg Quaternion.star_eq_negₓ'. -/
 @[simp]
 theorem star_eq_neg {a : ℍ[R]} : star a = -a ↔ a.re = 0 :=
   QuaternionAlgebra.star_eq_neg
@@ -1231,26 +2305,56 @@ theorem star_eq_neg {a : ℍ[R]} : star a = -a ↔ a.re = 0 :=
 
 end CharZero
 
+/- warning: quaternion.star_mul_eq_coe -> Quaternion.star_mul_eq_coe is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))), Eq.{succ u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HMul.hMul.{u1, u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (instHMul.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Distrib.toHasMul.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toDistrib.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (Star.star.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R 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(StarRing.toStarAddMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R 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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align quaternion.star_mul_eq_coe Quaternion.star_mul_eq_coeₓ'. -/
 theorem star_mul_eq_coe : star a * a = (star a * a).re :=
   a.star_mul_eq_coe
 #align quaternion.star_mul_eq_coe Quaternion.star_mul_eq_coe
 
+/- warning: quaternion.mul_star_eq_coe -> Quaternion.mul_star_eq_coe is a dubious translation:
+lean 3 declaration is
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(CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Distrib.toHasMul.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toDistrib.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R 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(AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (StarAddMonoid.toHasInvolutiveStar.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R 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(StarRing.toStarAddMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.starRing.{u1} R _inst_1)))) a))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) a (Star.star.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instStarQuaternionToOneToSemiringToCommSemiringToNegToRing.{u1} R _inst_1) a)) (Quaternion.coe.{u1} R _inst_1 (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (HMul.hMul.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) a (Star.star.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instStarQuaternionToOneToSemiringToCommSemiringToNegToRing.{u1} R _inst_1) a))))
+Case conversion may be inaccurate. Consider using '#align quaternion.mul_star_eq_coe Quaternion.mul_star_eq_coeₓ'. -/
 theorem mul_star_eq_coe : a * star a = (a * star a).re :=
   a.mul_star_eq_coe
 #align quaternion.mul_star_eq_coe Quaternion.mul_star_eq_coe
 
 open MulOpposite
 
+/- warning: quaternion.star_ae -> Quaternion.starAe is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R], AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (MulOpposite.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.algebra.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R], AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))
+Case conversion may be inaccurate. Consider using '#align quaternion.star_ae Quaternion.starAeₓ'. -/
 /-- Quaternion conjugate as an `alg_equiv` to the opposite ring. -/
 def starAe : ℍ[R] ≃ₐ[R] ℍ[R]ᵐᵒᵖ :=
   QuaternionAlgebra.starAe
 #align quaternion.star_ae Quaternion.starAe
 
+/- warning: quaternion.coe_star_ae -> Quaternion.coe_starAe is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R], Eq.{succ u1} ((Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (MulOpposite.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R 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(AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.algebra.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) 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(AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R 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+but is expected to have type
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(Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulOpposite.semiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOpposite.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulOpposite.op.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Star.star.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instStarQuaternionToOneToSemiringToCommSemiringToNegToRing.{u1} R _inst_1)))
+Case conversion may be inaccurate. Consider using '#align quaternion.coe_star_ae Quaternion.coe_starAeₓ'. -/
 @[simp]
 theorem coe_starAe : ⇑(starAe : ℍ[R] ≃ₐ[R] ℍ[R]ᵐᵒᵖ) = op ∘ star :=
   rfl
 #align quaternion.coe_star_ae Quaternion.coe_starAe
 
+/- warning: quaternion.norm_sq -> Quaternion.normSq is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R], MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R], MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))
+Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq Quaternion.normSqₓ'. -/
 /-- Square of the norm. -/
 def normSq : ℍ[R] →*₀ R where
   toFun a := (a * star a).re
@@ -1263,53 +2367,131 @@ def normSq : ℍ[R] →*₀ R where
           ← mul_assoc, x.mul_star_eq_coe, ← coe_mul]
 #align quaternion.norm_sq Quaternion.normSq
 
+/- warning: quaternion.norm_sq_def -> Quaternion.normSq_def is a dubious translation:
+lean 3 declaration is
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(CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.starRing.{u1} R _inst_1)))) a)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} 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(Quaternion.normSq.{u1} R _inst_1) a) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (HMul.hMul.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) a (Star.star.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instStarQuaternionToOneToSemiringToCommSemiringToNegToRing.{u1} R _inst_1) a)))
+Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_def Quaternion.normSq_defₓ'. -/
 theorem normSq_def : normSq a = (a * star a).re :=
   rfl
 #align quaternion.norm_sq_def Quaternion.normSq_def
 
+/- warning: quaternion.norm_sq_def' -> Quaternion.normSq_def' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) R 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(Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Quaternion.normSq.{u1} R _inst_1) a) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R 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a) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) 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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} 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Nat 2 (instOfNatNat 2))))
+Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_def' Quaternion.normSq_def'ₓ'. -/
 theorem normSq_def' : normSq a = a.1 ^ 2 + a.2 ^ 2 + a.3 ^ 2 + a.4 ^ 2 := by
   simp only [norm_sq_def, sq, mul_neg, sub_neg_eq_add, mul_re, star_re, star_im_i, star_im_j,
     star_im_k]
 #align quaternion.norm_sq_def' Quaternion.normSq_def'
 
+/- warning: quaternion.norm_sq_coe -> Quaternion.normSq_coe is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (Quaternion.coe.{u1} R _inst_1 x)) (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) x (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
+Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_coe Quaternion.normSq_coeₓ'. -/
 theorem normSq_coe : normSq (x : ℍ[R]) = x ^ 2 := by
   rw [norm_sq_def, star_coe, ← coe_mul, coe_re, sq]
 #align quaternion.norm_sq_coe Quaternion.normSq_coe
 
+/- warning: quaternion.norm_sq_star -> Quaternion.normSq_star is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R 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(Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Quaternion.normSq.{u1} R _inst_1) (Star.star.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (InvolutiveStar.toHasStar.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} 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(StarRing.toStarAddMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.starRing.{u1} R _inst_1)))) a)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> R) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Quaternion.normSq.{u1} R _inst_1) a)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (Star.star.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instStarQuaternionToOneToSemiringToCommSemiringToNegToRing.{u1} R _inst_1) a)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (_x : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (MulOneClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Quaternion.normSq.{u1} R _inst_1) (Star.star.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instStarQuaternionToOneToSemiringToCommSemiringToNegToRing.{u1} R _inst_1) a)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (_x : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (MulOneClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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+Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_star Quaternion.normSq_starₓ'. -/
 @[simp]
 theorem normSq_star : normSq (star a) = normSq a := by simp [norm_sq_def']
 #align quaternion.norm_sq_star Quaternion.normSq_star
 
+/- warning: quaternion.norm_sq_nat_cast -> Quaternion.normSq_nat_cast is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_nat_cast Quaternion.normSq_nat_castₓ'. -/
 @[norm_cast]
 theorem normSq_nat_cast (n : ℕ) : normSq (n : ℍ[R]) = n ^ 2 := by rw [← coe_nat_cast, norm_sq_coe]
 #align quaternion.norm_sq_nat_cast Quaternion.normSq_nat_cast
 
+/- warning: quaternion.norm_sq_int_cast -> Quaternion.normSq_int_cast is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (z : Int), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> R) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R 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(AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Quaternion.normSq.{u1} R _inst_1) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HasLiftT.mk.{1, succ u1} Int (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CoeTCₓ.coe.{1, succ u1} Int (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Int.castCoe.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddGroupWithOne.toHasIntCast.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommGroupWithOne.toAddGroupWithOne.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toAddCommGroupWithOne.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))))) z)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) z) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (z : Int), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (Int.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toIntCast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) z)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (_x : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Quaternion.normSq.{u1} R _inst_1) (Int.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toIntCast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) z)) (HPow.hPow.{u1, 0, u1} R Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (Int.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toIntCast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) z)) (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Int.cast.{u1} R (Ring.toIntCast.{u1} R (CommRing.toRing.{u1} R _inst_1)) z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
+Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_int_cast Quaternion.normSq_int_castₓ'. -/
 @[norm_cast]
 theorem normSq_int_cast (z : ℤ) : normSq (z : ℍ[R]) = z ^ 2 := by rw [← coe_int_cast, norm_sq_coe]
 #align quaternion.norm_sq_int_cast Quaternion.normSq_int_cast
 
+/- warning: quaternion.norm_sq_neg -> Quaternion.normSq_neg is a dubious translation:
+lean 3 declaration is
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_inst_1)))))) a)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> R) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Quaternion.normSq.{u1} R _inst_1) a)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (Neg.neg.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNeg.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) a)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (_x : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (MulOneClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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+Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_neg Quaternion.normSq_negₓ'. -/
 @[simp]
 theorem normSq_neg : normSq (-a) = normSq a := by simp only [norm_sq_def, star_neg, neg_mul_neg]
 #align quaternion.norm_sq_neg Quaternion.normSq_neg
 
+/- warning: quaternion.self_mul_star -> Quaternion.self_mul_star is a dubious translation:
+lean 3 declaration is
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(CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (instHMul.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Distrib.toHasMul.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toDistrib.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) a (Star.star.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (InvolutiveStar.toHasStar.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (StarAddMonoid.toHasInvolutiveStar.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.starRing.{u1} R _inst_1)))) a)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HasLiftT.mk.{succ u1, succ u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CoeTCₓ.coe.{succ u1, succ u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.hasCoeT.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> R) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Quaternion.normSq.{u1} R _inst_1) a))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) a (Star.star.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instStarQuaternionToOneToSemiringToCommSemiringToNegToRing.{u1} R _inst_1) a)) (Quaternion.coe.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R 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(Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} 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(CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Quaternion.normSq.{u1} R _inst_1) a))
+Case conversion may be inaccurate. Consider using '#align quaternion.self_mul_star Quaternion.self_mul_starₓ'. -/
 theorem self_mul_star : a * star a = normSq a := by rw [mul_star_eq_coe, norm_sq_def]
 #align quaternion.self_mul_star Quaternion.self_mul_star
 
+/- warning: quaternion.star_mul_self -> Quaternion.star_mul_self is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))), Eq.{succ u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HMul.hMul.{u1, u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} 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(AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toDistrib.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (Star.star.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (InvolutiveStar.toHasStar.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (StarAddMonoid.toHasInvolutiveStar.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.starRing.{u1} R _inst_1)))) a) a) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HasLiftT.mk.{succ u1, succ u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CoeTCₓ.coe.{succ u1, succ u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.hasCoeT.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> R) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Quaternion.normSq.{u1} R _inst_1) a))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Quaternion.{u1} R 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+Case conversion may be inaccurate. Consider using '#align quaternion.star_mul_self Quaternion.star_mul_selfₓ'. -/
 theorem star_mul_self : star a * a = normSq a := by rw [star_comm_self', self_mul_star]
 #align quaternion.star_mul_self Quaternion.star_mul_self
 
+/- warning: quaternion.im_sq -> Quaternion.im_sq is a dubious translation:
+lean 3 declaration is
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(AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HasLiftT.mk.{succ u1, succ u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CoeTCₓ.coe.{succ u1, succ u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.hasCoeT.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> R) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Quaternion.normSq.{u1} R _inst_1) (Quaternion.im.{u1} R _inst_1 a))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (Quaternion.im.{u1} R _inst_1 a)) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (Quaternion.im.{u1} R _inst_1 a)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (Quaternion.im.{u1} R _inst_1 a)) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (Quaternion.im.{u1} R _inst_1 a)) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (Quaternion.im.{u1} R _inst_1 a)) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (Quaternion.im.{u1} R _inst_1 a)) _inst_1))) (HPow.hPow.{u1, 0, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (Quaternion.im.{u1} R _inst_1 a)) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (Quaternion.im.{u1} R _inst_1 a)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (Quaternion.im.{u1} R _inst_1 a)) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (Quaternion.im.{u1} R _inst_1 a)) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (Quaternion.im.{u1} R _inst_1 a)) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (Quaternion.im.{u1} R _inst_1 a)) _inst_1))) (instHPow.{u1, 0} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (Quaternion.im.{u1} R _inst_1 a) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 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+Case conversion may be inaccurate. Consider using '#align quaternion.im_sq Quaternion.im_sqₓ'. -/
 theorem im_sq : a.im ^ 2 = -normSq a.im := by
   simp_rw [sq, ← star_mul_self, im_star, neg_mul, neg_neg]
 #align quaternion.im_sq Quaternion.im_sq
 
+/- warning: quaternion.coe_norm_sq_add -> Quaternion.coe_normSq_add is a dubious translation:
+lean 3 declaration is
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(NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> R) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Quaternion.normSq.{u1} R _inst_1) b)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (b : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) _inst_1))) (Quaternion.coe.{u1} ((fun 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_inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (_x : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b))) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) b) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) b) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) b) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) b) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) b) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) b) _inst_1))) (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (instHAdd.{u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Quaternion.instRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (instHAdd.{u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Quaternion.instRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) 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(CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (instHAdd.{u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} 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R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (CommSemiring.toSemiring.{u1} ((fun 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(NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R 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(CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Quaternion.normSq.{u1} R _inst_1) a)) (HMul.hMul.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) a (Star.star.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instStarQuaternionToOneToSemiringToCommSemiringToNegToRing.{u1} R _inst_1) b))) (HMul.hMul.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) b (Star.star.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instStarQuaternionToOneToSemiringToCommSemiringToNegToRing.{u1} R _inst_1) a))) (Quaternion.coe.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) b) _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (_x : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (MulOneClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Quaternion.normSq.{u1} R _inst_1) b)))
+Case conversion may be inaccurate. Consider using '#align quaternion.coe_norm_sq_add Quaternion.coe_normSq_addₓ'. -/
 theorem coe_normSq_add : (normSq (a + b) : ℍ[R]) = normSq a + a * star b + b * star a + normSq b :=
   by simp [← self_mul_star, mul_add, add_mul, add_assoc]
 #align quaternion.coe_norm_sq_add Quaternion.coe_normSq_add
 
+/- warning: quaternion.norm_sq_smul -> Quaternion.normSq_smul is a dubious translation:
+lean 3 declaration is
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(SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> R) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Quaternion.normSq.{u1} R _inst_1) q))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (r : R) (q : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HSMul.hSMul.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instSMulQuaternionToOneToSemiringToCommSemiringToNegToRing.{u1, u1} R R _inst_1 (Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) r q)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (_x : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (MulOneClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Quaternion.normSq.{u1} R _inst_1) (HSMul.hSMul.{u1, u1, u1} 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+Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_smul Quaternion.normSq_smulₓ'. -/
 theorem normSq_smul (r : R) (q : ℍ[R]) : normSq (r • q) = r ^ 2 * normSq q := by
   simp_rw [norm_sq_def, star_smul, smul_mul_smul, smul_re, sq, smul_eq_mul]
 #align quaternion.norm_sq_smul Quaternion.normSq_smul
 
+/- warning: quaternion.norm_sq_add -> Quaternion.normSq_add is a dubious translation:
+lean 3 declaration is
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(Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> R) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) R 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(AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (instHAdd.{u1} 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(AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R 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(AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R 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(AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> R) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Quaternion.normSq.{u1} R _inst_1) b)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (OfNat.ofNat.{u1} R 2 (OfNat.mk.{u1} R 2 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (HMul.hMul.{u1, u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (instHMul.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Distrib.toHasMul.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toDistrib.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))) a (Star.star.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (InvolutiveStar.toHasStar.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (StarAddMonoid.toHasInvolutiveStar.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonUnitalRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.starRing.{u1} R _inst_1)))) b)))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (b : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (_x : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (MulOneClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Quaternion.normSq.{u1} R _inst_1) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (Distrib.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) (NonUnitalNonAssocSemiring.toDistrib.{u1} ((fun 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(CommRing.toRing.{u1} R _inst_1))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) b) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R 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(Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (MulOneClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Quaternion.normSq.{u1} R _inst_1) b)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) _inst_1))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) 2 (instOfNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) 2 (Semiring.toNatCast.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) => R) (HAdd.hAdd.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Distrib.toAdd.{u1} 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) a b)) _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (HMul.hMul.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) a (Star.star.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instStarQuaternionToOneToSemiringToCommSemiringToNegToRing.{u1} R _inst_1) b)))))
+Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_add Quaternion.normSq_addₓ'. -/
 theorem normSq_add (a b : ℍ[R]) : normSq (a + b) = normSq a + normSq b + 2 * (a * star b).re :=
   calc
     normSq (a + b) = normSq a + (a * star b).re + ((b * star a).re + normSq b) := by
@@ -1330,6 +2512,12 @@ section LinearOrderedCommRing
 
 variable [LinearOrderedCommRing R] {a : ℍ[R]}
 
+/- warning: quaternion.norm_sq_eq_zero -> Quaternion.normSq_eq_zero is a dubious translation:
+lean 3 declaration is
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(AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (Quaternion.ring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Quaternion.normSq.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))) a) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))))))))) (Eq.{succ u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) a (OfNat.ofNat.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) 0 (OfNat.mk.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) 0 (Zero.zero.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (MulZeroClass.toHasZero.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (Quaternion.ring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedCommRing.{u1} R] {a : Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))}, Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (fun (_x : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (MulOneClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))))) (Quaternion.normSq.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))) a) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (IsDomain.toCancelCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (StrictOrderedCommSemiring.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1))) (LinearOrderedRing.isDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1)))))))) (Eq.{succ u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) a (OfNat.ofNat.{u1} (Quaternion.{u1} R 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+Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_eq_zero Quaternion.normSq_eq_zeroₓ'. -/
 @[simp]
 theorem normSq_eq_zero : normSq a = 0 ↔ a = 0 :=
   by
@@ -1339,16 +2527,34 @@ theorem normSq_eq_zero : normSq a = 0 ↔ a = 0 :=
   all_goals apply_rules [sq_nonneg, add_nonneg]
 #align quaternion.norm_sq_eq_zero Quaternion.normSq_eq_zero
 
+/- warning: quaternion.norm_sq_ne_zero -> Quaternion.normSq_ne_zero is a dubious translation:
+lean 3 declaration is
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(StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) 0 (Zero.zero.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (MulZeroClass.toHasZero.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (Quaternion.ring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedCommRing.{u1} R] {a : Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))}, Iff (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (fun (_x : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (MulOneClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R 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(LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))))
+Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_ne_zero Quaternion.normSq_ne_zeroₓ'. -/
 theorem normSq_ne_zero : normSq a ≠ 0 ↔ a ≠ 0 :=
   not_congr normSq_eq_zero
 #align quaternion.norm_sq_ne_zero Quaternion.normSq_ne_zero
 
+/- warning: quaternion.norm_sq_nonneg -> Quaternion.normSq_nonneg is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedCommRing.{u1} R] {a : Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))}, LE.le.{u1} R (Preorder.toHasLe.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (Quaternion.ring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (Quaternion.ring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) => (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) -> R) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (Quaternion.ring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Quaternion.normSq.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))) a)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedCommRing.{u1} R] {a : Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))}, LE.le.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (StrictOrderedRing.toPartialOrder.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedRing.toStrictOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (IsDomain.toCancelCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (StrictOrderedCommSemiring.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1))) (LinearOrderedRing.isDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (MulOneClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R 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R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R 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+Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_nonneg Quaternion.normSq_nonnegₓ'. -/
 @[simp]
 theorem normSq_nonneg : 0 ≤ normSq a := by
   rw [norm_sq_def']
   apply_rules [sq_nonneg, add_nonneg]
 #align quaternion.norm_sq_nonneg Quaternion.normSq_nonneg
 
+/- warning: quaternion.norm_sq_le_zero -> Quaternion.normSq_le_zero is a dubious translation:
+lean 3 declaration is
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(LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) 0 (Zero.zero.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R 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(Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (Quaternion.ring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedCommRing.{u1} R] {a : Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))}, Iff (LE.le.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (StrictOrderedRing.toPartialOrder.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedRing.toStrictOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (fun (_x : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (MulOneClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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_inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))))) (Quaternion.normSq.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))) a) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (IsDomain.toCancelCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (StrictOrderedCommSemiring.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1))) (LinearOrderedRing.isDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1)))))))) (Eq.{succ u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) a (OfNat.ofNat.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) 0 (Zero.toOfNat0.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))))
+Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_le_zero Quaternion.normSq_le_zeroₓ'. -/
 @[simp]
 theorem normSq_le_zero : normSq a ≤ 0 ↔ a = 0 := by
   simpa only [le_antisymm_iff, norm_sq_nonneg, and_true_iff] using @norm_sq_eq_zero _ _ a
@@ -1365,6 +2571,12 @@ instance : NoZeroDivisors ℍ[R] :=
 instance : IsDomain ℍ[R] :=
   NoZeroDivisors.to_isDomain _
 
+/- warning: quaternion.sq_eq_norm_sq -> Quaternion.sq_eq_normSq is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedCommRing.{u1} R] {a : Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))}, Iff (Eq.{succ u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (HPow.hPow.{u1, 0, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) Nat (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (instHPow.{u1, 0} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) Nat (Monoid.Pow.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (Ring.toMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (Quaternion.ring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) a (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (HasLiftT.mk.{succ u1, succ u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (CoeTCₓ.coe.{succ u1, succ u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (Quaternion.hasCoeT.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (Quaternion.ring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (Quaternion.ring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) => (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) -> R) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (Quaternion.ring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Quaternion.normSq.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))) a))) (Eq.{succ u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) a ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (HasLiftT.mk.{succ u1, succ u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (CoeTCₓ.coe.{succ u1, succ u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (Quaternion.hasCoeT.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))))) a)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedCommRing.{u1} R] {a : Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))}, Iff (Eq.{succ u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (StrictOrderedCommRing.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1))))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (StrictOrderedCommRing.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1))))) (HPow.hPow.{u1, 0, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) Nat (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (StrictOrderedCommRing.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1))))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (StrictOrderedCommRing.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1))))) (instHPow.{u1, 0} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) Nat (Monoid.Pow.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) a (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Quaternion.coe.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (StrictOrderedCommRing.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R 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+Case conversion may be inaccurate. Consider using '#align quaternion.sq_eq_norm_sq Quaternion.sq_eq_normSqₓ'. -/
 theorem sq_eq_normSq : a ^ 2 = normSq a ↔ a = a.re :=
   by
   simp_rw [← star_eq_self]
@@ -1373,6 +2585,12 @@ theorem sq_eq_normSq : a ^ 2 = normSq a ↔ a = a.re :=
   · rw [← star_mul_self, sq, mul_left_inj' hq0, eq_comm]
 #align quaternion.sq_eq_norm_sq Quaternion.sq_eq_normSq
 
