algebra.dual_number ⟷ Mathlib.Algebra.DualNumber

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

@@ -127,7 +127,7 @@ def lift : { e : A // e * e = 0 } ≃ (R[ε] →ₐ[R] A) :=
         dsimp
         simp_rw [smul_mul_smul]
         refine' ⟨fun h x y => h.symm ▸ smul_zero _, fun h => by simpa using h 1 1⟩)
-    TrivSqZeroExt.lift
+    TrivSqZeroExt.liftEquiv
 #align dual_number.lift DualNumber.lift
 -/
 
@@ -135,17 +135,15 @@ def lift : { e : A // e * e = 0 } ≃ (R[ε] →ₐ[R] A) :=
 -- When applied to `ε`, `dual_number.lift` produces the element of `A` that squares to 0.
 @[simp]
 theorem lift_apply_eps (e : { e : A // e * e = 0 }) : lift e (ε : R[ε]) = e :=
-  (TrivSqZeroExt.liftAux_apply_inr _ _ _).trans <| one_smul _ _
+  (TrivSqZeroExt.lift_apply_inr _ _ _).trans <| one_smul _ _
 #align dual_number.lift_apply_eps DualNumber.lift_apply_eps
 -/
 
-#print DualNumber.lift_eps /-
 -- Lifting `dual_number.eps` itself gives the identity.
 @[simp]
-theorem lift_eps : lift ⟨ε, eps_mul_eps⟩ = AlgHom.id R R[ε] :=
+theorem lift_inlAlgHom_eps : lift ⟨ε, eps_mul_eps⟩ = AlgHom.id R R[ε] :=
   algHom_ext <| lift_apply_eps _
-#align dual_number.lift_eps DualNumber.lift_eps
--/
+#align dual_number.lift_eps DualNumber.lift_inlAlgHom_epsₓ
 
 end DualNumber
 

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

@@ -3,7 +3,7 @@ Copyright (c) 2021 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 -/
-import Mathbin.Algebra.TrivSqZeroExt
+import Algebra.TrivSqZeroExt
 
 #align_import algebra.dual_number from "leanprover-community/mathlib"@"290a7ba01fbcab1b64757bdaa270d28f4dcede35"
 

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

@@ -2,14 +2,11 @@
 Copyright (c) 2021 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
-
-! This file was ported from Lean 3 source module algebra.dual_number
-! leanprover-community/mathlib commit 290a7ba01fbcab1b64757bdaa270d28f4dcede35
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.TrivSqZeroExt
 
+#align_import algebra.dual_number from "leanprover-community/mathlib"@"290a7ba01fbcab1b64757bdaa270d28f4dcede35"
+
 /-!
 # Dual numbers
 

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

@@ -59,10 +59,8 @@ def DualNumber.eps [Zero R] [One R] : DualNumber R :=
 #align dual_number.eps DualNumber.eps
 -/
 
--- mathport name: dual_number.eps
 scoped[DualNumber] notation "ε" => DualNumber.eps
 
--- mathport name: dual_number
 scoped[DualNumber] postfix:1024 "[ε]" => DualNumber
 
 open scoped DualNumber
@@ -85,21 +83,27 @@ theorem snd_eps [Zero R] [One R] : snd ε = (1 : R) :