+/- warning: quaternion.sq_eq_neg_norm_sq -> Quaternion.sq_eq_neg_normSq is a dubious translation:
+lean 3 declaration is
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(CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (Quaternion.ring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (Quaternion.ring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) => (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) -> R) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))))) (Quaternion.ring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Quaternion.normSq.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))) a)))) (Eq.{succ u1} R (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))))) a) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedCommRing.{u1} R] {a : Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))}, Iff (Eq.{succ u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (StrictOrderedCommRing.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1))))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (StrictOrderedCommRing.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1))))) (HPow.hPow.{u1, 0, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) Nat (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (StrictOrderedCommRing.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1))))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (StrictOrderedCommRing.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1))))) (instHPow.{u1, 0} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) Nat (Monoid.Pow.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (Quaternion.instRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) a (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Neg.neg.{u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (StrictOrderedCommRing.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1))))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (StrictOrderedCommRing.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1))))) (Ring.toNeg.{u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (StrictOrderedCommRing.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1))))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R 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((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (StrictOrderedCommRing.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) _inst_1)))) (Quaternion.coe.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) => R) a) (StrictOrderedCommRing.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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+Case conversion may be inaccurate. Consider using '#align quaternion.sq_eq_neg_norm_sq Quaternion.sq_eq_neg_normSqₓ'. -/
 theorem sq_eq_neg_normSq : a ^ 2 = -normSq a ↔ a.re = 0 :=
   by
   simp_rw [← star_eq_neg]
@@ -1401,16 +2619,34 @@ instance : GroupWithZero ℍ[R] :=
       rw [has_inv_inv, Algebra.mul_smul_comm, self_mul_star, smul_coe,
         inv_mul_cancel (norm_sq_ne_zero.2 ha), coe_one] }
 
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+Case conversion may be inaccurate. Consider using '#align quaternion.coe_inv Quaternion.coe_invₓ'. -/
 @[norm_cast, simp]
 theorem coe_inv (x : R) : ((x⁻¹ : R) : ℍ[R]) = x⁻¹ :=
   map_inv₀ (algebraMap R ℍ[R]) _
 #align quaternion.coe_inv Quaternion.coe_inv
 
+/- warning: quaternion.coe_div -> Quaternion.coe_div is a dubious translation:
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(AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (Quaternion.hasCoeT.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) x y)) (HDiv.hDiv.{u1, u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R 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R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (DivInvMonoid.toHasDiv.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (GroupWithZero.toDivInvMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R 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(DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (Quaternion.hasCoeT.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) x) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (HasLiftT.mk.{succ u1, succ u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (CoeTCₓ.coe.{succ u1, succ u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (Quaternion.hasCoeT.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) y))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} R] (x : R) (y : R), Eq.{succ u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.coe.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (LinearOrderedField.toDiv.{u1} R _inst_1)) x y)) (HDiv.hDiv.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (instHDiv.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (GroupWithZero.toDiv.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instGroupWithZero.{u1} R _inst_1))) (Quaternion.coe.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))) x) (Quaternion.coe.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))) y))
+Case conversion may be inaccurate. Consider using '#align quaternion.coe_div Quaternion.coe_divₓ'. -/
 @[norm_cast, simp]
 theorem coe_div (x y : R) : ((x / y : R) : ℍ[R]) = x / y :=
   map_div₀ (algebraMap R ℍ[R]) x y
 #align quaternion.coe_div Quaternion.coe_div
 
+/- warning: quaternion.coe_zpow -> Quaternion.coe_zpow is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} R] (x : R) (z : Int), Eq.{succ u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R 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HasLiftT.{succ u1, succ u1} a b] => self.0) R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (HasLiftT.mk.{succ u1, succ u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (CoeTCₓ.coe.{succ u1, succ u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (Quaternion.hasCoeT.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) x) z)
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+Case conversion may be inaccurate. Consider using '#align quaternion.coe_zpow Quaternion.coe_zpowₓ'. -/
 @[norm_cast, simp]
 theorem coe_zpow (x : R) (z : ℤ) : ((x ^ z : R) : ℍ[R]) = x ^ z :=
   map_zpow₀ (algebraMap R ℍ[R]) x z
@@ -1426,51 +2662,111 @@ instance : DivisionRing ℍ[R] :=
       rw [coe_mul_eq_smul]
       ext <;> exact DivisionRing.qsmul_eq_mul' _ _ }
 
+/- warning: quaternion.rat_cast_re -> Quaternion.rat_cast_re is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align quaternion.rat_cast_re Quaternion.rat_cast_reₓ'. -/
 @[simp, norm_cast]
 theorem rat_cast_re (q : ℚ) : (q : ℍ[R]).re = q :=
   rfl
 #align quaternion.rat_cast_re Quaternion.rat_cast_re
 
+/- warning: quaternion.rat_cast_im_i -> Quaternion.rat_cast_imI is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} R] (q : Rat), Eq.{succ u1} R (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Rat (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (HasLiftT.mk.{1, succ u1} Rat (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (CoeTCₓ.coe.{1, succ u1} Rat (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (Rat.castCoe.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (DivisionRing.toHasRatCast.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (Quaternion.divisionRing.{u1} R _inst_1))))) q)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} R] (q : Rat), Eq.{succ u1} R (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1))))))))) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (LinearOrderedSemifield.toSemifield.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align quaternion.rat_cast_im_i Quaternion.rat_cast_imIₓ'. -/
 @[simp, norm_cast]
 theorem rat_cast_imI (q : ℚ) : (q : ℍ[R]).imI = 0 :=
   rfl
 #align quaternion.rat_cast_im_i Quaternion.rat_cast_imI
 
+/- warning: quaternion.rat_cast_im_j -> Quaternion.rat_cast_imJ is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} R] (q : Rat), Eq.{succ u1} R (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Rat (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (HasLiftT.mk.{1, succ u1} Rat (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (CoeTCₓ.coe.{1, succ u1} Rat (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (Rat.castCoe.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (DivisionRing.toHasRatCast.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (Quaternion.divisionRing.{u1} R _inst_1))))) q)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} R] (q : Rat), Eq.{succ u1} R (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1))))))))) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (LinearOrderedSemifield.toSemifield.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align quaternion.rat_cast_im_j Quaternion.rat_cast_imJₓ'. -/
 @[simp, norm_cast]
 theorem rat_cast_imJ (q : ℚ) : (q : ℍ[R]).imJ = 0 :=
   rfl
 #align quaternion.rat_cast_im_j Quaternion.rat_cast_imJ
 
+/- warning: quaternion.rat_cast_im_k -> Quaternion.rat_cast_imK is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} R] (q : Rat), Eq.{succ u1} R (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Rat (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (HasLiftT.mk.{1, succ u1} Rat (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (CoeTCₓ.coe.{1, succ u1} Rat (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (Rat.castCoe.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (DivisionRing.toHasRatCast.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (Quaternion.divisionRing.{u1} R _inst_1))))) q)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} R] (q : Rat), Eq.{succ u1} R (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1))))))))) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (LinearOrderedSemifield.toSemifield.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align quaternion.rat_cast_im_k Quaternion.rat_cast_imKₓ'. -/
 @[simp, norm_cast]
 theorem rat_cast_imK (q : ℚ) : (q : ℍ[R]).imK = 0 :=
   rfl
 #align quaternion.rat_cast_im_k Quaternion.rat_cast_imK
 
+/- warning: quaternion.rat_cast_im -> Quaternion.rat_cast_im is a dubious translation:
+lean 3 declaration is
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(Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (CoeTCₓ.coe.{1, succ u1} Rat (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (Rat.castCoe.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R 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(OfNat.ofNat.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) 0 (OfNat.mk.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) 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(LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} R] (q : Rat), Eq.{succ u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.im.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (OfNat.ofNat.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) 0 (Zero.toOfNat0.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))
+Case conversion may be inaccurate. Consider using '#align quaternion.rat_cast_im Quaternion.rat_cast_imₓ'. -/
 @[simp, norm_cast]
 theorem rat_cast_im (q : ℚ) : (q : ℍ[R]).im = 0 :=
   rfl
 #align quaternion.rat_cast_im Quaternion.rat_cast_im
 
+/- warning: quaternion.coe_rat_cast -> Quaternion.coe_rat_cast is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} R] (q : Rat), Eq.{succ u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (HasLiftT.mk.{succ u1, succ u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (CoeTCₓ.coe.{succ u1, succ u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (Quaternion.hasCoeT.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Rat R (HasLiftT.mk.{1, succ u1} Rat R (CoeTCₓ.coe.{1, succ u1} Rat R (Rat.castCoe.{u1} R (DivisionRing.toHasRatCast.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) q)) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Rat (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (HasLiftT.mk.{1, succ u1} Rat (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (CoeTCₓ.coe.{1, succ u1} Rat (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (Rat.castCoe.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (DivisionRing.toHasRatCast.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (Quaternion.divisionRing.{u1} R _inst_1))))) q)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} R] (q : Rat), Eq.{succ u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.coe.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))) (Rat.cast.{u1} R (LinearOrderedField.toRatCast.{u1} R _inst_1) q)) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)
+Case conversion may be inaccurate. Consider using '#align quaternion.coe_rat_cast Quaternion.coe_rat_castₓ'. -/
 @[norm_cast]
 theorem coe_rat_cast (q : ℚ) : ↑(q : R) = (q : ℍ[R]) :=
   rfl
 #align quaternion.coe_rat_cast Quaternion.coe_rat_cast
 
+/- warning: quaternion.norm_sq_inv -> Quaternion.normSq_inv is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} R] (a : Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) => (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) -> R) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.normSq.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Inv.inv.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.hasInv.{u1} R _inst_1) a)) (Inv.inv.{u1} R (DivInvMonoid.toHasInv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) => (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) -> R) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.normSq.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) a))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Inv.inv.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instInv.{u1} R _inst_1) a)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (fun (_x : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (MulOneClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))))) (Quaternion.normSq.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Inv.inv.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instInv.{u1} R _inst_1) a)) (Inv.inv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) a) (LinearOrderedField.toInv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) a) _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (fun (_x : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (MulOneClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R 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+Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_inv Quaternion.normSq_invₓ'. -/
 @[simp]
 theorem normSq_inv : normSq a⁻¹ = (normSq a)⁻¹ :=
   map_inv₀ normSq _
 #align quaternion.norm_sq_inv Quaternion.normSq_inv
 
+/- warning: quaternion.norm_sq_div -> Quaternion.normSq_div is a dubious translation:
+lean 3 declaration is
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(Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) -> R) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.normSq.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (HDiv.hDiv.{u1, u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (instHDiv.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (DivInvMonoid.toHasDiv.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (DivisionRing.toDivInvMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.divisionRing.{u1} R _inst_1)))) a b)) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) => (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) -> R) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.normSq.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) a) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) => (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) -> R) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.normSq.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) b))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (b : Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (HDiv.hDiv.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (instHDiv.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (DivisionRing.toDiv.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instDivisionRingQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1))) a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R 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R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))))) (Quaternion.normSq.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (HDiv.hDiv.{u1, u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (instHDiv.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (DivisionRing.toDiv.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instDivisionRingQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1))) a b)) (HDiv.hDiv.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) b) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) a) (instHDiv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) a) (LinearOrderedField.toDiv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) a) _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (fun (_x : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (MulOneClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))))) (Quaternion.normSq.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (fun (_x : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R 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(Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))))) (Quaternion.normSq.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) b))
+Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_div Quaternion.normSq_divₓ'. -/
 @[simp]
 theorem normSq_div : normSq (a / b) = normSq a / normSq b :=
   map_div₀ normSq a b
 #align quaternion.norm_sq_div Quaternion.normSq_div
 
+/- warning: quaternion.norm_sq_zpow -> Quaternion.normSq_zpow is a dubious translation:
+lean 3 declaration is
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(LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R 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(Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) => (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) -> R) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.normSq.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (HPow.hPow.{u1, 0, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) Int (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (instHPow.{u1, 0} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) Int (DivInvMonoid.Pow.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (DivisionRing.toDivInvMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.divisionRing.{u1} R _inst_1)))) a z)) (HPow.hPow.{u1, 0, u1} R Int R (instHPow.{u1, 0} R Int (DivInvMonoid.Pow.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) => (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) -> R) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (NonAssocRing.toNonAssocSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.normSq.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) a) z)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} R] (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (z : Int), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (HPow.hPow.{u1, 0, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) Int (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (instHPow.{u1, 0} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) Int (DivInvMonoid.Pow.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (DivisionRing.toDivInvMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instDivisionRingQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1)))) a z)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (fun (_x : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (MulOneClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))))) (Quaternion.normSq.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (HPow.hPow.{u1, 0, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) Int (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (instHPow.{u1, 0} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) Int (DivInvMonoid.Pow.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (DivisionRing.toDivInvMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instDivisionRingQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1)))) a z)) (HPow.hPow.{u1, 0, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) a) Int ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) a) (instHPow.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) a) Int (DivInvMonoid.Pow.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) a) (DivisionRing.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) a) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) a) (LinearOrderedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) a) _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (fun (_x : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (MulOneClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (MulZeroOneClass.toMulOneClass.{u1} R 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+Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_zpow Quaternion.normSq_zpowₓ'. -/
 @[simp]
 theorem normSq_zpow (z : ℤ) : normSq (a ^ z) = normSq a ^ z :=
   map_zpow₀ normSq a z
 #align quaternion.norm_sq_zpow Quaternion.normSq_zpow
 
+/- warning: quaternion.norm_sq_rat_cast -> Quaternion.normSq_rat_cast is a dubious translation:
+lean 3 declaration is
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(Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))) (Quaternion.ring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.normSq.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Rat (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (HasLiftT.mk.{1, succ u1} Rat (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (CoeTCₓ.coe.{1, succ u1} Rat (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (Rat.castCoe.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (DivisionRing.toHasRatCast.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (Quaternion.divisionRing.{u1} R _inst_1))))) q)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Rat R (HasLiftT.mk.{1, succ u1} Rat R (CoeTCₓ.coe.{1, succ u1} Rat R (Rat.castCoe.{u1} R (DivisionRing.toHasRatCast.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) q) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} R] (q : Rat), Eq.{succ u1} (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (LinearOrderedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) _inst_1)))))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (LinearOrderedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) _inst_1)))))) (Quaternion.coe.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} 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(Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R 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(EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (fun (a : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) 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(CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (MulZeroOneClass.toMulOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) R (NonAssocSemiring.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Quaternion.instRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))))) (Quaternion.normSq.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q))) (HPow.hPow.{u1, 0, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) Nat (Quaternion.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (LinearOrderedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) _inst_1)))))) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) (LinearOrderedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) => R) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q)) _inst_1)))))) (instHPow.{u1, 0} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) Nat (Monoid.Pow.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (DivisionSemiring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (DivisionRing.toDivisionSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instDivisionRingQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1))))))) (Rat.cast.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_1)))))) (Ring.toNeg.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Quaternion.instRatCastQuaternionToOneToSemiringToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToNegToRingToStrictOrderedRingToLinearOrderedRingToLinearOrderedCommRing.{u1} R _inst_1) q) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
+Case conversion may be inaccurate. Consider using '#align quaternion.norm_sq_rat_cast Quaternion.normSq_rat_castₓ'. -/
 @[norm_cast]
 theorem normSq_rat_cast (q : ℚ) : normSq (q : ℍ[R]) = q ^ 2 := by rw [← coe_rat_cast, norm_sq_coe]
 #align quaternion.norm_sq_rat_cast Quaternion.normSq_rat_cast
@@ -1491,6 +2787,7 @@ private theorem pow_four [Infinite R] : (#R) ^ 4 = (#R) :=
   power_nat_eq (aleph0_le_mk R) <| by simp
 #align cardinal.pow_four cardinal.pow_four
 
+#print Cardinal.mk_quaternionAlgebra /-
 /-- The cardinality of a quaternion algebra, as a type. -/
 theorem mk_quaternionAlgebra : (#ℍ[R,c₁,c₂]) = (#R) ^ 4 :=
   by
@@ -1498,21 +2795,28 @@ theorem mk_quaternionAlgebra : (#ℍ[R,c₁,c₂]) = (#R) ^ 4 :=
   simp only [mk_prod, lift_id]
   ring
 #align cardinal.mk_quaternion_algebra Cardinal.mk_quaternionAlgebra
+-/
 
+#print Cardinal.mk_quaternionAlgebra_of_infinite /-
 @[simp]
 theorem mk_quaternionAlgebra_of_infinite [Infinite R] : (#ℍ[R,c₁,c₂]) = (#R) := by
   rw [mk_quaternion_algebra, pow_four]
 #align cardinal.mk_quaternion_algebra_of_infinite Cardinal.mk_quaternionAlgebra_of_infinite
+-/
 
+#print Cardinal.mk_univ_quaternionAlgebra /-
 /-- The cardinality of a quaternion algebra, as a set. -/
 theorem mk_univ_quaternionAlgebra : (#(Set.univ : Set ℍ[R,c₁,c₂])) = (#R) ^ 4 := by
   rw [mk_univ, mk_quaternion_algebra]
 #align cardinal.mk_univ_quaternion_algebra Cardinal.mk_univ_quaternionAlgebra
+-/
 
+#print Cardinal.mk_univ_quaternionAlgebra_of_infinite /-
 @[simp]
 theorem mk_univ_quaternionAlgebra_of_infinite [Infinite R] :
     (#(Set.univ : Set ℍ[R,c₁,c₂])) = (#R) := by rw [mk_univ_quaternion_algebra, pow_four]
 #align cardinal.mk_univ_quaternion_algebra_of_infinite Cardinal.mk_univ_quaternionAlgebra_of_infinite
+-/
 
 end QuaternionAlgebra
 
@@ -1520,26 +2824,34 @@ section Quaternion
 
 variable (R : Type _) [One R] [Neg R]
 
+#print Cardinal.mk_quaternion /-
 /-- The cardinality of the quaternions, as a type. -/
 @[simp]
 theorem mk_quaternion : (#ℍ[R]) = (#R) ^ 4 :=
   mk_quaternionAlgebra _ _
 #align cardinal.mk_quaternion Cardinal.mk_quaternion
+-/
 
+#print Cardinal.mk_quaternion_of_infinite /-
 @[simp]
 theorem mk_quaternion_of_infinite [Infinite R] : (#ℍ[R]) = (#R) := by rw [mk_quaternion, pow_four]
 #align cardinal.mk_quaternion_of_infinite Cardinal.mk_quaternion_of_infinite
+-/
 
+#print Cardinal.mk_univ_quaternion /-
 /-- The cardinality of the quaternions, as a set. -/
 @[simp]
 theorem mk_univ_quaternion : (#(Set.univ : Set ℍ[R])) = (#R) ^ 4 :=
   mk_univ_quaternionAlgebra _ _
 #align cardinal.mk_univ_quaternion Cardinal.mk_univ_quaternion
+-/
 
+#print Cardinal.mk_univ_quaternion_of_infinite /-
 @[simp]
 theorem mk_univ_quaternion_of_infinite [Infinite R] : (#(Set.univ : Set ℍ[R])) = (#R) := by
   rw [mk_univ_quaternion, pow_four]
 #align cardinal.mk_univ_quaternion_of_infinite Cardinal.mk_univ_quaternion_of_infinite
+-/
 
 end Quaternion
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/86d04064ca33ee3d3405fbfc497d494fd2dd4796

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 
 ! This file was ported from Lean 3 source module algebra.quaternion
-! leanprover-community/mathlib commit dc7ac07acd84584426773e69e51035bea9a770e7
+! leanprover-community/mathlib commit cf7a7252c1989efe5800e0b3cdfeb4228ac6b40e
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -27,7 +27,7 @@ algebraic structures on `ℍ[R]`.
   [quaternion algebra](https://en.wikipedia.org/wiki/Quaternion_algebra) with coefficients `a`, `b`
 * `quaternion R`, `ℍ[R]` : the space of quaternions, a.k.a. `quaternion_algebra R (-1) (-1)`;
 * `quaternion.norm_sq` : square of the norm of a quaternion;
-* `quaternion.conj` : conjugate of a quaternion;
+* `quaternion.star_ring` : provides the conjugate of a quaternion as `has_star.star`;
 
 We also define the following algebraic structures on `ℍ[R]`:
 
@@ -562,134 +562,79 @@ theorem smul_coe : x • (y : ℍ[R,c₁,c₂]) = ↑(x * y) := by rw [coe_mul,
 #align quaternion_algebra.smul_coe QuaternionAlgebra.smul_coe
 
 /-- Quaternion conjugate. -/
-def conj : ℍ[R,c₁,c₂] ≃ₗ[R] ℍ[R,c₁,c₂] :=
-  LinearEquiv.ofInvolutive
-    { toFun := fun a => ⟨a.1, -a.2, -a.3, -a.4⟩
-      map_add' := fun a b => by ext <;> simp [neg_add]
-      map_smul' := fun r a => by ext <;> simp } fun a => by simp
-#align quaternion_algebra.conj QuaternionAlgebra.conj
+instance : Star ℍ[R,c₁,c₂] where unit a := ⟨a.1, -a.2, -a.3, -a.4⟩
 
 @[simp]
-theorem re_conj : (conj a).re = a.re :=
+theorem re_star : (star a).re = a.re :=
   rfl
-#align quaternion_algebra.re_conj QuaternionAlgebra.re_conj
+#align quaternion_algebra.re_star QuaternionAlgebra.re_star
 
 @[simp]
-theorem imI_conj : (conj a).imI = -a.imI :=
+theorem imI_star : (star a).imI = -a.imI :=
   rfl
-#align quaternion_algebra.im_i_conj QuaternionAlgebra.imI_conj
+#align quaternion_algebra.im_i_star QuaternionAlgebra.imI_star
 
 @[simp]
-theorem imJ_conj : (conj a).imJ = -a.imJ :=
+theorem imJ_star : (star a).imJ = -a.imJ :=
   rfl
-#align quaternion_algebra.im_j_conj QuaternionAlgebra.imJ_conj
+#align quaternion_algebra.im_j_star QuaternionAlgebra.imJ_star
 
 @[simp]
-theorem imK_conj : (conj a).imK = -a.imK :=
+theorem imK_star : (star a).imK = -a.imK :=
   rfl
-#align quaternion_algebra.im_k_conj QuaternionAlgebra.imK_conj
+#align quaternion_algebra.im_k_star QuaternionAlgebra.imK_star
 
 @[simp]
-theorem im_conj : (conj a).im = -a.im :=
+theorem im_star : (star a).im = -a.im :=
   ext _ _ neg_zero.symm rfl rfl rfl
-#align quaternion_algebra.im_conj QuaternionAlgebra.im_conj
+#align quaternion_algebra.im_star QuaternionAlgebra.im_star
 
 @[simp]
-theorem conj_mk (a₁ a₂ a₃ a₄ : R) : conj (mk a₁ a₂ a₃ a₄ : ℍ[R,c₁,c₂]) = ⟨a₁, -a₂, -a₃, -a₄⟩ :=
+theorem star_mk (a₁ a₂ a₃ a₄ : R) : star (mk a₁ a₂ a₃ a₄ : ℍ[R,c₁,c₂]) = ⟨a₁, -a₂, -a₃, -a₄⟩ :=
   rfl
-#align quaternion_algebra.conj_mk QuaternionAlgebra.conj_mk
+#align quaternion_algebra.star_mk QuaternionAlgebra.star_mk
 
-@[simp]
-theorem conj_conj : a.conj.conj = a :=
-  ext _ _ rfl (neg_neg _) (neg_neg _) (neg_neg _)
-#align quaternion_algebra.conj_conj QuaternionAlgebra.conj_conj
-
-theorem conj_add : (a + b).conj = a.conj + b.conj :=
-  conj.map_add a b
-#align quaternion_algebra.conj_add QuaternionAlgebra.conj_add
-
-@[simp]
-theorem conj_mul : (a * b).conj = b.conj * a.conj := by ext <;> simp <;> ring
-#align quaternion_algebra.conj_mul QuaternionAlgebra.conj_mul
-
-instance : StarRing ℍ[R,c₁,c₂] where
-  unit := conj
-  star_involutive := conj_conj
-  star_add := conj_add
-  star_mul := conj_mul
-
-@[simp]
-theorem star_def (a : ℍ[R,c₁,c₂]) : star a = conj a :=
-  rfl
-#align quaternion_algebra.star_def QuaternionAlgebra.star_def
-
-theorem conj_conj_mul : (a.conj * b).conj = b.conj * a :=
-  star_star_mul _ _
-#align quaternion_algebra.conj_conj_mul QuaternionAlgebra.conj_conj_mul
-
-theorem conj_mul_conj : (a * b.conj).conj = b * a.conj :=
-  star_mul_star _ _
-#align quaternion_algebra.conj_mul_conj QuaternionAlgebra.conj_mul_conj
-
-theorem self_add_conj' : a + a.conj = ↑(2 * a.re) := by ext <;> simp [two_mul]
-#align quaternion_algebra.self_add_conj' QuaternionAlgebra.self_add_conj'
-
-theorem self_add_conj : a + a.conj = 2 * a.re := by simp only [self_add_conj', two_mul, coe_add]
-#align quaternion_algebra.self_add_conj QuaternionAlgebra.self_add_conj
+instance : StarRing ℍ[R,c₁,c₂]
+    where
+  star_involutive x := by simp [Star.star]
+  star_add a b := by ext <;> simp [neg_add]
+  star_mul a b := by ext <;> simp <;> ring
 
-theorem conj_add_self' : a.conj + a = ↑(2 * a.re) := by rw [add_comm, self_add_conj']
-#align quaternion_algebra.conj_add_self' QuaternionAlgebra.conj_add_self'
+theorem self_add_star' : a + star a = ↑(2 * a.re) := by ext <;> simp [two_mul]
+#align quaternion_algebra.self_add_star' QuaternionAlgebra.self_add_star'
 
-theorem conj_add_self : a.conj + a = 2 * a.re := by rw [add_comm, self_add_conj]
-#align quaternion_algebra.conj_add_self QuaternionAlgebra.conj_add_self
+theorem self_add_star : a + star a = 2 * a.re := by simp only [self_add_star', two_mul, coe_add]
+#align quaternion_algebra.self_add_star QuaternionAlgebra.self_add_star
 
-theorem conj_eq_two_re_sub : a.conj = ↑(2 * a.re) - a :=
-  eq_sub_iff_add_eq.2 a.conj_add_self'
-#align quaternion_algebra.conj_eq_two_re_sub QuaternionAlgebra.conj_eq_two_re_sub
+theorem star_add_self' : star a + a = ↑(2 * a.re) := by rw [add_comm, self_add_star']
+#align quaternion_algebra.star_add_self' QuaternionAlgebra.star_add_self'
 
-theorem commute_conj_self : Commute a.conj a :=
-  by
-  rw [a.conj_eq_two_re_sub]
-  exact (coe_commute (2 * a.re) a).sub_left (Commute.refl a)
-#align quaternion_algebra.commute_conj_self QuaternionAlgebra.commute_conj_self
+theorem star_add_self : star a + a = 2 * a.re := by rw [add_comm, self_add_star]
+#align quaternion_algebra.star_add_self QuaternionAlgebra.star_add_self
 
-theorem commute_self_conj : Commute a a.conj :=
-  a.commute_conj_self.symm
-#align quaternion_algebra.commute_self_conj QuaternionAlgebra.commute_self_conj
+theorem star_eq_two_re_sub : star a = ↑(2 * a.re) - a :=
+  eq_sub_iff_add_eq.2 a.star_add_self'
+#align quaternion_algebra.star_eq_two_re_sub QuaternionAlgebra.star_eq_two_re_sub
 
-theorem commute_conj_conj {a b : ℍ[R,c₁,c₂]} (h : Commute a b) : Commute a.conj b.conj :=
-  h.star_star
-#align quaternion_algebra.commute_conj_conj QuaternionAlgebra.commute_conj_conj
+instance : IsStarNormal a :=
+  ⟨by
+    rw [a.star_eq_two_re_sub]
+    exact (coe_commute (2 * a.re) a).sub_left (Commute.refl a)⟩
 
 @[simp, norm_cast]
-theorem conj_coe : conj (x : ℍ[R,c₁,c₂]) = x := by ext <;> simp
-#align quaternion_algebra.conj_coe QuaternionAlgebra.conj_coe
+theorem star_coe : star (x : ℍ[R,c₁,c₂]) = x := by ext <;> simp
+#align quaternion_algebra.star_coe QuaternionAlgebra.star_coe
 
 @[simp]
-theorem conj_im : conj a.im = -a.im :=
-  im_conj _
-#align quaternion_algebra.conj_im QuaternionAlgebra.conj_im
-
-@[simp, norm_cast]
-theorem conj_nat_cast (n : ℕ) : conj (n : ℍ[R,c₁,c₂]) = n :=
-  @star_natCast ℍ[R,c₁,c₂] _ _ n
-#align quaternion_algebra.conj_nat_cast QuaternionAlgebra.conj_nat_cast
-
-@[simp, norm_cast]
-theorem conj_int_cast (z : ℤ) : conj (z : ℍ[R,c₁,c₂]) = z :=
-  @star_intCast ℍ[R,c₁,c₂] _ _ z
-#align quaternion_algebra.conj_int_cast QuaternionAlgebra.conj_int_cast
+theorem star_im : star a.im = -a.im :=
+  im_star _
+#align quaternion_algebra.star_im QuaternionAlgebra.star_im
 
 @[simp]
-theorem conj_smul [Monoid S] [DistribMulAction S R] (s : S) (a : ℍ[R,c₁,c₂]) :
-    conj (s • a) = s • conj a :=
+theorem star_smul [Monoid S] [DistribMulAction S R] (s : S) (a : ℍ[R,c₁,c₂]) :
+    star (s • a) = s • star a :=
   ext _ _ rfl (smul_neg _ _).symm (smul_neg _ _).symm (smul_neg _ _).symm
-#align quaternion_algebra.conj_smul QuaternionAlgebra.conj_smul
-
-@[simp]
-theorem conj_one : conj (1 : ℍ[R,c₁,c₂]) = 1 :=
-  conj_coe 1
-#align quaternion_algebra.conj_one QuaternionAlgebra.conj_one
+#align quaternion_algebra.star_smul QuaternionAlgebra.star_smul
 
 theorem eq_re_of_eq_coe {a : ℍ[R,c₁,c₂]} {x : R} (h : a = x) : a = a.re := by rw [h, coe_re]
 #align quaternion_algebra.eq_re_of_eq_coe QuaternionAlgebra.eq_re_of_eq_coe
@@ -704,58 +649,41 @@ section CharZero
 variable [NoZeroDivisors R] [CharZero R]
 
 @[simp]
-theorem conj_eq_self {c₁ c₂ : R} {a : ℍ[R,c₁,c₂]} : conj a = a ↔ a = a.re := by
+theorem star_eq_self {c₁ c₂ : R} {a : ℍ[R,c₁,c₂]} : star a = a ↔ a = a.re := by
   simp [ext_iff, neg_eq_iff_add_eq_zero, add_self_eq_zero]
-#align quaternion_algebra.conj_eq_self QuaternionAlgebra.conj_eq_self
+#align quaternion_algebra.star_eq_self QuaternionAlgebra.star_eq_self
 
-theorem conj_eq_neg {c₁ c₂ : R} {a : ℍ[R,c₁,c₂]} : conj a = -a ↔ a.re = 0 := by
+theorem star_eq_neg {c₁ c₂ : R} {a : ℍ[R,c₁,c₂]} : star a = -a ↔ a.re = 0 := by
   simp [ext_iff, eq_neg_iff_add_eq_zero]
-#align quaternion_algebra.conj_eq_neg QuaternionAlgebra.conj_eq_neg
+#align quaternion_algebra.star_eq_neg QuaternionAlgebra.star_eq_neg
 
 end CharZero
 
--- Can't use `rw ← conj_eq_self` in the proof without additional assumptions
-theorem conj_mul_eq_coe : conj a * a = (conj a * a).re := by ext <;> simp <;> ring
-#align quaternion_algebra.conj_mul_eq_coe QuaternionAlgebra.conj_mul_eq_coe
+-- Can't use `rw ← star_eq_self` in the proof without additional assumptions
+theorem star_mul_eq_coe : star a * a = (star a * a).re := by ext <;> simp <;> ring
+#align quaternion_algebra.star_mul_eq_coe QuaternionAlgebra.star_mul_eq_coe
 
-theorem mul_conj_eq_coe : a * conj a = (a * conj a).re :=
+theorem mul_star_eq_coe : a * star a = (a * star a).re :=
   by
-  rw [a.commute_self_conj.eq]
-  exact a.conj_mul_eq_coe
-#align quaternion_algebra.mul_conj_eq_coe QuaternionAlgebra.mul_conj_eq_coe
-
-theorem conj_zero : conj (0 : ℍ[R,c₁,c₂]) = 0 :=
-  conj.map_zero
-#align quaternion_algebra.conj_zero QuaternionAlgebra.conj_zero
-
-theorem conj_neg : (-a).conj = -a.conj :=
-  (conj : ℍ[R,c₁,c₂] ≃ₗ[R] _).map_neg a
-#align quaternion_algebra.conj_neg QuaternionAlgebra.conj_neg
-
-theorem conj_sub : (a - b).conj = a.conj - b.conj :=
-  (conj : ℍ[R,c₁,c₂] ≃ₗ[R] _).map_sub a b
-#align quaternion_algebra.conj_sub QuaternionAlgebra.conj_sub
-
-@[simp]
-theorem conj_pow (n : ℕ) : (a ^ n).conj = a.conj ^ n :=
-  star_pow _ _
-#align quaternion_algebra.conj_pow QuaternionAlgebra.conj_pow
+  rw [← star_comm_self']
+  exact a.star_mul_eq_coe
+#align quaternion_algebra.mul_star_eq_coe QuaternionAlgebra.mul_star_eq_coe
 
 open MulOpposite
 
 /-- Quaternion conjugate as an `alg_equiv` to the opposite ring. -/
-def conjAe : ℍ[R,c₁,c₂] ≃ₐ[R] ℍ[R,c₁,c₂]ᵐᵒᵖ :=
-  { conj.toAddEquiv.trans opAddEquiv with
-    toFun := op ∘ conj
-    invFun := conj ∘ unop
+def starAe : ℍ[R,c₁,c₂] ≃ₐ[R] ℍ[R,c₁,c₂]ᵐᵒᵖ :=
+  { starAddEquiv.trans opAddEquiv with
+    toFun := op ∘ star
+    invFun := star ∘ unop
     map_mul' := fun x y => by simp
     commutes' := fun r => by simp }
-#align quaternion_algebra.conj_ae QuaternionAlgebra.conjAe
+#align quaternion_algebra.star_ae QuaternionAlgebra.starAe
 
 @[simp]
-theorem coe_conjAe : ⇑(conjAe : ℍ[R,c₁,c₂] ≃ₐ[R] _) = op ∘ conj :=
+theorem coe_starAe : ⇑(starAe : ℍ[R,c₁,c₂] ≃ₐ[R] _) = op ∘ star :=
   rfl
-#align quaternion_algebra.coe_conj_ae QuaternionAlgebra.coe_conjAe
+#align quaternion_algebra.coe_star_ae QuaternionAlgebra.coe_starAe
 
 end QuaternionAlgebra
 
@@ -1218,124 +1146,66 @@ theorem finrank_eq_four [StrongRankCondition R] : FiniteDimensional.finrank R 
   QuaternionAlgebra.finrank_eq_four _ _
 #align quaternion.finrank_eq_four Quaternion.finrank_eq_four
 
-/-- Quaternion conjugate. -/
-def conj : ℍ[R] ≃ₗ[R] ℍ[R] :=
-  QuaternionAlgebra.conj
-#align quaternion.conj Quaternion.conj
-
 @[simp]
-theorem conj_re : a.conj.re = a.re :=
+theorem star_re : (star a).re = a.re :=
   rfl
-#align quaternion.conj_re Quaternion.conj_re
+#align quaternion.star_re Quaternion.star_re
 
 @[simp]
-theorem conj_imI : a.conj.imI = -a.imI :=
+theorem star_imI : (star a).imI = -a.imI :=
   rfl
-#align quaternion.conj_im_i Quaternion.conj_imI
+#align quaternion.star_im_i Quaternion.star_imI
 
 @[simp]
-theorem conj_imJ : a.conj.imJ = -a.imJ :=
+theorem star_imJ : (star a).imJ = -a.imJ :=
   rfl
-#align quaternion.conj_im_j Quaternion.conj_imJ
+#align quaternion.star_im_j Quaternion.star_imJ
 
 @[simp]
-theorem conj_imK : a.conj.imK = -a.imK :=
+theorem star_imK : (star a).imK = -a.imK :=
   rfl
-#align quaternion.conj_im_k Quaternion.conj_imK
+#align quaternion.star_im_k Quaternion.star_imK
 
 @[simp]
-theorem conj_im : a.conj.im = -a.im :=
-  a.im_conj
-#align quaternion.conj_im Quaternion.conj_im
+theorem star_im : (star a).im = -a.im :=
+  a.im_star
+#align quaternion.star_im Quaternion.star_im
 
-@[simp]
-theorem conj_conj : a.conj.conj = a :=
-  a.conj_conj
-#align quaternion.conj_conj Quaternion.conj_conj
+theorem self_add_star' : a + star a = ↑(2 * a.re) :=
+  a.self_add_star'
+#align quaternion.self_add_star' Quaternion.self_add_star'
 
-@[simp]
-theorem conj_add : (a + b).conj = a.conj + b.conj :=
-  a.conj_add b
-#align quaternion.conj_add Quaternion.conj_add
+theorem self_add_star : a + star a = 2 * a.re :=
+  a.self_add_star
+#align quaternion.self_add_star Quaternion.self_add_star
 
-@[simp]
-theorem conj_mul : (a * b).conj = b.conj * a.conj :=
-  a.conj_mul b
-#align quaternion.conj_mul Quaternion.conj_mul
-
-theorem conj_conj_mul : (a.conj * b).conj = b.conj * a :=
-  a.conj_conj_mul b
-#align quaternion.conj_conj_mul Quaternion.conj_conj_mul
-
-theorem conj_mul_conj : (a * b.conj).conj = b * a.conj :=
-  a.conj_mul_conj b
-#align quaternion.conj_mul_conj Quaternion.conj_mul_conj
-
-theorem self_add_conj' : a + a.conj = ↑(2 * a.re) :=
-  a.self_add_conj'
-#align quaternion.self_add_conj' Quaternion.self_add_conj'
-
-theorem self_add_conj : a + a.conj = 2 * a.re :=
-  a.self_add_conj
-#align quaternion.self_add_conj Quaternion.self_add_conj
-
-theorem conj_add_self' : a.conj + a = ↑(2 * a.re) :=
-  a.conj_add_self'
-#align quaternion.conj_add_self' Quaternion.conj_add_self'
-
-theorem conj_add_self : a.conj + a = 2 * a.re :=
-  a.conj_add_self
-#align quaternion.conj_add_self Quaternion.conj_add_self
-
-theorem conj_eq_two_re_sub : a.conj = ↑(2 * a.re) - a :=
-  a.conj_eq_two_re_sub
-#align quaternion.conj_eq_two_re_sub Quaternion.conj_eq_two_re_sub
-
-theorem commute_conj_self : Commute a.conj a :=
-  a.commute_conj_self
-#align quaternion.commute_conj_self Quaternion.commute_conj_self
-
-theorem commute_self_conj : Commute a a.conj :=
-  a.commute_self_conj
-#align quaternion.commute_self_conj Quaternion.commute_self_conj
-
-theorem commute_conj_conj {a b : ℍ[R]} (h : Commute a b) : Commute a.conj b.conj :=
-  QuaternionAlgebra.commute_conj_conj h
-#align quaternion.commute_conj_conj Quaternion.commute_conj_conj
-
-alias commute_conj_conj ← commute.quaternion_conj
-#align quaternion.commute.quaternion_conj Quaternion.Commute.quaternion_conj
-
-@[simp, norm_cast]
-theorem conj_coe : conj (x : ℍ[R]) = x :=
-  QuaternionAlgebra.conj_coe x
-#align quaternion.conj_coe Quaternion.conj_coe
+theorem star_add_self' : star a + a = ↑(2 * a.re) :=
+  a.star_add_self'
+#align quaternion.star_add_self' Quaternion.star_add_self'
 
-@[simp]
-theorem im_conj : a.im.conj = -a.im :=
-  QuaternionAlgebra.im_conj _
-#align quaternion.im_conj Quaternion.im_conj
+theorem star_add_self : star a + a = 2 * a.re :=
+  a.star_add_self
+#align quaternion.star_add_self Quaternion.star_add_self
 
-@[simp, norm_cast]
-theorem conj_nat_cast (n : ℕ) : conj (n : ℍ[R]) = n :=
-  QuaternionAlgebra.conj_nat_cast _
-#align quaternion.conj_nat_cast Quaternion.conj_nat_cast
+theorem star_eq_two_re_sub : star a = ↑(2 * a.re) - a :=
+  a.star_eq_two_re_sub
+#align quaternion.star_eq_two_re_sub Quaternion.star_eq_two_re_sub
 
 @[simp, norm_cast]
-theorem conj_int_cast (z : ℤ) : conj (z : ℍ[R]) = z :=
-  QuaternionAlgebra.conj_int_cast _
-#align quaternion.conj_int_cast Quaternion.conj_int_cast
+theorem star_coe : star (x : ℍ[R]) = x :=
+  QuaternionAlgebra.star_coe x
+#align quaternion.star_coe Quaternion.star_coe
 
 @[simp]
-theorem conj_smul [Monoid S] [DistribMulAction S R] (s : S) (a : ℍ[R]) :
-    conj (s • a) = s • conj a :=
-  QuaternionAlgebra.conj_smul _ _
-#align quaternion.conj_smul Quaternion.conj_smul
+theorem im_star : star a.im = -a.im :=
+  QuaternionAlgebra.im_star _
+#align quaternion.im_star Quaternion.im_star
 
 @[simp]
-theorem conj_one : conj (1 : ℍ[R]) = 1 :=
-  conj_coe 1
-#align quaternion.conj_one Quaternion.conj_one
+theorem star_smul [Monoid S] [DistribMulAction S R] (s : S) (a : ℍ[R]) :
+    star (s • a) = s • star a :=
+  QuaternionAlgebra.star_smul _ _
+#align quaternion.star_smul Quaternion.star_smul
 
 theorem eq_re_of_eq_coe {a : ℍ[R]} {x : R} (h : a = x) : a = a.re :=
   QuaternionAlgebra.eq_re_of_eq_coe h
@@ -1350,85 +1220,65 @@ section CharZero
 variable [NoZeroDivisors R] [CharZero R]
 
 @[simp]
-theorem conj_eq_self {a : ℍ[R]} : conj a = a ↔ a = a.re :=
-  QuaternionAlgebra.conj_eq_self
-#align quaternion.conj_eq_self Quaternion.conj_eq_self
+theorem star_eq_self {a : ℍ[R]} : star a = a ↔ a = a.re :=
+  QuaternionAlgebra.star_eq_self
+#align quaternion.star_eq_self Quaternion.star_eq_self
 
 @[simp]
-theorem conj_eq_neg {a : ℍ[R]} : conj a = -a ↔ a.re = 0 :=
-  QuaternionAlgebra.conj_eq_neg
-#align quaternion.conj_eq_neg Quaternion.conj_eq_neg
+theorem star_eq_neg {a : ℍ[R]} : star a = -a ↔ a.re = 0 :=
+  QuaternionAlgebra.star_eq_neg
+#align quaternion.star_eq_neg Quaternion.star_eq_neg
 
 end CharZero
 
-theorem conj_mul_eq_coe : conj a * a = (conj a * a).re :=
-  a.conj_mul_eq_coe
-#align quaternion.conj_mul_eq_coe Quaternion.conj_mul_eq_coe
-
-theorem mul_conj_eq_coe : a * conj a = (a * conj a).re :=
-  a.mul_conj_eq_coe
-#align quaternion.mul_conj_eq_coe Quaternion.mul_conj_eq_coe
-
-@[simp]
-theorem conj_zero : conj (0 : ℍ[R]) = 0 :=
-  QuaternionAlgebra.conj_zero
-#align quaternion.conj_zero Quaternion.conj_zero
-
-@[simp]
-theorem conj_neg : (-a).conj = -a.conj :=
-  a.conj_neg
-#align quaternion.conj_neg Quaternion.conj_neg
-
-@[simp]
-theorem conj_sub : (a - b).conj = a.conj - b.conj :=
-  a.conj_sub b
-#align quaternion.conj_sub Quaternion.conj_sub
+theorem star_mul_eq_coe : star a * a = (star a * a).re :=
+  a.star_mul_eq_coe
+#align quaternion.star_mul_eq_coe Quaternion.star_mul_eq_coe
 
-@[simp]
-theorem conj_pow (n : ℕ) : conj (a ^ n) = conj a ^ n :=
-  a.conj_pow n
-#align quaternion.conj_pow Quaternion.conj_pow
+theorem mul_star_eq_coe : a * star a = (a * star a).re :=
+  a.mul_star_eq_coe
+#align quaternion.mul_star_eq_coe Quaternion.mul_star_eq_coe
 
 open MulOpposite
 
 /-- Quaternion conjugate as an `alg_equiv` to the opposite ring. -/
-def conjAe : ℍ[R] ≃ₐ[R] ℍ[R]ᵐᵒᵖ :=
-  QuaternionAlgebra.conjAe
-#align quaternion.conj_ae Quaternion.conjAe
+def starAe : ℍ[R] ≃ₐ[R] ℍ[R]ᵐᵒᵖ :=
+  QuaternionAlgebra.starAe
+#align quaternion.star_ae Quaternion.starAe
 
 @[simp]
-theorem coe_conjAe : ⇑(conjAe : ℍ[R] ≃ₐ[R] ℍ[R]ᵐᵒᵖ) = op ∘ conj :=
+theorem coe_starAe : ⇑(starAe : ℍ[R] ≃ₐ[R] ℍ[R]ᵐᵒᵖ) = op ∘ star :=
   rfl
-#align quaternion.coe_conj_ae Quaternion.coe_conjAe
+#align quaternion.coe_star_ae Quaternion.coe_starAe
 
 /-- Square of the norm. -/
 def normSq : ℍ[R] →*₀ R where
-  toFun a := (a * a.conj).re
-  map_zero' := by rw [conj_zero, MulZeroClass.zero_mul, zero_re]
-  map_one' := by rw [conj_one, one_mul, one_re]
+  toFun a := (a * star a).re
+  map_zero' := by rw [star_zero, MulZeroClass.zero_mul, zero_re]
+  map_one' := by rw [star_one, one_mul, one_re]
   map_mul' x y :=
     coe_injective <| by
       conv_lhs =>
-        rw [← mul_conj_eq_coe, conj_mul, mul_assoc, ← mul_assoc y, y.mul_conj_eq_coe, coe_commutes,
-          ← mul_assoc, x.mul_conj_eq_coe, ← coe_mul]
+        rw [← mul_star_eq_coe, star_mul, mul_assoc, ← mul_assoc y, y.mul_star_eq_coe, coe_commutes,
+          ← mul_assoc, x.mul_star_eq_coe, ← coe_mul]
 #align quaternion.norm_sq Quaternion.normSq
 
-theorem normSq_def : normSq a = (a * a.conj).re :=
+theorem normSq_def : normSq a = (a * star a).re :=
   rfl
 #align quaternion.norm_sq_def Quaternion.normSq_def
 
 theorem normSq_def' : normSq a = a.1 ^ 2 + a.2 ^ 2 + a.3 ^ 2 + a.4 ^ 2 := by
-  simp only [norm_sq_def, sq, mul_neg, sub_neg_eq_add, mul_re, conj_re, conj_im_i, conj_im_j,
-    conj_im_k]
+  simp only [norm_sq_def, sq, mul_neg, sub_neg_eq_add, mul_re, star_re, star_im_i, star_im_j,
+    star_im_k]
 #align quaternion.norm_sq_def' Quaternion.normSq_def'
 
 theorem normSq_coe : normSq (x : ℍ[R]) = x ^ 2 := by
-  rw [norm_sq_def, conj_coe, ← coe_mul, coe_re, sq]
+  rw [norm_sq_def, star_coe, ← coe_mul, coe_re, sq]
 #align quaternion.norm_sq_coe Quaternion.normSq_coe
 
 @[simp]
-theorem normSq_conj : normSq (conj a) = normSq a := by simp [norm_sq_def']
-#align quaternion.norm_sq_conj Quaternion.normSq_conj
+theorem normSq_star : normSq (star a) = normSq a := by simp [norm_sq_def']
+#align quaternion.norm_sq_star Quaternion.normSq_star
 
 @[norm_cast]
 theorem normSq_nat_cast (n : ℕ) : normSq (n : ℍ[R]) = n ^ 2 := by rw [← coe_nat_cast, norm_sq_coe]
@@ -1439,34 +1289,34 @@ theorem normSq_int_cast (z : ℤ) : normSq (z : ℍ[R]) = z ^ 2 := by rw [← co
 #align quaternion.norm_sq_int_cast Quaternion.normSq_int_cast
 
 @[simp]
-theorem normSq_neg : normSq (-a) = normSq a := by simp only [norm_sq_def, conj_neg, neg_mul_neg]
+theorem normSq_neg : normSq (-a) = normSq a := by simp only [norm_sq_def, star_neg, neg_mul_neg]
 #align quaternion.norm_sq_neg Quaternion.normSq_neg
 
-theorem self_mul_conj : a * a.conj = normSq a := by rw [mul_conj_eq_coe, norm_sq_def]
-#align quaternion.self_mul_conj Quaternion.self_mul_conj
+theorem self_mul_star : a * star a = normSq a := by rw [mul_star_eq_coe, norm_sq_def]
+#align quaternion.self_mul_star Quaternion.self_mul_star
 
-theorem conj_mul_self : a.conj * a = normSq a := by rw [← a.commute_self_conj.eq, self_mul_conj]
-#align quaternion.conj_mul_self Quaternion.conj_mul_self
+theorem star_mul_self : star a * a = normSq a := by rw [star_comm_self', self_mul_star]
+#align quaternion.star_mul_self Quaternion.star_mul_self
 
 theorem im_sq : a.im ^ 2 = -normSq a.im := by
-  simp_rw [sq, ← conj_mul_self, im_conj, neg_mul, neg_neg]
+  simp_rw [sq, ← star_mul_self, im_star, neg_mul, neg_neg]
 #align quaternion.im_sq Quaternion.im_sq
 
-theorem coe_normSq_add : (normSq (a + b) : ℍ[R]) = normSq a + a * b.conj + b * a.conj + normSq b :=
-  by simp [← self_mul_conj, mul_add, add_mul, add_assoc]
+theorem coe_normSq_add : (normSq (a + b) : ℍ[R]) = normSq a + a * star b + b * star a + normSq b :=
+  by simp [← self_mul_star, mul_add, add_mul, add_assoc]
 #align quaternion.coe_norm_sq_add Quaternion.coe_normSq_add
 
 theorem normSq_smul (r : R) (q : ℍ[R]) : normSq (r • q) = r ^ 2 * normSq q := by
-  simp_rw [norm_sq_def, conj_smul, smul_mul_smul, smul_re, sq, smul_eq_mul]
+  simp_rw [norm_sq_def, star_smul, smul_mul_smul, smul_re, sq, smul_eq_mul]
 #align quaternion.norm_sq_smul Quaternion.normSq_smul
 
-theorem normSq_add (a b : ℍ[R]) : normSq (a + b) = normSq a + normSq b + 2 * (a * conj b).re :=
+theorem normSq_add (a b : ℍ[R]) : normSq (a + b) = normSq a + normSq b + 2 * (a * star b).re :=
   calc
-    normSq (a + b) = normSq a + (a * conj b).re + ((b * conj a).re + normSq b) := by
-      simp_rw [norm_sq_def, conj_add, add_mul, mul_add, add_re]
-    _ = normSq a + normSq b + ((a * conj b).re + (b * conj a).re) := by abel
-    _ = normSq a + normSq b + 2 * (a * conj b).re := by
-      rw [← add_re, ← conj_mul_conj a b, self_add_conj', coe_re]
+    normSq (a + b) = normSq a + (a * star b).re + ((b * star a).re + normSq b) := by
+      simp_rw [norm_sq_def, star_add, add_mul, mul_add, add_re]
+    _ = normSq a + normSq b + ((a * star b).re + (b * star a).re) := by abel
+    _ = normSq a + normSq b + 2 * (a * star b).re := by
+      rw [← add_re, ← star_mul_star a b, self_add_star', coe_re]
     
 #align quaternion.norm_sq_add Quaternion.normSq_add
 
@@ -1517,18 +1367,18 @@ instance : IsDomain ℍ[R] :=
 
 theorem sq_eq_normSq : a ^ 2 = normSq a ↔ a = a.re :=
   by
-  simp_rw [← conj_eq_self]
+  simp_rw [← star_eq_self]
   obtain rfl | hq0 := eq_or_ne a 0
   · simp
-  · rw [← conj_mul_self, sq, mul_left_inj' hq0, eq_comm]
+  · rw [← star_mul_self, sq, mul_left_inj' hq0, eq_comm]
 #align quaternion.sq_eq_norm_sq Quaternion.sq_eq_normSq
 
 theorem sq_eq_neg_normSq : a ^ 2 = -normSq a ↔ a.re = 0 :=
   by
-  simp_rw [← conj_eq_neg]
+  simp_rw [← star_eq_neg]
   obtain rfl | hq0 := eq_or_ne a 0
   · simp
-  rw [← conj_mul_self, ← mul_neg, ← neg_sq, sq, mul_left_inj' (neg_ne_zero.mpr hq0), eq_comm]
+  rw [← star_mul_self, ← mul_neg, ← neg_sq, sq, mul_left_inj' (neg_ne_zero.mpr hq0), eq_comm]
 #align quaternion.sq_eq_neg_norm_sq Quaternion.sq_eq_neg_normSq
 
 end LinearOrderedCommRing
@@ -1539,16 +1389,16 @@ variable [LinearOrderedField R] (a b : ℍ[R])
 
 @[simps (config := { attrs := [] })]
 instance : Inv ℍ[R] :=
-  ⟨fun a => (normSq a)⁻¹ • a.conj⟩
+  ⟨fun a => (normSq a)⁻¹ • star a⟩
 
 instance : GroupWithZero ℍ[R] :=
   { Quaternion.nontrivial,
     (by infer_instance : MonoidWithZero
         ℍ[R]) with
     inv := Inv.inv
-    inv_zero := by rw [has_inv_inv, conj_zero, smul_zero]
+    inv_zero := by rw [has_inv_inv, star_zero, smul_zero]
     mul_inv_cancel := fun a ha => by
-      rw [has_inv_inv, Algebra.mul_smul_comm, self_mul_conj, smul_coe,
+      rw [has_inv_inv, Algebra.mul_smul_comm, self_mul_star, smul_coe,
         inv_mul_cancel (norm_sq_ne_zero.2 ha), coe_one] }
 
 @[norm_cast, simp]
@@ -1606,19 +1456,6 @@ theorem coe_rat_cast (q : ℚ) : ↑(q : R) = (q : ℍ[R]) :=
   rfl
 #align quaternion.coe_rat_cast Quaternion.coe_rat_cast
 
-theorem conj_inv : conj a⁻¹ = (conj a)⁻¹ :=
-  star_inv' a
-#align quaternion.conj_inv Quaternion.conj_inv
-
-theorem conj_zpow (z : ℤ) : conj (a ^ z) = conj a ^ z :=
-  star_zpow₀ a z
-#align quaternion.conj_zpow Quaternion.conj_zpow
-
-@[simp, norm_cast]
-theorem conj_rat_cast (q : ℚ) : conj (q : ℍ[R]) = q :=
-  @star_ratCast ℍ[R] _ _ q
-#align quaternion.conj_rat_cast Quaternion.conj_rat_cast
-
 @[simp]
 theorem normSq_inv : normSq a⁻¹ = (normSq a)⁻¹ :=
   map_inv₀ normSq _

mathlib commit https://github.com/leanprover-community/mathlib/commit/9b2b58d6b14b895b2f375108e765cb47de71aebd

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 
 ! This file was ported from Lean 3 source module algebra.quaternion
-! leanprover-community/mathlib commit 039a089d2a4b93c761b234f3e5f5aeb752bac60f
+! leanprover-community/mathlib commit dc7ac07acd84584426773e69e51035bea9a770e7
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -612,10 +612,23 @@ theorem conj_add : (a + b).conj = a.conj + b.conj :=
 theorem conj_mul : (a * b).conj = b.conj * a.conj := by ext <;> simp <;> ring
 #align quaternion_algebra.conj_mul QuaternionAlgebra.conj_mul
 
-theorem conj_conj_mul : (a.conj * b).conj = b.conj * a := by rw [conj_mul, conj_conj]
+instance : StarRing ℍ[R,c₁,c₂] where
+  unit := conj
+  star_involutive := conj_conj
+  star_add := conj_add
+  star_mul := conj_mul
+
+@[simp]
+theorem star_def (a : ℍ[R,c₁,c₂]) : star a = conj a :=
+  rfl
+#align quaternion_algebra.star_def QuaternionAlgebra.star_def
+
+theorem conj_conj_mul : (a.conj * b).conj = b.conj * a :=
+  star_star_mul _ _
 #align quaternion_algebra.conj_conj_mul QuaternionAlgebra.conj_conj_mul
 
-theorem conj_mul_conj : (a * b.conj).conj = b * a.conj := by rw [conj_mul, conj_conj]
+theorem conj_mul_conj : (a * b.conj).conj = b * a.conj :=
+  star_mul_star _ _
 #align quaternion_algebra.conj_mul_conj QuaternionAlgebra.conj_mul_conj
 
 theorem self_add_conj' : a + a.conj = ↑(2 * a.re) := by ext <;> simp [two_mul]
@@ -645,11 +658,7 @@ theorem commute_self_conj : Commute a a.conj :=
 #align quaternion_algebra.commute_self_conj QuaternionAlgebra.commute_self_conj
 
 theorem commute_conj_conj {a b : ℍ[R,c₁,c₂]} (h : Commute a b) : Commute a.conj b.conj :=
-  calc
-    a.conj * b.conj = (b * a).conj := (conj_mul b a).symm
-    _ = (a * b).conj := by rw [h.eq]
-    _ = b.conj * a.conj := conj_mul a b
-    
+  h.star_star
 #align quaternion_algebra.commute_conj_conj QuaternionAlgebra.commute_conj_conj
 
 @[simp, norm_cast]
@@ -662,11 +671,13 @@ theorem conj_im : conj a.im = -a.im :=
 #align quaternion_algebra.conj_im QuaternionAlgebra.conj_im
 
 @[simp, norm_cast]
-theorem conj_nat_cast (n : ℕ) : conj (n : ℍ[R,c₁,c₂]) = n := by rw [← coe_nat_cast, conj_coe]
+theorem conj_nat_cast (n : ℕ) : conj (n : ℍ[R,c₁,c₂]) = n :=
+  @star_natCast ℍ[R,c₁,c₂] _ _ n
 #align quaternion_algebra.conj_nat_cast QuaternionAlgebra.conj_nat_cast
 
 @[simp, norm_cast]
-theorem conj_int_cast (z : ℤ) : conj (z : ℍ[R,c₁,c₂]) = z := by rw [← coe_int_cast, conj_coe]
+theorem conj_int_cast (z : ℤ) : conj (z : ℍ[R,c₁,c₂]) = z :=
+  @star_intCast ℍ[R,c₁,c₂] _ _ z
 #align quaternion_algebra.conj_int_cast QuaternionAlgebra.conj_int_cast
 
 @[simp]
@@ -725,17 +736,6 @@ theorem conj_sub : (a - b).conj = a.conj - b.conj :=
   (conj : ℍ[R,c₁,c₂] ≃ₗ[R] _).map_sub a b
 #align quaternion_algebra.conj_sub QuaternionAlgebra.conj_sub
 
-instance : StarRing ℍ[R,c₁,c₂] where
-  unit := conj
-  star_involutive := conj_conj
-  star_add := conj_add
-  star_mul := conj_mul
-
-@[simp]
-theorem star_def (a : ℍ[R,c₁,c₂]) : star a = conj a :=
-  rfl
-#align quaternion_algebra.star_def QuaternionAlgebra.star_def
-
 @[simp]
 theorem conj_pow (n : ℕ) : (a ^ n).conj = a.conj ^ n :=
   star_pow _ _

mathlib commit https://github.com/leanprover-community/mathlib/commit/09079525fd01b3dda35e96adaa08d2f943e1648c

@@ -55,7 +55,7 @@ quaternion
 -/
 
 
-/- ./././Mathport/Syntax/Translate/Command.lean:424:34: infer kinds are unsupported in Lean 4: mk {} -/
+/- ./././Mathport/Syntax/Translate/Command.lean:429:34: infer kinds are unsupported in Lean 4: mk {} -/
 /-- Quaternion algebra over a type with fixed coefficients $a=i^2$ and $b=j^2$.
 Implemented as a structure with four fields: `re`, `im_i`, `im_j`, and `im_k`. -/
 @[nolint unused_arguments, ext]

mathlib commit https://github.com/leanprover-community/mathlib/commit/06a655b5fcfbda03502f9158bbf6c0f1400886f9

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 
 ! This file was ported from Lean 3 source module algebra.quaternion
-! leanprover-community/mathlib commit da3fc4a33ff6bc75f077f691dc94c217b8d41559
+! leanprover-community/mathlib commit 039a089d2a4b93c761b234f3e5f5aeb752bac60f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -513,17 +513,17 @@ instance : Module.Finite R ℍ[R,c₁,c₂] :=
 instance : Module.Free R ℍ[R,c₁,c₂] :=
   Module.Free.of_basis (basisOneIJK c₁ c₂)
 
-theorem dim_eq_four [StrongRankCondition R] : Module.rank R ℍ[R,c₁,c₂] = 4 :=
+theorem rank_eq_four [StrongRankCondition R] : Module.rank R ℍ[R,c₁,c₂] = 4 :=
   by
-  rw [dim_eq_card_basis (basis_one_i_j_k c₁ c₂), Fintype.card_fin]
+  rw [rank_eq_card_basis (basis_one_i_j_k c₁ c₂), Fintype.card_fin]
   norm_num
-#align quaternion_algebra.dim_eq_four QuaternionAlgebra.dim_eq_four
+#align quaternion_algebra.rank_eq_four QuaternionAlgebra.rank_eq_four
 
 theorem finrank_eq_four [StrongRankCondition R] : FiniteDimensional.finrank R ℍ[R,c₁,c₂] = 4 :=
   by
   have : Cardinal.toNat 4 = 4 := by
     rw [← Cardinal.toNat_cast 4, Nat.cast_bit0, Nat.cast_bit0, Nat.cast_one]
-  rw [FiniteDimensional.finrank, dim_eq_four, this]
+  rw [FiniteDimensional.finrank, rank_eq_four, this]
 #align quaternion_algebra.finrank_eq_four QuaternionAlgebra.finrank_eq_four
 
 end
@@ -1210,9 +1210,9 @@ instance : Module.Finite R ℍ[R] :=
 instance : Module.Free R ℍ[R] :=
   QuaternionAlgebra.Module.free _ _
 
-theorem dim_eq_four [StrongRankCondition R] : Module.rank R ℍ[R] = 4 :=
-  QuaternionAlgebra.dim_eq_four _ _
-#align quaternion.dim_eq_four Quaternion.dim_eq_four
+theorem rank_eq_four [StrongRankCondition R] : Module.rank R ℍ[R] = 4 :=
+  QuaternionAlgebra.rank_eq_four _ _
+#align quaternion.rank_eq_four Quaternion.rank_eq_four
 
 theorem finrank_eq_four [StrongRankCondition R] : FiniteDimensional.finrank R ℍ[R] = 4 :=
   QuaternionAlgebra.finrank_eq_four _ _

mathlib commit https://github.com/leanprover-community/mathlib/commit/da3fc4a33ff6bc75f077f691dc94c217b8d41559

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 
 ! This file was ported from Lean 3 source module algebra.quaternion
-! leanprover-community/mathlib commit d90149e913bf65828b011379540c3379e01105fd
+! leanprover-community/mathlib commit da3fc4a33ff6bc75f077f691dc94c217b8d41559
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -688,13 +688,22 @@ theorem eq_re_iff_mem_range_coe {a : ℍ[R,c₁,c₂]} :
   ⟨fun h => ⟨a.re, h.symm⟩, fun ⟨x, h⟩ => eq_re_of_eq_coe h.symm⟩
 #align quaternion_algebra.eq_re_iff_mem_range_coe QuaternionAlgebra.eq_re_iff_mem_range_coe
 
+section CharZero
+
+variable [NoZeroDivisors R] [CharZero R]
+
 @[simp]
-theorem conj_fixed {R : Type _} [CommRing R] [NoZeroDivisors R] [CharZero R] {c₁ c₂ : R}
-    {a : ℍ[R,c₁,c₂]} : conj a = a ↔ a = a.re := by
+theorem conj_eq_self {c₁ c₂ : R} {a : ℍ[R,c₁,c₂]} : conj a = a ↔ a = a.re := by
   simp [ext_iff, neg_eq_iff_add_eq_zero, add_self_eq_zero]
-#align quaternion_algebra.conj_fixed QuaternionAlgebra.conj_fixed
+#align quaternion_algebra.conj_eq_self QuaternionAlgebra.conj_eq_self
+
+theorem conj_eq_neg {c₁ c₂ : R} {a : ℍ[R,c₁,c₂]} : conj a = -a ↔ a.re = 0 := by
+  simp [ext_iff, eq_neg_iff_add_eq_zero]
+#align quaternion_algebra.conj_eq_neg QuaternionAlgebra.conj_eq_neg
 
--- Can't use `rw ← conj_fixed` in the proof without additional assumptions
+end CharZero
+
+-- Can't use `rw ← conj_eq_self` in the proof without additional assumptions
 theorem conj_mul_eq_coe : conj a * a = (conj a * a).re := by ext <;> simp <;> ring
 #align quaternion_algebra.conj_mul_eq_coe QuaternionAlgebra.conj_mul_eq_coe
 
@@ -1336,11 +1345,21 @@ theorem eq_re_iff_mem_range_coe {a : ℍ[R]} : a = a.re ↔ a ∈ Set.range (coe
   QuaternionAlgebra.eq_re_iff_mem_range_coe
 #align quaternion.eq_re_iff_mem_range_coe Quaternion.eq_re_iff_mem_range_coe
 
+section CharZero
+
+variable [NoZeroDivisors R] [CharZero R]
+
+@[simp]
+theorem conj_eq_self {a : ℍ[R]} : conj a = a ↔ a = a.re :=
+  QuaternionAlgebra.conj_eq_self
+#align quaternion.conj_eq_self Quaternion.conj_eq_self
+
 @[simp]
-theorem conj_fixed {R : Type _} [CommRing R] [NoZeroDivisors R] [CharZero R] {a : ℍ[R]} :
-    conj a = a ↔ a = a.re :=
-  QuaternionAlgebra.conj_fixed
-#align quaternion.conj_fixed Quaternion.conj_fixed
+theorem conj_eq_neg {a : ℍ[R]} : conj a = -a ↔ a.re = 0 :=
+  QuaternionAlgebra.conj_eq_neg
+#align quaternion.conj_eq_neg Quaternion.conj_eq_neg
+
+end CharZero
 
 theorem conj_mul_eq_coe : conj a * a = (conj a * a).re :=
   a.conj_mul_eq_coe
@@ -1437,6 +1456,20 @@ theorem coe_normSq_add : (normSq (a + b) : ℍ[R]) = normSq a + a * b.conj + b *
   by simp [← self_mul_conj, mul_add, add_mul, add_assoc]
 #align quaternion.coe_norm_sq_add Quaternion.coe_normSq_add
 
+theorem normSq_smul (r : R) (q : ℍ[R]) : normSq (r • q) = r ^ 2 * normSq q := by
+  simp_rw [norm_sq_def, conj_smul, smul_mul_smul, smul_re, sq, smul_eq_mul]
+#align quaternion.norm_sq_smul Quaternion.normSq_smul
+
+theorem normSq_add (a b : ℍ[R]) : normSq (a + b) = normSq a + normSq b + 2 * (a * conj b).re :=
+  calc
+    normSq (a + b) = normSq a + (a * conj b).re + ((b * conj a).re + normSq b) := by
+      simp_rw [norm_sq_def, conj_add, add_mul, mul_add, add_re]
+    _ = normSq a + normSq b + ((a * conj b).re + (b * conj a).re) := by abel
+    _ = normSq a + normSq b + 2 * (a * conj b).re := by
+      rw [← add_re, ← conj_mul_conj a b, self_add_conj', coe_re]
+    
+#align quaternion.norm_sq_add Quaternion.normSq_add
+
 end Quaternion
 
 namespace Quaternion
@@ -1482,6 +1515,22 @@ instance : NoZeroDivisors ℍ[R] :=
 instance : IsDomain ℍ[R] :=
   NoZeroDivisors.to_isDomain _
 
+theorem sq_eq_normSq : a ^ 2 = normSq a ↔ a = a.re :=
+  by
+  simp_rw [← conj_eq_self]
+  obtain rfl | hq0 := eq_or_ne a 0
+  · simp
+  · rw [← conj_mul_self, sq, mul_left_inj' hq0, eq_comm]
+#align quaternion.sq_eq_norm_sq Quaternion.sq_eq_normSq
+
+theorem sq_eq_neg_normSq : a ^ 2 = -normSq a ↔ a.re = 0 :=
+  by
+  simp_rw [← conj_eq_neg]
+  obtain rfl | hq0 := eq_or_ne a 0
+  · simp
+  rw [← conj_mul_self, ← mul_neg, ← neg_sq, sq, mul_left_inj' (neg_ne_zero.mpr hq0), eq_comm]
+#align quaternion.sq_eq_neg_norm_sq Quaternion.sq_eq_neg_normSq
+
 end LinearOrderedCommRing
 
 section Field

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

@@ -1385,7 +1385,7 @@ theorem coe_conjAe : ⇑(conjAe : ℍ[R] ≃ₐ[R] ℍ[R]ᵐᵒᵖ) = op ∘ con
 /-- Square of the norm. -/
 def normSq : ℍ[R] →*₀ R where
   toFun a := (a * a.conj).re
-  map_zero' := by rw [conj_zero, zero_mul, zero_re]
+  map_zero' := by rw [conj_zero, MulZeroClass.zero_mul, zero_re]
   map_one' := by rw [conj_one, one_mul, one_re]
   map_mul' x y :=
     coe_injective <| by

mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211

@@ -511,7 +511,7 @@ instance : Module.Finite R ℍ[R,c₁,c₂] :=
   Module.Finite.of_basis (basisOneIJK c₁ c₂)
 
 instance : Module.Free R ℍ[R,c₁,c₂] :=
-  Module.Free.ofBasis (basisOneIJK c₁ c₂)
+  Module.Free.of_basis (basisOneIJK c₁ c₂)
 
 theorem dim_eq_four [StrongRankCondition R] : Module.rank R ℍ[R,c₁,c₂] = 4 :=
   by

mathlib commit https://github.com/leanprover-community/mathlib/commit/271bf175e6c51b8d31d6c0107b7bb4a967c7277e

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 
 ! This file was ported from Lean 3 source module algebra.quaternion
-! leanprover-community/mathlib commit 48085f140e684306f9e7da907cd5932056d1aded
+! leanprover-community/mathlib commit d90149e913bf65828b011379540c3379e01105fd
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -104,25 +104,55 @@ theorem mk.eta {R : Type _} {c₁ c₂} : ∀ a : ℍ[R,c₁,c₂], mk a.1 a.2 a
 
 variable {S T R : Type _} [CommRing R] {c₁ c₂ : R} (r x y z : R) (a b c : ℍ[R,c₁,c₂])
 
+/-- The imaginary part of a quaternion. -/
+def im (x : ℍ[R,c₁,c₂]) : ℍ[R,c₁,c₂] :=
+  ⟨0, x.imI, x.imJ, x.imK⟩
+#align quaternion_algebra.im QuaternionAlgebra.im
+
+@[simp]
+theorem im_re : a.im.re = 0 :=
+  rfl
+#align quaternion_algebra.im_re QuaternionAlgebra.im_re
+
+@[simp]
+theorem im_imI : a.im.imI = a.imI :=
+  rfl
+#align quaternion_algebra.im_im_i QuaternionAlgebra.im_imI
+
+@[simp]
+theorem im_imJ : a.im.imJ = a.imJ :=
+  rfl
+#align quaternion_algebra.im_im_j QuaternionAlgebra.im_imJ
+
+@[simp]
+theorem im_imK : a.im.imK = a.imK :=
+  rfl
+#align quaternion_algebra.im_im_k QuaternionAlgebra.im_imK
+
+@[simp]
+theorem im_idem : a.im.im = a.im :=
+  rfl
+#align quaternion_algebra.im_idem QuaternionAlgebra.im_idem
+
 instance : CoeTC R ℍ[R,c₁,c₂] :=
   ⟨fun x => ⟨x, 0, 0, 0⟩⟩
 
-@[simp]
+@[simp, norm_cast]
 theorem coe_re : (x : ℍ[R,c₁,c₂]).re = x :=
   rfl
 #align quaternion_algebra.coe_re QuaternionAlgebra.coe_re
 
-@[simp]
+@[simp, norm_cast]
 theorem coe_imI : (x : ℍ[R,c₁,c₂]).imI = 0 :=
   rfl
 #align quaternion_algebra.coe_im_i QuaternionAlgebra.coe_imI
 
-@[simp]
+@[simp, norm_cast]
 theorem coe_imJ : (x : ℍ[R,c₁,c₂]).imJ = 0 :=
   rfl
 #align quaternion_algebra.coe_im_j QuaternionAlgebra.coe_imJ
 
-@[simp]
+@[simp, norm_cast]
 theorem coe_imK : (x : ℍ[R,c₁,c₂]).imK = 0 :=
   rfl
 #align quaternion_algebra.coe_im_k QuaternionAlgebra.coe_imK
@@ -193,6 +223,26 @@ theorem mk_sub_mk (a₁ a₂ a₃ a₄ b₁ b₂ b₃ b₄ : R) :
   rfl
 #align quaternion_algebra.mk_sub_mk QuaternionAlgebra.mk_sub_mk
 
+@[simp, norm_cast]
+theorem coe_im : (x : ℍ[R,c₁,c₂]).im = 0 :=
+  rfl
+#align quaternion_algebra.coe_im QuaternionAlgebra.coe_im
+
+@[simp]
+theorem re_add_im : ↑a.re + a.im = a :=
+  ext _ _ (add_zero _) (zero_add _) (zero_add _) (zero_add _)
+#align quaternion_algebra.re_add_im QuaternionAlgebra.re_add_im
+
+@[simp]
+theorem sub_self_im : a - a.im = a.re :=
+  ext _ _ (sub_zero _) (sub_self _) (sub_self _) (sub_self _)
+#align quaternion_algebra.sub_self_im QuaternionAlgebra.sub_self_im
+
+@[simp]
+theorem sub_self_re : a - a.re = a.im :=
+  ext _ _ (sub_self _) (sub_zero _) (sub_zero _) (sub_zero _)
+#align quaternion_algebra.sub_self_re QuaternionAlgebra.sub_self_re
+
 /-- Multiplication is given by
 
 * `1 * x = x * 1 = x`;
@@ -315,6 +365,11 @@ theorem nat_cast_imK (n : ℕ) : (n : ℍ[R,c₁,c₂]).imK = 0 :=
   rfl
 #align quaternion_algebra.nat_cast_im_k QuaternionAlgebra.nat_cast_imK
 
+@[simp, norm_cast]
+theorem nat_cast_im (n : ℕ) : (n : ℍ[R,c₁,c₂]).im = 0 :=
+  rfl
+#align quaternion_algebra.nat_cast_im QuaternionAlgebra.nat_cast_im
+
 @[norm_cast]
 theorem coe_nat_cast (n : ℕ) : ↑(n : R) = (n : ℍ[R,c₁,c₂]) :=
   rfl
@@ -340,6 +395,11 @@ theorem int_cast_imK (z : ℤ) : (z : ℍ[R,c₁,c₂]).imK = 0 :=
   rfl
 #align quaternion_algebra.int_cast_im_k QuaternionAlgebra.int_cast_imK
 
+@[simp, norm_cast]
+theorem int_cast_im (z : ℤ) : (z : ℍ[R,c₁,c₂]).im = 0 :=
+  rfl
+#align quaternion_algebra.int_cast_im QuaternionAlgebra.int_cast_im
+
 @[norm_cast]
 theorem coe_int_cast (z : ℤ) : ↑(z : R) = (z : ℍ[R,c₁,c₂]) :=
   rfl
@@ -529,6 +589,11 @@ theorem imK_conj : (conj a).imK = -a.imK :=
   rfl
 #align quaternion_algebra.im_k_conj QuaternionAlgebra.imK_conj
 
+@[simp]
+theorem im_conj : (conj a).im = -a.im :=
+  ext _ _ neg_zero.symm rfl rfl rfl
+#align quaternion_algebra.im_conj QuaternionAlgebra.im_conj
+
 @[simp]
 theorem conj_mk (a₁ a₂ a₃ a₄ : R) : conj (mk a₁ a₂ a₃ a₄ : ℍ[R,c₁,c₂]) = ⟨a₁, -a₂, -a₃, -a₄⟩ :=
   rfl
@@ -591,6 +656,11 @@ theorem commute_conj_conj {a b : ℍ[R,c₁,c₂]} (h : Commute a b) : Commute a
 theorem conj_coe : conj (x : ℍ[R,c₁,c₂]) = x := by ext <;> simp
 #align quaternion_algebra.conj_coe QuaternionAlgebra.conj_coe
 
+@[simp]
+theorem conj_im : conj a.im = -a.im :=
+  im_conj _
+#align quaternion_algebra.conj_im QuaternionAlgebra.conj_im
+
 @[simp, norm_cast]
 theorem conj_nat_cast (n : ℕ) : conj (n : ℍ[R,c₁,c₂]) = n := by rw [← coe_nat_cast, conj_coe]
 #align quaternion_algebra.conj_nat_cast QuaternionAlgebra.conj_nat_cast
@@ -747,6 +817,51 @@ theorem ext_iff {a b : ℍ[R]} :
   QuaternionAlgebra.ext_iff a b
 #align quaternion.ext_iff Quaternion.ext_iff
 
+/-- The imaginary part of a quaternion. -/
+def im (x : ℍ[R]) : ℍ[R] :=
+  x.im
+#align quaternion.im Quaternion.im
+
+@[simp]
+theorem im_re : a.im.re = 0 :=
+  rfl
+#align quaternion.im_re Quaternion.im_re
+
+@[simp]
+theorem im_imI : a.im.imI = a.imI :=
+  rfl
+#align quaternion.im_im_i Quaternion.im_imI
+
+@[simp]
+theorem im_imJ : a.im.imJ = a.imJ :=
+  rfl
+#align quaternion.im_im_j Quaternion.im_imJ
+
+@[simp]
+theorem im_imK : a.im.imK = a.imK :=
+  rfl
+#align quaternion.im_im_k Quaternion.im_imK
+
+@[simp]
+theorem im_idem : a.im.im = a.im :=
+  rfl
+#align quaternion.im_idem Quaternion.im_idem
+
+@[simp]
+theorem re_add_im : ↑a.re + a.im = a :=
+  a.re_add_im
+#align quaternion.re_add_im Quaternion.re_add_im
+
+@[simp]
+theorem sub_self_im : a - a.im = a.re :=
+  a.sub_self_im
+#align quaternion.sub_self_im Quaternion.sub_self_im
+
+@[simp]
+theorem sub_self_re : a - a.re = a.im :=
+  a.sub_self_re
+#align quaternion.sub_self_re Quaternion.sub_self_re
+
 @[simp, norm_cast]
 theorem coe_re : (x : ℍ[R]).re = x :=
   rfl
@@ -767,6 +882,11 @@ theorem coe_imK : (x : ℍ[R]).imK = 0 :=
   rfl
 #align quaternion.coe_im_k Quaternion.coe_imK
 
+@[simp, norm_cast]
+theorem coe_im : (x : ℍ[R]).im = 0 :=
+  rfl
+#align quaternion.coe_im Quaternion.coe_im
+
 @[simp]
 theorem zero_re : (0 : ℍ[R]).re = 0 :=
   rfl
@@ -787,6 +907,11 @@ theorem zero_imK : (0 : ℍ[R]).imK = 0 :=
   rfl
 #align quaternion.zero_im_k Quaternion.zero_imK
 
+@[simp]
+theorem zero_im : (0 : ℍ[R]).im = 0 :=
+  rfl
+#align quaternion.zero_im Quaternion.zero_im
+
 @[simp, norm_cast]
 theorem coe_zero : ((0 : R) : ℍ[R]) = 0 :=
   rfl
@@ -812,6 +937,11 @@ theorem one_imK : (1 : ℍ[R]).imK = 0 :=
   rfl
 #align quaternion.one_im_k Quaternion.one_imK
 
+@[simp]
+theorem one_im : (1 : ℍ[R]).im = 0 :=
+  rfl
+#align quaternion.one_im Quaternion.one_im
+
 @[simp, norm_cast]
 theorem coe_one : ((1 : R) : ℍ[R]) = 1 :=
   rfl
@@ -837,6 +967,11 @@ theorem add_imK : (a + b).imK = a.imK + b.imK :=
   rfl
 #align quaternion.add_im_k Quaternion.add_imK
 
+@[simp]
+theorem add_im : (a + b).im = a.im + b.im :=
+  ext _ _ (add_zero _).symm rfl rfl rfl
+#align quaternion.add_im Quaternion.add_im
+
 @[simp, norm_cast]
 theorem coe_add : ((x + y : R) : ℍ[R]) = x + y :=
   QuaternionAlgebra.coe_add x y
@@ -862,6 +997,11 @@ theorem neg_imK : (-a).imK = -a.imK :=
   rfl
 #align quaternion.neg_im_k Quaternion.neg_imK
 
+@[simp]
+theorem neg_im : (-a).im = -a.im :=
+  ext _ _ neg_zero.symm rfl rfl rfl
+#align quaternion.neg_im Quaternion.neg_im
+
 @[simp, norm_cast]
 theorem coe_neg : ((-x : R) : ℍ[R]) = -x :=
   QuaternionAlgebra.coe_neg x
@@ -887,6 +1027,11 @@ theorem sub_imK : (a - b).imK = a.imK - b.imK :=
   rfl
 #align quaternion.sub_im_k Quaternion.sub_imK
 
+@[simp]
+theorem sub_im : (a - b).im = a.im - b.im :=
+  ext _ _ (sub_zero _).symm rfl rfl rfl
+#align quaternion.sub_im Quaternion.sub_im
+
 @[simp, norm_cast]
 theorem coe_sub : ((x - y : R) : ℍ[R]) = x - y :=
   QuaternionAlgebra.coe_sub x y
@@ -946,6 +1091,11 @@ theorem nat_cast_imK (n : ℕ) : (n : ℍ[R]).imK = 0 :=
   rfl
 #align quaternion.nat_cast_im_k Quaternion.nat_cast_imK
 
+@[simp, norm_cast]
+theorem nat_cast_im (n : ℕ) : (n : ℍ[R]).im = 0 :=
+  rfl
+#align quaternion.nat_cast_im Quaternion.nat_cast_im
+
 @[norm_cast]
 theorem coe_nat_cast (n : ℕ) : ↑(n : R) = (n : ℍ[R]) :=
   rfl
@@ -971,6 +1121,11 @@ theorem int_cast_imK (z : ℤ) : (z : ℍ[R]).imK = 0 :=
   rfl
 #align quaternion.int_cast_im_k Quaternion.int_cast_imK
 
+@[simp, norm_cast]
+theorem int_cast_im (z : ℤ) : (z : ℍ[R]).im = 0 :=
+  rfl
+#align quaternion.int_cast_im Quaternion.int_cast_im
+
 @[norm_cast]
 theorem coe_int_cast (z : ℤ) : ↑(z : R) = (z : ℍ[R]) :=
   rfl
@@ -1005,6 +1160,11 @@ theorem smul_imK [SMul S R] (s : S) : (s • a).imK = s • a.imK :=
   rfl
 #align quaternion.smul_im_k Quaternion.smul_imK
 
+@[simp]
+theorem smul_im [SMulZeroClass S R] (s : S) : (s • a).im = s • a.im :=
+  ext _ _ (smul_zero _).symm rfl rfl rfl
+#align quaternion.smul_im Quaternion.smul_im
+
 @[simp, norm_cast]
 theorem coe_smul [SMulZeroClass S R] (s : S) (r : R) : (↑(s • r) : ℍ[R]) = s • ↑r :=
   QuaternionAlgebra.coe_smul _ _
@@ -1074,6 +1234,11 @@ theorem conj_imK : a.conj.imK = -a.imK :=
   rfl
 #align quaternion.conj_im_k Quaternion.conj_imK
 
+@[simp]
+theorem conj_im : a.conj.im = -a.im :=
+  a.im_conj
+#align quaternion.conj_im Quaternion.conj_im
+
 @[simp]
 theorem conj_conj : a.conj.conj = a :=
   a.conj_conj
@@ -1137,6 +1302,11 @@ theorem conj_coe : conj (x : ℍ[R]) = x :=
   QuaternionAlgebra.conj_coe x
 #align quaternion.conj_coe Quaternion.conj_coe
 
+@[simp]
+theorem im_conj : a.im.conj = -a.im :=
+  QuaternionAlgebra.im_conj _
+#align quaternion.im_conj Quaternion.im_conj
+
 @[simp, norm_cast]
 theorem conj_nat_cast (n : ℕ) : conj (n : ℍ[R]) = n :=
   QuaternionAlgebra.conj_nat_cast _
@@ -1259,6 +1429,10 @@ theorem self_mul_conj : a * a.conj = normSq a := by rw [mul_conj_eq_coe, norm_sq
 theorem conj_mul_self : a.conj * a = normSq a := by rw [← a.commute_self_conj.eq, self_mul_conj]
 #align quaternion.conj_mul_self Quaternion.conj_mul_self
 
+theorem im_sq : a.im ^ 2 = -normSq a.im := by
+  simp_rw [sq, ← conj_mul_self, im_conj, neg_mul, neg_neg]
+#align quaternion.im_sq Quaternion.im_sq
+
 theorem coe_normSq_add : (normSq (a + b) : ℍ[R]) = normSq a + a * b.conj + b * a.conj + normSq b :=
   by simp [← self_mul_conj, mul_add, add_mul, add_assoc]
 #align quaternion.coe_norm_sq_add Quaternion.coe_normSq_add
@@ -1373,6 +1547,11 @@ theorem rat_cast_imK (q : ℚ) : (q : ℍ[R]).imK = 0 :=
   rfl
 #align quaternion.rat_cast_im_k Quaternion.rat_cast_imK
 
+@[simp, norm_cast]
+theorem rat_cast_im (q : ℚ) : (q : ℍ[R]).im = 0 :=
+  rfl
+#align quaternion.rat_cast_im Quaternion.rat_cast_im
+
 @[norm_cast]
 theorem coe_rat_cast (q : ℚ) : ↑(q : R) = (q : ℍ[R]) :=
   rfl

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

A PR analogous to #12338 and #12361: reformatting proofs following the multiple goals linter of #12339.

@@ -1297,7 +1297,7 @@ variable [LinearOrderedCommRing R] {a : ℍ[R]}
 theorem normSq_eq_zero : normSq a = 0 ↔ a = 0 := by
   refine' ⟨fun h => _, fun h => h.symm ▸ normSq.map_zero⟩
   rw [normSq_def', add_eq_zero_iff', add_eq_zero_iff', add_eq_zero_iff'] at h
-  exact ext a 0 (pow_eq_zero h.1.1.1) (pow_eq_zero h.1.1.2) (pow_eq_zero h.1.2) (pow_eq_zero h.2)
+  · exact ext a 0 (pow_eq_zero h.1.1.1) (pow_eq_zero h.1.1.2) (pow_eq_zero h.1.2) (pow_eq_zero h.2)
   all_goals apply_rules [sq_nonneg, add_nonneg]
 #align quaternion.norm_sq_eq_zero Quaternion.normSq_eq_zero
 

Define the canonical coercion from the nonnegative rationals to any division semiring.

From LeanAPAP

@@ -1373,8 +1373,14 @@ theorem coe_zpow (x : R) (z : ℤ) : ((x ^ z : R) : ℍ[R]) = (x : ℍ[R]) ^ z :
   map_zpow₀ (algebraMap R ℍ[R]) x z
 #align quaternion.coe_zpow Quaternion.coe_zpow
 
+instance instNNRatCast : NNRatCast ℍ[R] where nnratCast q := (q : R)
 instance instRatCast : RatCast ℍ[R] where ratCast q := (q : R)
 
+@[simp, norm_cast] lemma re_nnratCast (q : ℚ≥0) : (q : ℍ[R]).re = q := rfl
+@[simp, norm_cast] lemma im_nnratCast (q : ℚ≥0) : (q : ℍ[R]).im = 0 := rfl
+@[simp, norm_cast] lemma imI_nnratCast (q : ℚ≥0) : (q : ℍ[R]).imI = 0 := rfl
+@[simp, norm_cast] lemma imJ_nnratCast (q : ℚ≥0) : (q : ℍ[R]).imJ = 0 := rfl
+@[simp, norm_cast] lemma imK_nnratCast (q : ℚ≥0) : (q : ℍ[R]).imK = 0 := rfl
 @[simp, norm_cast] lemma ratCast_re (q : ℚ) : (q : ℍ[R]).re = q := rfl
 @[simp, norm_cast] lemma ratCast_im (q : ℚ) : (q : ℍ[R]).im = 0 := rfl
 @[simp, norm_cast] lemma ratCast_imI (q : ℚ) : (q : ℍ[R]).imI = 0 := rfl
@@ -1386,14 +1392,18 @@ instance instRatCast : RatCast ℍ[R] where ratCast q := (q : R)
 #align quaternion.rat_cast_im_j Quaternion.ratCast_imJ
 #align quaternion.rat_cast_im_k Quaternion.ratCast_imK
 
+@[norm_cast] lemma coe_nnratCast (q : ℚ≥0) : ↑(q : R) = (q : ℍ[R]) := rfl
 @[norm_cast] lemma coe_ratCast (q : ℚ) : ↑(q : R) = (q : ℍ[R]) := rfl
 #align quaternion.coe_rat_cast Quaternion.coe_ratCast
 
 instance instDivisionRing : DivisionRing ℍ[R] where
   __ := Quaternion.instGroupWithZero
   __ := Quaternion.instRing
-  ratCast_def q := by rw [← coe_ratCast, Rat.cast_def, coe_div, coe_intCast, coe_natCast]
+  nnqsmul := (· • ·)
   qsmul := (· • ·)
+  nnratCast_def q := by rw [← coe_nnratCast, NNRat.cast_def, coe_div, coe_natCast, coe_natCast]
+  ratCast_def q := by rw [← coe_ratCast, Rat.cast_def, coe_div, coe_intCast, coe_natCast]
+  nnqsmul_def q x := by rw [← coe_nnratCast, coe_mul_eq_smul]; ext <;> exact NNRat.smul_def _ _
   qsmul_def q x := by rw [← coe_ratCast, coe_mul_eq_smul]; ext <;> exact Rat.smul_def _ _
 
 --@[simp] Porting note (#10618): `simp` can prove it

Now that I am defining NNRat.cast, I want a definitive answer to this naming issue. Plenty of lemmas in mathlib already use natCast/intCast/ratCast over nat_cast/int_cast/rat_cast, and this matches with the general expectation that underscore-separated name parts correspond to a single declaration.

@@ -406,64 +406,64 @@ instance : AddCommGroupWithOne ℍ[R,c₁,c₂] where
     rw [Int.cast_negSucc, coe_neg]
 
 @[simp, norm_cast]
-theorem nat_cast_re (n : ℕ) : (n : ℍ[R,c₁,c₂]).re = n :=
+theorem natCast_re (n : ℕ) : (n : ℍ[R,c₁,c₂]).re = n :=
   rfl
-#align quaternion_algebra.nat_cast_re QuaternionAlgebra.nat_cast_re
+#align quaternion_algebra.nat_cast_re QuaternionAlgebra.natCast_re
 
 @[simp, norm_cast]
-theorem nat_cast_imI (n : ℕ) : (n : ℍ[R,c₁,c₂]).imI = 0 :=
+theorem natCast_imI (n : ℕ) : (n : ℍ[R,c₁,c₂]).imI = 0 :=
   rfl
-#align quaternion_algebra.nat_cast_im_i QuaternionAlgebra.nat_cast_imI
+#align quaternion_algebra.nat_cast_im_i QuaternionAlgebra.natCast_imI
 
 @[simp, norm_cast]
-theorem nat_cast_imJ (n : ℕ) : (n : ℍ[R,c₁,c₂]).imJ = 0 :=
+theorem natCast_imJ (n : ℕ) : (n : ℍ[R,c₁,c₂]).imJ = 0 :=
   rfl
-#align quaternion_algebra.nat_cast_im_j QuaternionAlgebra.nat_cast_imJ
+#align quaternion_algebra.nat_cast_im_j QuaternionAlgebra.natCast_imJ
 
 @[simp, norm_cast]
-theorem nat_cast_imK (n : ℕ) : (n : ℍ[R,c₁,c₂]).imK = 0 :=
+theorem natCast_imK (n : ℕ) : (n : ℍ[R,c₁,c₂]).imK = 0 :=
   rfl
-#align quaternion_algebra.nat_cast_im_k QuaternionAlgebra.nat_cast_imK
+#align quaternion_algebra.nat_cast_im_k QuaternionAlgebra.natCast_imK
 
 @[simp, norm_cast]
-theorem nat_cast_im (n : ℕ) : (n : ℍ[R,c₁,c₂]).im = 0 :=
+theorem natCast_im (n : ℕ) : (n : ℍ[R,c₁,c₂]).im = 0 :=
   rfl
-#align quaternion_algebra.nat_cast_im QuaternionAlgebra.nat_cast_im
+#align quaternion_algebra.nat_cast_im QuaternionAlgebra.natCast_im
 
 @[norm_cast]
-theorem coe_nat_cast (n : ℕ) : ↑(n : R) = (n : ℍ[R,c₁,c₂]) :=
+theorem coe_natCast (n : ℕ) : ↑(n : R) = (n : ℍ[R,c₁,c₂]) :=
   rfl
-#align quaternion_algebra.coe_nat_cast QuaternionAlgebra.coe_nat_cast
+#align quaternion_algebra.coe_nat_cast QuaternionAlgebra.coe_natCast
 
 @[simp, norm_cast]
-theorem int_cast_re (z : ℤ) : (z : ℍ[R,c₁,c₂]).re = z :=
+theorem intCast_re (z : ℤ) : (z : ℍ[R,c₁,c₂]).re = z :=
   rfl
-#align quaternion_algebra.int_cast_re QuaternionAlgebra.int_cast_re
+#align quaternion_algebra.int_cast_re QuaternionAlgebra.intCast_re
 
 @[simp, norm_cast]
-theorem int_cast_imI (z : ℤ) : (z : ℍ[R,c₁,c₂]).imI = 0 :=
+theorem intCast_imI (z : ℤ) : (z : ℍ[R,c₁,c₂]).imI = 0 :=
   rfl
-#align quaternion_algebra.int_cast_im_i QuaternionAlgebra.int_cast_imI
+#align quaternion_algebra.int_cast_im_i QuaternionAlgebra.intCast_imI
 
 @[simp, norm_cast]
-theorem int_cast_imJ (z : ℤ) : (z : ℍ[R,c₁,c₂]).imJ = 0 :=
+theorem intCast_imJ (z : ℤ) : (z : ℍ[R,c₁,c₂]).imJ = 0 :=
   rfl
-#align quaternion_algebra.int_cast_im_j QuaternionAlgebra.int_cast_imJ
+#align quaternion_algebra.int_cast_im_j QuaternionAlgebra.intCast_imJ
 
 @[simp, norm_cast]
-theorem int_cast_imK (z : ℤ) : (z : ℍ[R,c₁,c₂]).imK = 0 :=
+theorem intCast_imK (z : ℤ) : (z : ℍ[R,c₁,c₂]).imK = 0 :=
   rfl
-#align quaternion_algebra.int_cast_im_k QuaternionAlgebra.int_cast_imK
+#align quaternion_algebra.int_cast_im_k QuaternionAlgebra.intCast_imK
 
 @[simp, norm_cast]
-theorem int_cast_im (z : ℤ) : (z : ℍ[R,c₁,c₂]).im = 0 :=
+theorem intCast_im (z : ℤ) : (z : ℍ[R,c₁,c₂]).im = 0 :=
   rfl
-#align quaternion_algebra.int_cast_im QuaternionAlgebra.int_cast_im
+#align quaternion_algebra.int_cast_im QuaternionAlgebra.intCast_im
 
 @[norm_cast]
-theorem coe_int_cast (z : ℤ) : ↑(z : R) = (z : ℍ[R,c₁,c₂]) :=
+theorem coe_intCast (z : ℤ) : ↑(z : R) = (z : ℍ[R,c₁,c₂]) :=
   rfl
-#align quaternion_algebra.coe_int_cast QuaternionAlgebra.coe_int_cast
+#align quaternion_algebra.coe_int_cast QuaternionAlgebra.coe_intCast
 
 instance instRing : Ring ℍ[R,c₁,c₂] where
   __ := inferInstanceAs (AddCommGroupWithOne ℍ[R,c₁,c₂])
@@ -1002,52 +1002,52 @@ theorem coe_pow (n : ℕ) : (↑(x ^ n) : ℍ[R]) = (x : ℍ[R]) ^ n :=
 #align quaternion.coe_pow Quaternion.coe_pow
 
 @[simp, norm_cast]
-theorem nat_cast_re (n : ℕ) : (n : ℍ[R]).re = n := rfl
-#align quaternion.nat_cast_re Quaternion.nat_cast_re
+theorem natCast_re (n : ℕ) : (n : ℍ[R]).re = n := rfl
+#align quaternion.nat_cast_re Quaternion.natCast_re
 
 @[simp, norm_cast]
-theorem nat_cast_imI (n : ℕ) : (n : ℍ[R]).imI = 0 := rfl
-#align quaternion.nat_cast_im_i Quaternion.nat_cast_imI
+theorem natCast_imI (n : ℕ) : (n : ℍ[R]).imI = 0 := rfl
+#align quaternion.nat_cast_im_i Quaternion.natCast_imI
 
 @[simp, norm_cast]
-theorem nat_cast_imJ (n : ℕ) : (n : ℍ[R]).imJ = 0 := rfl
-#align quaternion.nat_cast_im_j Quaternion.nat_cast_imJ
+theorem natCast_imJ (n : ℕ) : (n : ℍ[R]).imJ = 0 := rfl
+#align quaternion.nat_cast_im_j Quaternion.natCast_imJ
 
 @[simp, norm_cast]
-theorem nat_cast_imK (n : ℕ) : (n : ℍ[R]).imK = 0 := rfl
-#align quaternion.nat_cast_im_k Quaternion.nat_cast_imK
+theorem natCast_imK (n : ℕ) : (n : ℍ[R]).imK = 0 := rfl
+#align quaternion.nat_cast_im_k Quaternion.natCast_imK
 
 @[simp, norm_cast]
-theorem nat_cast_im (n : ℕ) : (n : ℍ[R]).im = 0 := rfl
-#align quaternion.nat_cast_im Quaternion.nat_cast_im
+theorem natCast_im (n : ℕ) : (n : ℍ[R]).im = 0 := rfl
+#align quaternion.nat_cast_im Quaternion.natCast_im
 
 @[norm_cast]
-theorem coe_nat_cast (n : ℕ) : ↑(n : R) = (n : ℍ[R]) := rfl
-#align quaternion.coe_nat_cast Quaternion.coe_nat_cast
+theorem coe_natCast (n : ℕ) : ↑(n : R) = (n : ℍ[R]) := rfl
+#align quaternion.coe_nat_cast Quaternion.coe_natCast
 
 @[simp, norm_cast]
-theorem int_cast_re (z : ℤ) : (z : ℍ[R]).re = z := rfl
-#align quaternion.int_cast_re Quaternion.int_cast_re
+theorem intCast_re (z : ℤ) : (z : ℍ[R]).re = z := rfl
+#align quaternion.int_cast_re Quaternion.intCast_re
 
 @[simp, norm_cast]
-theorem int_cast_imI (z : ℤ) : (z : ℍ[R]).imI = 0 := rfl
-#align quaternion.int_cast_im_i Quaternion.int_cast_imI
+theorem intCast_imI (z : ℤ) : (z : ℍ[R]).imI = 0 := rfl
+#align quaternion.int_cast_im_i Quaternion.intCast_imI
 
 @[simp, norm_cast]
-theorem int_cast_imJ (z : ℤ) : (z : ℍ[R]).imJ = 0 := rfl
-#align quaternion.int_cast_im_j Quaternion.int_cast_imJ
+theorem intCast_imJ (z : ℤ) : (z : ℍ[R]).imJ = 0 := rfl
+#align quaternion.int_cast_im_j Quaternion.intCast_imJ
 
 @[simp, norm_cast]
-theorem int_cast_imK (z : ℤ) : (z : ℍ[R]).imK = 0 := rfl
-#align quaternion.int_cast_im_k Quaternion.int_cast_imK
+theorem intCast_imK (z : ℤ) : (z : ℍ[R]).imK = 0 := rfl
+#align quaternion.int_cast_im_k Quaternion.intCast_imK
 
 @[simp, norm_cast]
-theorem int_cast_im (z : ℤ) : (z : ℍ[R]).im = 0 := rfl
-#align quaternion.int_cast_im Quaternion.int_cast_im
+theorem intCast_im (z : ℤ) : (z : ℍ[R]).im = 0 := rfl
+#align quaternion.int_cast_im Quaternion.intCast_im
 
 @[norm_cast]
-theorem coe_int_cast (z : ℤ) : ↑(z : R) = (z : ℍ[R]) := rfl
-#align quaternion.coe_int_cast Quaternion.coe_int_cast
+theorem coe_intCast (z : ℤ) : ↑(z : R) = (z : ℍ[R]) := rfl
+#align quaternion.coe_int_cast Quaternion.coe_intCast
 
 theorem coe_injective : Function.Injective (coe : R → ℍ[R]) :=
   QuaternionAlgebra.coe_injective
@@ -1243,14 +1243,14 @@ theorem normSq_star : normSq (star a) = normSq a := by simp [normSq_def']
 #align quaternion.norm_sq_star Quaternion.normSq_star
 
 @[norm_cast]
-theorem normSq_nat_cast (n : ℕ) : normSq (n : ℍ[R]) = (n : R) ^ 2 := by
-  rw [← coe_nat_cast, normSq_coe]
-#align quaternion.norm_sq_nat_cast Quaternion.normSq_nat_cast
+theorem normSq_natCast (n : ℕ) : normSq (n : ℍ[R]) = (n : R) ^ 2 := by
+  rw [← coe_natCast, normSq_coe]
+#align quaternion.norm_sq_nat_cast Quaternion.normSq_natCast
 
 @[norm_cast]
-theorem normSq_int_cast (z : ℤ) : normSq (z : ℍ[R]) = (z : R) ^ 2 := by
-  rw [← coe_int_cast, normSq_coe]
-#align quaternion.norm_sq_int_cast Quaternion.normSq_int_cast
+theorem normSq_intCast (z : ℤ) : normSq (z : ℍ[R]) = (z : R) ^ 2 := by
+  rw [← coe_intCast, normSq_coe]
+#align quaternion.norm_sq_int_cast Quaternion.normSq_intCast
 
 @[simp]
 theorem normSq_neg : normSq (-a) = normSq a := by simp only [normSq_def, star_neg, neg_mul_neg]
@@ -1375,26 +1375,26 @@ theorem coe_zpow (x : R) (z : ℤ) : ((x ^ z : R) : ℍ[R]) = (x : ℍ[R]) ^ z :
 
 instance instRatCast : RatCast ℍ[R] where ratCast q := (q : R)
 
-@[simp, norm_cast] lemma rat_cast_re (q : ℚ) : (q : ℍ[R]).re = q := rfl
-@[simp, norm_cast] lemma rat_cast_im (q : ℚ) : (q : ℍ[R]).im = 0 := rfl
-@[simp, norm_cast] lemma rat_cast_imI (q : ℚ) : (q : ℍ[R]).imI = 0 := rfl
-@[simp, norm_cast] lemma rat_cast_imJ (q : ℚ) : (q : ℍ[R]).imJ = 0 := rfl
-@[simp, norm_cast] lemma rat_cast_imK (q : ℚ) : (q : ℍ[R]).imK = 0 := rfl
-#align quaternion.rat_cast_re Quaternion.rat_cast_re
-#align quaternion.rat_cast_im Quaternion.rat_cast_im
-#align quaternion.rat_cast_im_i Quaternion.rat_cast_imI
-#align quaternion.rat_cast_im_j Quaternion.rat_cast_imJ
-#align quaternion.rat_cast_im_k Quaternion.rat_cast_imK
+@[simp, norm_cast] lemma ratCast_re (q : ℚ) : (q : ℍ[R]).re = q := rfl
+@[simp, norm_cast] lemma ratCast_im (q : ℚ) : (q : ℍ[R]).im = 0 := rfl
+@[simp, norm_cast] lemma ratCast_imI (q : ℚ) : (q : ℍ[R]).imI = 0 := rfl
+@[simp, norm_cast] lemma ratCast_imJ (q : ℚ) : (q : ℍ[R]).imJ = 0 := rfl
+@[simp, norm_cast] lemma ratCast_imK (q : ℚ) : (q : ℍ[R]).imK = 0 := rfl
+#align quaternion.rat_cast_re Quaternion.ratCast_re
+#align quaternion.rat_cast_im Quaternion.ratCast_im
+#align quaternion.rat_cast_im_i Quaternion.ratCast_imI
+#align quaternion.rat_cast_im_j Quaternion.ratCast_imJ
+#align quaternion.rat_cast_im_k Quaternion.ratCast_imK
 
-@[norm_cast] lemma coe_rat_cast (q : ℚ) : ↑(q : R) = (q : ℍ[R]) := rfl
-#align quaternion.coe_rat_cast Quaternion.coe_rat_cast
+@[norm_cast] lemma coe_ratCast (q : ℚ) : ↑(q : R) = (q : ℍ[R]) := rfl
+#align quaternion.coe_rat_cast Quaternion.coe_ratCast
 
 instance instDivisionRing : DivisionRing ℍ[R] where
   __ := Quaternion.instGroupWithZero
   __ := Quaternion.instRing
-  ratCast_def q := by rw [← coe_rat_cast, Rat.cast_def, coe_div, coe_int_cast, coe_nat_cast]
+  ratCast_def q := by rw [← coe_ratCast, Rat.cast_def, coe_div, coe_intCast, coe_natCast]
   qsmul := (· • ·)
-  qsmul_def q x := by rw [← coe_rat_cast, coe_mul_eq_smul]; ext <;> exact Rat.smul_def _ _
+  qsmul_def q x := by rw [← coe_ratCast, coe_mul_eq_smul]; ext <;> exact Rat.smul_def _ _
 
 --@[simp] Porting note (#10618): `simp` can prove it
 theorem normSq_inv : normSq a⁻¹ = (normSq a)⁻¹ :=
@@ -1412,9 +1412,9 @@ theorem normSq_zpow (z : ℤ) : normSq (a ^ z) = normSq a ^ z :=
 #align quaternion.norm_sq_zpow Quaternion.normSq_zpow
 
 @[norm_cast]
-theorem normSq_rat_cast (q : ℚ) : normSq (q : ℍ[R]) = (q : ℍ[R]) ^ 2 := by
-  rw [← coe_rat_cast, normSq_coe, coe_pow]
-#align quaternion.norm_sq_rat_cast Quaternion.normSq_rat_cast
+theorem normSq_ratCast (q : ℚ) : normSq (q : ℍ[R]) = (q : ℍ[R]) ^ 2 := by
+  rw [← coe_ratCast, normSq_coe, coe_pow]
+#align quaternion.norm_sq_rat_cast Quaternion.normSq_ratCast
 
 end Field
 

This renames

• Int.cast_ofNat to Int.cast_natCast
• Int.int_cast_ofNat to Int.cast_ofNat

I think the history here is that this lemma was previously about Int.ofNat, before we globally fixed the simp-normal form to be Nat.cast.

Since the Int.cast_ofNat name is repurposed, it can't be deprecated. Int.int_cast_ofNat is such a wonky name that it was probably never used.

@@ -400,7 +400,7 @@ instance : AddCommGroupWithOne ℍ[R,c₁,c₂] where
   natCast_zero := by simp
   natCast_succ := by simp
   intCast n := ((n : R) : ℍ[R,c₁,c₂])
-  intCast_ofNat _ := congr_arg coe (Int.cast_ofNat _)
+  intCast_ofNat _ := congr_arg coe (Int.cast_natCast _)
   intCast_negSucc n := by
     change coe _ = -coe _
     rw [Int.cast_negSucc, coe_neg]

Soon, there will be NNRat analogs of the Rat fields in the definition of Field. NNRat is less nicely a structure than Rat, hence there is a need to reduce the dependency of Field on the internals of Rat.

This PR achieves this by restating Field.ratCast_mk' in terms of Rat.num, Rat.den. This requires fixing a few downstream instances.

Reduce the diff of #11203.

Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com>

@@ -1373,50 +1373,28 @@ theorem coe_zpow (x : R) (z : ℤ) : ((x ^ z : R) : ℍ[R]) = (x : ℍ[R]) ^ z :
   map_zpow₀ (algebraMap R ℍ[R]) x z
 #align quaternion.coe_zpow Quaternion.coe_zpow
 
--- Porting note: split from `DivisionRing` instance
-instance : RatCast ℍ[R] where
-  ratCast := fun q => ↑(q : R)
+instance instRatCast : RatCast ℍ[R] where ratCast q := (q : R)
 
-@[simp, norm_cast]
-theorem rat_cast_re (q : ℚ) : (q : ℍ[R]).re = q :=
-  rfl
+@[simp, norm_cast] lemma rat_cast_re (q : ℚ) : (q : ℍ[R]).re = q := rfl
+@[simp, norm_cast] lemma rat_cast_im (q : ℚ) : (q : ℍ[R]).im = 0 := rfl
+@[simp, norm_cast] lemma rat_cast_imI (q : ℚ) : (q : ℍ[R]).imI = 0 := rfl
+@[simp, norm_cast] lemma rat_cast_imJ (q : ℚ) : (q : ℍ[R]).imJ = 0 := rfl
+@[simp, norm_cast] lemma rat_cast_imK (q : ℚ) : (q : ℍ[R]).imK = 0 := rfl
 #align quaternion.rat_cast_re Quaternion.rat_cast_re
-
-@[simp, norm_cast]
-theorem rat_cast_imI (q : ℚ) : (q : ℍ[R]).imI = 0 :=
-  rfl
+#align quaternion.rat_cast_im Quaternion.rat_cast_im
 #align quaternion.rat_cast_im_i Quaternion.rat_cast_imI
-
-@[simp, norm_cast]
-theorem rat_cast_imJ (q : ℚ) : (q : ℍ[R]).imJ = 0 :=
-  rfl
 #align quaternion.rat_cast_im_j Quaternion.rat_cast_imJ
-
-@[simp, norm_cast]
-theorem rat_cast_imK (q : ℚ) : (q : ℍ[R]).imK = 0 :=
-  rfl
 #align quaternion.rat_cast_im_k Quaternion.rat_cast_imK
 
-@[simp, norm_cast]
-theorem rat_cast_im (q : ℚ) : (q : ℍ[R]).im = 0 :=
-  rfl
-#align quaternion.rat_cast_im Quaternion.rat_cast_im
-
-@[norm_cast]
-theorem coe_rat_cast (q : ℚ) : ↑(q : R) = (q : ℍ[R]) :=
-  rfl
+@[norm_cast] lemma coe_rat_cast (q : ℚ) : ↑(q : R) = (q : ℍ[R]) := rfl
 #align quaternion.coe_rat_cast Quaternion.coe_rat_cast
 
--- Porting note: moved below `coe_rat_cast`, as `coe_rat_cast` is needed in the `rw`s
-instance : DivisionRing ℍ[R] :=
-  { Quaternion.instGroupWithZero,
-    Quaternion.instRing with
-    ratCast_mk := fun n d hd h => by
-      rw [← coe_rat_cast, Rat.cast_mk', coe_mul, coe_int_cast, coe_inv, coe_nat_cast]
-    qsmul := (· • ·)
-    qsmul_eq_mul' := fun q x => by
-      rw [← coe_rat_cast, coe_mul_eq_smul]
-      ext <;> exact DivisionRing.qsmul_eq_mul' _ _ }
+instance instDivisionRing : DivisionRing ℍ[R] where
+  __ := Quaternion.instGroupWithZero
+  __ := Quaternion.instRing
+  ratCast_def q := by rw [← coe_rat_cast, Rat.cast_def, coe_div, coe_int_cast, coe_nat_cast]
+  qsmul := (· • ·)
+  qsmul_def q x := by rw [← coe_rat_cast, coe_mul_eq_smul]; ext <;> exact Rat.smul_def _ _
 
 --@[simp] Porting note (#10618): `simp` can prove it
 theorem normSq_inv : normSq a⁻¹ = (normSq a)⁻¹ :=

Quoting [@digama0](https://github.com/digama0):

These were actually never meant to go in the file, they are basically debugging information and only useful on significantly broken mathport files. You can safely remove all of them.

@@ -760,7 +760,6 @@ def Quaternion (R : Type*) [One R] [Neg R] :=
   QuaternionAlgebra R (-1) (-1)
 #align quaternion Quaternion
 
--- mathport name: quaternion
 scoped[Quaternion] notation "ℍ[" R "]" => Quaternion R
 
 /-- The equivalence between the quaternions over `R` and `R × R × R × R`. -/

Per the style guidelines, λ is disallowed in mathlib. This is close to exhaustive; I left some tactic code alone when it seemed to me that tactic could be upstreamed soon.

Notes

• In lines I was modifying anyway, I also converted => to ↦.
• Also contains some mild in-passing indentation fixes in Mathlib/Order/SupClosed.
• Some doc comments still contained Lean 3 syntax λ x, , which I also replaced.

@@ -393,7 +393,7 @@ theorem coe_smul [SMulZeroClass S R] (s : S) (r : R) :
 
 instance : AddCommGroup ℍ[R,c₁,c₂] :=
   (equivProd c₁ c₂).injective.addCommGroup _ rfl (fun _ _ ↦ rfl) (fun _ ↦ rfl) (fun _ _ ↦ rfl)
-    (λ _ _ ↦ rfl) (λ _ _ ↦ rfl)
+    (fun _ _ ↦ rfl) (fun _ _ ↦ rfl)
 
 instance : AddCommGroupWithOne ℍ[R,c₁,c₂] where
   natCast n := ((n : R) : ℍ[R,c₁,c₂])

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

• converts "--porting note" into "-- Porting note";
• converts "porting note" into "Porting note".

@@ -164,7 +164,7 @@ theorem coe_inj {x y : R} : (x : ℍ[R,c₁,c₂]) = y ↔ x = y :=
   coe_injective.eq_iff
 #align quaternion_algebra.coe_inj QuaternionAlgebra.coe_inj
 
--- porting note: removed `simps`, added simp lemmas manually
+-- Porting note: removed `simps`, added simp lemmas manually
 instance : Zero ℍ[R,c₁,c₂] := ⟨⟨0, 0, 0, 0⟩⟩
 
 @[simp] theorem zero_re : (0 : ℍ[R,c₁,c₂]).re = 0 := rfl
@@ -187,7 +187,7 @@ theorem coe_zero : ((0 : R) : ℍ[R,c₁,c₂]) = 0 := rfl
 
 instance : Inhabited ℍ[R,c₁,c₂] := ⟨0⟩
 
--- porting note: removed `simps`, added simp lemmas manually
+-- Porting note: removed `simps`, added simp lemmas manually
 instance : One ℍ[R,c₁,c₂] := ⟨⟨1, 0, 0, 0⟩⟩
 
 @[simp] theorem one_re : (1 : ℍ[R,c₁,c₂]).re = 1 := rfl
@@ -208,7 +208,7 @@ instance : One ℍ[R,c₁,c₂] := ⟨⟨1, 0, 0, 0⟩⟩
 theorem coe_one : ((1 : R) : ℍ[R,c₁,c₂]) = 1 := rfl
 #align quaternion_algebra.coe_one QuaternionAlgebra.coe_one
 
--- porting note: removed `simps`, added simp lemmas manually
+-- Porting note: removed `simps`, added simp lemmas manually
 instance : Add ℍ[R,c₁,c₂] :=
   ⟨fun a b => ⟨a.1 + b.1, a.2 + b.2, a.3 + b.3, a.4 + b.4⟩⟩
 
@@ -237,7 +237,7 @@ theorem mk_add_mk (a₁ a₂ a₃ a₄ b₁ b₂ b₃ b₄ : R) :
 theorem coe_add : ((x + y : R) : ℍ[R,c₁,c₂]) = x + y := by ext <;> simp
 #align quaternion_algebra.coe_add QuaternionAlgebra.coe_add
 
--- porting note: removed `simps`, added simp lemmas manually
+-- Porting note: removed `simps`, added simp lemmas manually
 instance : Neg ℍ[R,c₁,c₂] := ⟨fun a => ⟨-a.1, -a.2, -a.3, -a.4⟩⟩
 
 @[simp] theorem neg_re : (-a).re = -a.re := rfl
@@ -353,7 +353,7 @@ section
 
 variable [SMul S R] [SMul T R] (s : S)
 
--- porting note: Lean 4 auto drops the unused `[Ring R]` argument
+-- Porting note: Lean 4 auto drops the unused `[Ring R]` argument
 instance : SMul S ℍ[R,c₁,c₂] where smul s a := ⟨s • a.1, s • a.2, s • a.3, s • a.4⟩
 
 instance [SMul S T] [IsScalarTower S T R] : IsScalarTower S T ℍ[R,c₁,c₂] where
@@ -812,7 +812,7 @@ instance [SMul S R] [SMul T R] [SMulCommClass S T R] : SMulCommClass S T ℍ[R]
 protected instance algebra [CommSemiring S] [Algebra S R] : Algebra S ℍ[R] :=
   inferInstanceAs <| Algebra S ℍ[R,-1,-1]
 
--- porting note: added shortcut
+-- Porting note: added shortcut
 instance : Star ℍ[R] := QuaternionAlgebra.instStarQuaternionAlgebra
 instance : StarRing ℍ[R] := QuaternionAlgebra.instStarRing
 instance : IsStarNormal a := inferInstanceAs <| IsStarNormal (R := ℍ[R,-1,-1]) a
@@ -1354,7 +1354,7 @@ instance instGroupWithZero : GroupWithZero ℍ[R] :=
     inv := Inv.inv
     inv_zero := by rw [instInv_inv, star_zero, smul_zero]
     mul_inv_cancel := fun a ha => by
-      -- porting note: the aliased definition confuse TC search
+      -- Porting note: the aliased definition confuse TC search
       letI : Semiring ℍ[R] := inferInstanceAs (Semiring ℍ[R,-1,-1])
       rw [instInv_inv, Algebra.mul_smul_comm (normSq a)⁻¹ a (star a), self_mul_star, smul_coe,
         inv_mul_cancel (normSq_ne_zero.2 ha), coe_one] }
@@ -1374,7 +1374,7 @@ theorem coe_zpow (x : R) (z : ℤ) : ((x ^ z : R) : ℍ[R]) = (x : ℍ[R]) ^ z :
   map_zpow₀ (algebraMap R ℍ[R]) x z
 #align quaternion.coe_zpow Quaternion.coe_zpow
 
--- porting note: split from `DivisionRing` instance
+-- Porting note: split from `DivisionRing` instance
 instance : RatCast ℍ[R] where
   ratCast := fun q => ↑(q : R)
 
@@ -1408,7 +1408,7 @@ theorem coe_rat_cast (q : ℚ) : ↑(q : R) = (q : ℍ[R]) :=
   rfl
 #align quaternion.coe_rat_cast Quaternion.coe_rat_cast
 
--- porting note: moved below `coe_rat_cast`, as `coe_rat_cast` is needed in the `rw`s
+-- Porting note: moved below `coe_rat_cast`, as `coe_rat_cast` is needed in the `rw`s
 instance : DivisionRing ℍ[R] :=
   { Quaternion.instGroupWithZero,
     Quaternion.instRing with

Classify by adding issue number (#10618) to porting notes claiming anything semantically equivalent to simp can prove this or simp can simplify this.

@@ -1419,17 +1419,17 @@ instance : DivisionRing ℍ[R] :=
       rw [← coe_rat_cast, coe_mul_eq_smul]
       ext <;> exact DivisionRing.qsmul_eq_mul' _ _ }
 
---@[simp] Porting note: `simp` can prove it
+--@[simp] Porting note (#10618): `simp` can prove it
 theorem normSq_inv : normSq a⁻¹ = (normSq a)⁻¹ :=
   map_inv₀ normSq _
 #align quaternion.norm_sq_inv Quaternion.normSq_inv
 
---@[simp] Porting note: `simp` can prove it
+--@[simp] Porting note (#10618): `simp` can prove it
 theorem normSq_div : normSq (a / b) = normSq a / normSq b :=
   map_div₀ normSq a b
 #align quaternion.norm_sq_div Quaternion.normSq_div
 
---@[simp] Porting note: `simp` can prove it
+--@[simp] Porting note (#10618): `simp` can prove it
 theorem normSq_zpow (z : ℤ) : normSq (a ^ z) = normSq a ^ z :=
   map_zpow₀ normSq a z
 #align quaternion.norm_sq_zpow Quaternion.normSq_zpow
@@ -1471,7 +1471,7 @@ theorem mk_univ_quaternionAlgebra : #(Set.univ : Set ℍ[R,c₁,c₂]) = #R ^ 4
   rw [mk_univ, mk_quaternionAlgebra]
 #align cardinal.mk_univ_quaternion_algebra Cardinal.mk_univ_quaternionAlgebra
 
---@[simp] Porting note: `simp` can prove it
+--@[simp] Porting note (#10618): `simp` can prove it
 theorem mk_univ_quaternionAlgebra_of_infinite [Infinite R] :
     #(Set.univ : Set ℍ[R,c₁,c₂]) = #R := by rw [mk_univ_quaternionAlgebra, pow_four]
 #align cardinal.mk_univ_quaternion_algebra_of_infinite Cardinal.mk_univ_quaternionAlgebra_of_infinite
@@ -1494,7 +1494,7 @@ theorem mk_quaternion_of_infinite [Infinite R] : #(ℍ[R]) = #R :=
 #align cardinal.mk_quaternion_of_infinite Cardinal.mk_quaternion_of_infinite
 
 /-- The cardinality of the quaternions, as a set. -/
---@[simp] Porting note: `simp` can prove it
+--@[simp] Porting note (#10618): `simp` can prove it
 theorem mk_univ_quaternion : #(Set.univ : Set ℍ[R]) = #R ^ 4 :=
   mk_univ_quaternionAlgebra _ _
 #align cardinal.mk_univ_quaternion Cardinal.mk_univ_quaternion

The files Mathlib.LinearAlgebra.FreeModule.Rank, Mathlib.LinearAlgebra.FreeModule.Finite.Rank, Mathlib.LinearAlgebra.Dimension and Mathlib.LinearAlgebra.Finrank were reorganized into a folder Mathlib.LinearAlgebra.Dimension, containing the following files

• Basic.lean: Contains the definition of Module.rank.
• Finrank.lean: Contains the definition of FiniteDimensional.finrank.
• StrongRankCondition.lean: Contains results about rank and finrank over rings satisfying strong rank condition
• Free.lean: Contains results about rank and finrank of free modules
• Finite.lean: Contains conditions or consequences for rank to be finite or zero
• Constructions.lean: Contains the calculation of the rank of various constructions.
• DivisionRing.lean: Contains results about rank and finrank of spaces over division rings.
• LinearMap.lean: Contains results about LinearMap.rank

API changes: IsNoetherian.rank_lt_aleph0 and FiniteDimensional.rank_lt_aleph0 are replaced with rank_lt_aleph0. Module.Free.finite_basis was renamed to Module.Finite.finite_basis. FiniteDimensional.finrank_eq_rank was renamed to finrank_eq_rank. rank_eq_cardinal_basis and rank_eq_cardinal_basis' were removed in favour of Basis.mk_eq_mk and Basis.mk_eq_mk''.

Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com>

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 -/
 import Mathlib.Algebra.Algebra.Equiv
-import Mathlib.LinearAlgebra.Finrank
+import Mathlib.LinearAlgebra.Dimension.StrongRankCondition
 import Mathlib.LinearAlgebra.FreeModule.Basic
 import Mathlib.LinearAlgebra.FreeModule.Finite.Basic
 import Mathlib.SetTheory.Cardinal.Ordinal

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -1413,10 +1413,10 @@ instance : DivisionRing ℍ[R] :=
   { Quaternion.instGroupWithZero,
     Quaternion.instRing with
     ratCast_mk := fun n d hd h => by
-      rw [←coe_rat_cast, Rat.cast_mk', coe_mul, coe_int_cast, coe_inv, coe_nat_cast]
+      rw [← coe_rat_cast, Rat.cast_mk', coe_mul, coe_int_cast, coe_inv, coe_nat_cast]
     qsmul := (· • ·)
     qsmul_eq_mul' := fun q x => by
-      rw [←coe_rat_cast, coe_mul_eq_smul]
+      rw [← coe_rat_cast, coe_mul_eq_smul]
       ext <;> exact DivisionRing.qsmul_eq_mul' _ _ }
 
 --@[simp] Porting note: `simp` can prove it

@@ -1447,17 +1447,15 @@ namespace Cardinal
 
 open Quaternion
 
-local infixr:80 " ^ℕ " => @HPow.hPow Cardinal ℕ Cardinal _
-
 section QuaternionAlgebra
 
 variable {R : Type*} (c₁ c₂ : R)
 
-private theorem pow_four [Infinite R] : #R ^ℕ 4 = #R :=
+private theorem pow_four [Infinite R] : #R ^ 4 = #R :=
   power_nat_eq (aleph0_le_mk R) <| by decide
 
 /-- The cardinality of a quaternion algebra, as a type. -/
-theorem mk_quaternionAlgebra : #(ℍ[R,c₁,c₂]) = #R ^ℕ 4 := by
+theorem mk_quaternionAlgebra : #(ℍ[R,c₁,c₂]) = #R ^ 4 := by
   rw [mk_congr (QuaternionAlgebra.equivProd c₁ c₂)]
   simp only [mk_prod, lift_id]
   ring
@@ -1469,7 +1467,7 @@ theorem mk_quaternionAlgebra_of_infinite [Infinite R] : #(ℍ[R,c₁,c₂]) = #R
 #align cardinal.mk_quaternion_algebra_of_infinite Cardinal.mk_quaternionAlgebra_of_infinite
 
 /-- The cardinality of a quaternion algebra, as a set. -/
-theorem mk_univ_quaternionAlgebra : #(Set.univ : Set ℍ[R,c₁,c₂]) = #R ^ℕ 4 := by
+theorem mk_univ_quaternionAlgebra : #(Set.univ : Set ℍ[R,c₁,c₂]) = #R ^ 4 := by
   rw [mk_univ, mk_quaternionAlgebra]
 #align cardinal.mk_univ_quaternion_algebra Cardinal.mk_univ_quaternionAlgebra
 
@@ -1486,7 +1484,7 @@ variable (R : Type*) [One R] [Neg R]
 
 /-- The cardinality of the quaternions, as a type. -/
 @[simp]
-theorem mk_quaternion : #(ℍ[R]) = #R ^ℕ 4 :=
+theorem mk_quaternion : #(ℍ[R]) = #R ^ 4 :=
   mk_quaternionAlgebra _ _
 #align cardinal.mk_quaternion Cardinal.mk_quaternion
 
@@ -1497,7 +1495,7 @@ theorem mk_quaternion_of_infinite [Infinite R] : #(ℍ[R]) = #R :=
 
 /-- The cardinality of the quaternions, as a set. -/
 --@[simp] Porting note: `simp` can prove it
-theorem mk_univ_quaternion : #(Set.univ : Set ℍ[R]) = #R ^ℕ 4 :=
+theorem mk_univ_quaternion : #(Set.univ : Set ℍ[R]) = #R ^ 4 :=
   mk_univ_quaternionAlgebra _ _
 #align cardinal.mk_univ_quaternion Cardinal.mk_univ_quaternion
 

PR contents

This is the supremum of

• #8284
• #8056
• #8023
• #8332
• #8226 (already approved)
• #7834 (already approved)

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

• leanprover/lean4#2778
• leanprover/lean4#2790
• leanprover/lean4#2783
• leanprover/lean4#2825
• leanprover/lean4#2722

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

• switching to using explicit lemmas that have the intended level of application
• (config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
• Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

@@ -1454,7 +1454,7 @@ section QuaternionAlgebra
 variable {R : Type*} (c₁ c₂ : R)
 
 private theorem pow_four [Infinite R] : #R ^ℕ 4 = #R :=
-  power_nat_eq (aleph0_le_mk R) <| by simp
+  power_nat_eq (aleph0_le_mk R) <| by decide
 
 /-- The cardinality of a quaternion algebra, as a type. -/
 theorem mk_quaternionAlgebra : #(ℍ[R,c₁,c₂]) = #R ^ℕ 4 := by

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -1267,8 +1267,8 @@ theorem im_sq : a.im ^ 2 = -normSq a.im := by
   simp_rw [sq, ← star_mul_self, im_star, neg_mul, neg_neg]
 #align quaternion.im_sq Quaternion.im_sq
 
-theorem coe_normSq_add : normSq (a + b) = normSq a + a * star b + b * star a + normSq b :=
-  by simp only [star_add, ← self_mul_star, mul_add, add_mul, add_assoc, add_left_comm]
+theorem coe_normSq_add : normSq (a + b) = normSq a + a * star b + b * star a + normSq b := by
+  simp only [star_add, ← self_mul_star, mul_add, add_mul, add_assoc, add_left_comm]
 #align quaternion.coe_norm_sq_add Quaternion.coe_normSq_add
 
 theorem normSq_smul (r : R) (q : ℍ[R]) : normSq (r • q) = r ^ 2 * normSq q := by

This eliminates (fun a ↦ β) α in the type when applying a FunLike.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -1267,7 +1267,7 @@ theorem im_sq : a.im ^ 2 = -normSq a.im := by
   simp_rw [sq, ← star_mul_self, im_star, neg_mul, neg_neg]
 #align quaternion.im_sq Quaternion.im_sq
 
-theorem coe_normSq_add : (normSq (a + b) : ℍ[R]) = normSq a + a * star b + b * star a + normSq b :=
+theorem coe_normSq_add : normSq (a + b) = normSq a + a * star b + b * star a + normSq b :=
   by simp only [star_add, ← self_mul_star, mul_add, add_mul, add_assoc, add_left_comm]
 #align quaternion.coe_norm_sq_add Quaternion.coe_normSq_add
 

Use .asFn and .lemmasOnly as simps configuration options.

For reference, these are defined here:

https://github.com/leanprover-community/mathlib4/blob/4055c8b471380825f07416b12cb0cf266da44d84/Mathlib/Tactic/Simps/Basic.lean#L843-L851

@@ -1344,7 +1344,7 @@ section Field
 
 variable [LinearOrderedField R] (a b : ℍ[R])
 
-@[simps (config := { isSimp := false })]
+@[simps (config := .lemmasOnly)]
 instance instInv : Inv ℍ[R] :=
   ⟨fun a => (normSq a)⁻¹ • star a⟩
 

Co-authored-by: Eric Rodriguez <37984851+ericrbg@users.noreply.github.com>

@@ -102,6 +102,9 @@ theorem mk.eta {R : Type*} {c₁ c₂} (a : ℍ[R,c₁,c₂]) : mk a.1 a.2 a.3 a
 
 variable {S T R : Type*} [CommRing R] {c₁ c₂ : R} (r x y z : R) (a b c : ℍ[R,c₁,c₂])
 
+instance [Subsingleton R] : Subsingleton ℍ[R, c₁, c₂] := (equivTuple c₁ c₂).subsingleton
+instance [Nontrivial R] : Nontrivial ℍ[R, c₁, c₂] := (equivTuple c₁ c₂).surjective.nontrivial
+
 /-- The imaginary part of a quaternion. -/
 def im (x : ℍ[R,c₁,c₂]) : ℍ[R,c₁,c₂] :=
   ⟨0, x.imI, x.imJ, x.imK⟩
@@ -492,6 +495,15 @@ theorem algebraMap_eq (r : R) : algebraMap R ℍ[R,c₁,c₂] r = ⟨r, 0, 0, 0
   rfl
 #align quaternion_algebra.algebra_map_eq QuaternionAlgebra.algebraMap_eq
 
+theorem algebraMap_injective : (algebraMap R ℍ[R,c₁,c₂] : _ → _).Injective :=
+  fun _ _ ↦ by simp [algebraMap_eq]
+
+instance [NoZeroDivisors R] : NoZeroSMulDivisors R ℍ[R,c₁,c₂] := ⟨by
+  rintro t ⟨a, b, c, d⟩ h
+  rw [or_iff_not_imp_left]
+  intro ht
+  simpa [QuaternionAlgebra.ext_iff, ht] using h⟩
+
 section
 
 variable (c₁ c₂)
@@ -572,6 +584,21 @@ theorem finrank_eq_four [StrongRankCondition R] : FiniteDimensional.finrank R 
   rw [FiniteDimensional.finrank, rank_eq_four, Cardinal.toNat_ofNat]
 #align quaternion_algebra.finrank_eq_four QuaternionAlgebra.finrank_eq_four
 
+/-- There is a natural equivalence when swapping the coefficients of a quaternion algebra. -/
+@[simps]
+def swapEquiv : ℍ[R,c₁,c₂] ≃ₐ[R] ℍ[R, c₂, c₁] where
+  toFun t := ⟨t.1, t.3, t.2, -t.4⟩
+  invFun t := ⟨t.1, t.3, t.2, -t.4⟩
+  left_inv _ := by simp
+  right_inv _ := by simp
+  map_mul' _ _ := by
+    ext
+      <;> simp only [mul_re, mul_imJ, mul_imI, add_left_inj, mul_imK, neg_mul, neg_add_rev,
+                     neg_sub, mk_mul_mk, mul_neg, neg_neg, sub_neg_eq_add]
+      <;> ring
+  map_add' _ _ := by ext <;> simp [add_comm]
+  commutes' _ := by simp [algebraMap_eq]
+
 end
 
 @[norm_cast, simp]
@@ -754,6 +781,11 @@ theorem Quaternion.equivTuple_apply (R : Type*) [One R] [Neg R] (x : ℍ[R]) :
   rfl
 #align quaternion.equiv_tuple_apply Quaternion.equivTuple_apply
 
+instance {R : Type*} [One R] [Neg R] [Subsingleton R] : Subsingleton ℍ[R] :=
+  inferInstanceAs (Subsingleton <| ℍ[R, -1, -1])
+instance {R : Type*} [One R] [Neg R] [Nontrivial R] : Nontrivial ℍ[R] :=
+  inferInstanceAs (Nontrivial <| ℍ[R, -1, -1])
+
 namespace Quaternion
 
 variable {S T R : Type*} [CommRing R] (r x y z : R) (a b c : ℍ[R])
@@ -1072,6 +1104,9 @@ theorem algebraMap_def : ⇑(algebraMap R ℍ[R]) = coe :=
   rfl
 #align quaternion.algebra_map_def Quaternion.algebraMap_def
 
+theorem algebraMap_injective : (algebraMap R ℍ[R] : _ → _).Injective :=
+  QuaternionAlgebra.algebraMap_injective
+
 theorem smul_coe : x • (y : ℍ[R]) = ↑(x * y) :=
   QuaternionAlgebra.smul_coe x y
 #align quaternion.smul_coe Quaternion.smul_coe

@@ -353,11 +353,11 @@ variable [SMul S R] [SMul T R] (s : S)
 -- porting note: Lean 4 auto drops the unused `[Ring R]` argument
 instance : SMul S ℍ[R,c₁,c₂] where smul s a := ⟨s • a.1, s • a.2, s • a.3, s • a.4⟩
 
-instance [SMul S T] [IsScalarTower S T R] : IsScalarTower S T ℍ[R,c₁,c₂]
-    where smul_assoc s t x := by ext <;> exact smul_assoc _ _ _
+instance [SMul S T] [IsScalarTower S T R] : IsScalarTower S T ℍ[R,c₁,c₂] where
+  smul_assoc s t x := by ext <;> exact smul_assoc _ _ _
 
-instance [SMulCommClass S T R] : SMulCommClass S T ℍ[R,c₁,c₂]
-    where smul_comm s t x := by ext <;> exact smul_comm _ _ _
+instance [SMulCommClass S T R] : SMulCommClass S T ℍ[R,c₁,c₂] where
+  smul_comm s t x := by ext <;> exact smul_comm _ _ _
 
 @[simp] theorem smul_re : (s • a).re = s • a.re := rfl
 #align quaternion_algebra.smul_re QuaternionAlgebra.smul_re

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

This has nice performance benefits.

@@ -54,7 +54,7 @@ quaternion
 /-- Quaternion algebra over a type with fixed coefficients $a=i^2$ and $b=j^2$.
 Implemented as a structure with four fields: `re`, `imI`, `imJ`, and `imK`. -/
 @[ext]
-structure QuaternionAlgebra (R : Type _) (a b : R) where
+structure QuaternionAlgebra (R : Type*) (a b : R) where
   /-- Real part of a quaternion. -/
   re : R
   imI : R
@@ -74,7 +74,7 @@ namespace QuaternionAlgebra
 
 /-- The equivalence between a quaternion algebra over `R` and `R × R × R × R`. -/
 @[simps]
-def equivProd {R : Type _} (c₁ c₂ : R) : ℍ[R,c₁,c₂] ≃ R × R × R × R where
+def equivProd {R : Type*} (c₁ c₂ : R) : ℍ[R,c₁,c₂] ≃ R × R × R × R where
   toFun a := ⟨a.1, a.2, a.3, a.4⟩
   invFun a := ⟨a.1, a.2.1, a.2.2.1, a.2.2.2⟩
   left_inv _ := rfl
@@ -83,7 +83,7 @@ def equivProd {R : Type _} (c₁ c₂ : R) : ℍ[R,c₁,c₂] ≃ R × R × R ×
 
 /-- The equivalence between a quaternion algebra over `R` and `Fin 4 → R`. -/
 @[simps symm_apply]
-def equivTuple {R : Type _} (c₁ c₂ : R) : ℍ[R,c₁,c₂] ≃ (Fin 4 → R) where
+def equivTuple {R : Type*} (c₁ c₂ : R) : ℍ[R,c₁,c₂] ≃ (Fin 4 → R) where
   toFun a := ![a.1, a.2, a.3, a.4]
   invFun a := ⟨a 0, a 1, a 2, a 3⟩
   left_inv _ := rfl
@@ -91,16 +91,16 @@ def equivTuple {R : Type _} (c₁ c₂ : R) : ℍ[R,c₁,c₂] ≃ (Fin 4 → R)
 #align quaternion_algebra.equiv_tuple QuaternionAlgebra.equivTuple
 
 @[simp]
-theorem equivTuple_apply {R : Type _} (c₁ c₂ : R) (x : ℍ[R,c₁,c₂]) :
+theorem equivTuple_apply {R : Type*} (c₁ c₂ : R) (x : ℍ[R,c₁,c₂]) :
     equivTuple c₁ c₂ x = ![x.re, x.imI, x.imJ, x.imK] :=
   rfl
 #align quaternion_algebra.equiv_tuple_apply QuaternionAlgebra.equivTuple_apply
 
 @[simp]
-theorem mk.eta {R : Type _} {c₁ c₂} (a : ℍ[R,c₁,c₂]) : mk a.1 a.2 a.3 a.4 = a := rfl
+theorem mk.eta {R : Type*} {c₁ c₂} (a : ℍ[R,c₁,c₂]) : mk a.1 a.2 a.3 a.4 = a := rfl
 #align quaternion_algebra.mk.eta QuaternionAlgebra.mk.eta
 
-variable {S T R : Type _} [CommRing R] {c₁ c₂ : R} (r x y z : R) (a b c : ℍ[R,c₁,c₂])
+variable {S T R : Type*} [CommRing R] {c₁ c₂ : R} (r x y z : R) (a b c : ℍ[R,c₁,c₂])
 
 /-- The imaginary part of a quaternion. -/
 def im (x : ℍ[R,c₁,c₂]) : ℍ[R,c₁,c₂] :=
@@ -729,7 +729,7 @@ end QuaternionAlgebra
 
 /-- Space of quaternions over a type. Implemented as a structure with four fields:
 `re`, `im_i`, `im_j`, and `im_k`. -/
-def Quaternion (R : Type _) [One R] [Neg R] :=
+def Quaternion (R : Type*) [One R] [Neg R] :=
   QuaternionAlgebra R (-1) (-1)
 #align quaternion Quaternion
 
@@ -738,25 +738,25 @@ scoped[Quaternion] notation "ℍ[" R "]" => Quaternion R
 
 /-- The equivalence between the quaternions over `R` and `R × R × R × R`. -/
 @[simps!]
-def Quaternion.equivProd (R : Type _) [One R] [Neg R] : ℍ[R] ≃ R × R × R × R :=
+def Quaternion.equivProd (R : Type*) [One R] [Neg R] : ℍ[R] ≃ R × R × R × R :=
   QuaternionAlgebra.equivProd _ _
 #align quaternion.equiv_prod Quaternion.equivProd
 
 /-- The equivalence between the quaternions over `R` and `Fin 4 → R`. -/
 @[simps! symm_apply]
-def Quaternion.equivTuple (R : Type _) [One R] [Neg R] : ℍ[R] ≃ (Fin 4 → R) :=
+def Quaternion.equivTuple (R : Type*) [One R] [Neg R] : ℍ[R] ≃ (Fin 4 → R) :=
   QuaternionAlgebra.equivTuple _ _
 #align quaternion.equiv_tuple Quaternion.equivTuple
 
 @[simp]
-theorem Quaternion.equivTuple_apply (R : Type _) [One R] [Neg R] (x : ℍ[R]) :
+theorem Quaternion.equivTuple_apply (R : Type*) [One R] [Neg R] (x : ℍ[R]) :
     Quaternion.equivTuple R x = ![x.re, x.imI, x.imJ, x.imK] :=
   rfl
 #align quaternion.equiv_tuple_apply Quaternion.equivTuple_apply
 
 namespace Quaternion
 
-variable {S T R : Type _} [CommRing R] (r x y z : R) (a b c : ℍ[R])
+variable {S T R : Type*} [CommRing R] (r x y z : R) (a b c : ℍ[R])
 
 export QuaternionAlgebra (re imI imJ imK)
 
@@ -1253,7 +1253,7 @@ end Quaternion
 
 namespace Quaternion
 
-variable {R : Type _}
+variable {R : Type*}
 
 section LinearOrderedCommRing
 
@@ -1416,7 +1416,7 @@ local infixr:80 " ^ℕ " => @HPow.hPow Cardinal ℕ Cardinal _
 
 section QuaternionAlgebra
 
-variable {R : Type _} (c₁ c₂ : R)
+variable {R : Type*} (c₁ c₂ : R)
 
 private theorem pow_four [Infinite R] : #R ^ℕ 4 = #R :=
   power_nat_eq (aleph0_le_mk R) <| by simp
@@ -1447,7 +1447,7 @@ end QuaternionAlgebra
 
 section Quaternion
 
-variable (R : Type _) [One R] [Neg R]
+variable (R : Type*) [One R] [Neg R]
 
 /-- The cardinality of the quaternions, as a type. -/
 @[simp]

Per https://github.com/leanprover/lean4/issues/2343, we are going to need to change the automatic generation of instance names, as they become too long.

This PR ensures that everywhere in Mathlib that refers to an instance by name, that name is given explicitly, rather than being automatically generated.

There are four exceptions, which are now commented, with links to https://github.com/leanprover/lean4/issues/2343.

This was implemented by running Mathlib against a modified Lean that appended _ᾰ to all automatically generated names, and fixing everything.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -608,7 +608,7 @@ theorem smul_coe : x • (y : ℍ[R,c₁,c₂]) = ↑(x * y) := by rw [coe_mul,
 #align quaternion_algebra.smul_coe QuaternionAlgebra.smul_coe
 
 /-- Quaternion conjugate. -/
-instance : Star ℍ[R,c₁,c₂] where star a := ⟨a.1, -a.2, -a.3, -a.4⟩
+instance instStarQuaternionAlgebra : Star ℍ[R,c₁,c₂] where star a := ⟨a.1, -a.2, -a.3, -a.4⟩
 
 @[simp] theorem re_star : (star a).re = a.re := rfl
 #align quaternion_algebra.re_star QuaternionAlgebra.re_star

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2020 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module algebra.quaternion
-! leanprover-community/mathlib commit cf7a7252c1989efe5800e0b3cdfeb4228ac6b40e
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Algebra.Equiv
 import Mathlib.LinearAlgebra.Finrank
@@ -14,6 +9,8 @@ import Mathlib.LinearAlgebra.FreeModule.Basic
 import Mathlib.LinearAlgebra.FreeModule.Finite.Basic
 import Mathlib.SetTheory.Cardinal.Ordinal
 
+#align_import algebra.quaternion from "leanprover-community/mathlib"@"cf7a7252c1989efe5800e0b3cdfeb4228ac6b40e"
+
 /-!
 # Quaternions
 

Lean 3 @[simps { attrs := [] }] should be translated to @[simps (config := { isSimp := false })] to avoid adding @[simp] attribute.

@@ -1312,7 +1312,7 @@ section Field
 
 variable [LinearOrderedField R] (a b : ℍ[R])
 
-@[simps (config := { attrs := [] })]
+@[simps (config := { isSimp := false })]
 instance instInv : Inv ℍ[R] :=
   ⟨fun a => (normSq a)⁻¹ • star a⟩
 

@@ -1421,29 +1421,29 @@ section QuaternionAlgebra
 
 variable {R : Type _} (c₁ c₂ : R)
 
-private theorem pow_four [Infinite R] : (#R) ^ℕ 4 = (#R) :=
+private theorem pow_four [Infinite R] : #R ^ℕ 4 = #R :=
   power_nat_eq (aleph0_le_mk R) <| by simp
 
 /-- The cardinality of a quaternion algebra, as a type. -/
-theorem mk_quaternionAlgebra : (#ℍ[R,c₁,c₂]) = (#R) ^ℕ 4 := by
+theorem mk_quaternionAlgebra : #(ℍ[R,c₁,c₂]) = #R ^ℕ 4 := by
   rw [mk_congr (QuaternionAlgebra.equivProd c₁ c₂)]
   simp only [mk_prod, lift_id]
   ring
 #align cardinal.mk_quaternion_algebra Cardinal.mk_quaternionAlgebra
 
 @[simp]
-theorem mk_quaternionAlgebra_of_infinite [Infinite R] : (#ℍ[R,c₁,c₂]) = (#R) := by
+theorem mk_quaternionAlgebra_of_infinite [Infinite R] : #(ℍ[R,c₁,c₂]) = #R := by
   rw [mk_quaternionAlgebra, pow_four]
 #align cardinal.mk_quaternion_algebra_of_infinite Cardinal.mk_quaternionAlgebra_of_infinite
 
 /-- The cardinality of a quaternion algebra, as a set. -/
-theorem mk_univ_quaternionAlgebra : (#(Set.univ : Set ℍ[R,c₁,c₂])) = (#R) ^ℕ 4 := by
+theorem mk_univ_quaternionAlgebra : #(Set.univ : Set ℍ[R,c₁,c₂]) = #R ^ℕ 4 := by
   rw [mk_univ, mk_quaternionAlgebra]
 #align cardinal.mk_univ_quaternion_algebra Cardinal.mk_univ_quaternionAlgebra
 
 --@[simp] Porting note: `simp` can prove it
 theorem mk_univ_quaternionAlgebra_of_infinite [Infinite R] :
-    (#(Set.univ : Set ℍ[R,c₁,c₂])) = (#R) := by rw [mk_univ_quaternionAlgebra, pow_four]
+    #(Set.univ : Set ℍ[R,c₁,c₂]) = #R := by rw [mk_univ_quaternionAlgebra, pow_four]
 #align cardinal.mk_univ_quaternion_algebra_of_infinite Cardinal.mk_univ_quaternionAlgebra_of_infinite
 
 end QuaternionAlgebra
@@ -1454,23 +1454,23 @@ variable (R : Type _) [One R] [Neg R]
 
 /-- The cardinality of the quaternions, as a type. -/
 @[simp]
-theorem mk_quaternion : (#ℍ[R]) = (#R) ^ℕ 4 :=
+theorem mk_quaternion : #(ℍ[R]) = #R ^ℕ 4 :=
   mk_quaternionAlgebra _ _
 #align cardinal.mk_quaternion Cardinal.mk_quaternion
 
---@[simp] Porting note: LHS can be simplified to `(#R)^4`
-theorem mk_quaternion_of_infinite [Infinite R] : (#ℍ[R]) = (#R) :=
+--@[simp] Porting note: LHS can be simplified to `#R^4`
+theorem mk_quaternion_of_infinite [Infinite R] : #(ℍ[R]) = #R :=
   mk_quaternionAlgebra_of_infinite _ _
 #align cardinal.mk_quaternion_of_infinite Cardinal.mk_quaternion_of_infinite
 
 /-- The cardinality of the quaternions, as a set. -/
 --@[simp] Porting note: `simp` can prove it
-theorem mk_univ_quaternion : (#(Set.univ : Set ℍ[R])) = (#R) ^ℕ 4 :=
+theorem mk_univ_quaternion : #(Set.univ : Set ℍ[R]) = #R ^ℕ 4 :=
   mk_univ_quaternionAlgebra _ _
 #align cardinal.mk_univ_quaternion Cardinal.mk_univ_quaternion
 
---@[simp] Porting note: LHS can be simplified to `(#R)^4`
-theorem mk_univ_quaternion_of_infinite [Infinite R] : (#(Set.univ : Set ℍ[R])) = (#R) :=
+--@[simp] Porting note: LHS can be simplified to `#R^4`
+theorem mk_univ_quaternion_of_infinite [Infinite R] : #(Set.univ : Set ℍ[R]) = #R :=
   mk_univ_quaternionAlgebra_of_infinite _ _
 #align cardinal.mk_univ_quaternion_of_infinite Cardinal.mk_univ_quaternion_of_infinite
 

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

@@ -1376,7 +1376,7 @@ theorem coe_rat_cast (q : ℚ) : ↑(q : R) = (q : ℍ[R]) :=
   rfl
 #align quaternion.coe_rat_cast Quaternion.coe_rat_cast
 
--- porting note: moved below `coe_rat_cast`, added this lemma to the `rw`s
+-- porting note: moved below `coe_rat_cast`, as `coe_rat_cast` is needed in the `rw`s
 instance : DivisionRing ℍ[R] :=
   { Quaternion.instGroupWithZero,
     Quaternion.instRing with

I wrote a script to find lines that contain an odd number of backticks

@@ -315,7 +315,7 @@ theorem sub_self_re : a - a.re = a.im :=
 * `j * j = c₂`;
 * `i * j = k`, `j * i = -k`;
 * `k * k = -c₁ * c₂`;
-* `i * k = c₁ * j`, `k * i = `-c₁ * j`;
+* `i * k = c₁ * j`, `k * i = -c₁ * j`;
 * `j * k = -c₂ * i`, `k * j = c₂ * i`.  -/
 instance : Mul ℍ[R,c₁,c₂] :=
   ⟨fun a b =>

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -37,7 +37,7 @@ We also define the following algebraic structures on `ℍ[R]`:
 
 ## Notation
 
-The following notation is available with `open_locale Quaternion`.
+The following notation is available with `open Quaternion` or `open scoped Quaternion`.
 
 * `ℍ[R, c₁, c₂]` : `QuaternionAlgebra R c₁ c₂`
 * `ℍ[R]` : quaternions over `R`.
@@ -780,7 +780,7 @@ instance [SMul S T] [SMul S R] [SMul T R] [IsScalarTower S T R] : IsScalarTower
 instance [SMul S R] [SMul T R] [SMulCommClass S T R] : SMulCommClass S T ℍ[R] :=
   inferInstanceAs <| SMulCommClass S T ℍ[R,-1,-1]
 
-instance [CommSemiring S] [Algebra S R] : Algebra S ℍ[R] :=
+protected instance algebra [CommSemiring S] [Algebra S R] : Algebra S ℍ[R] :=
   inferInstanceAs <| Algebra S ℍ[R,-1,-1]
 
 -- porting note: added shortcut

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>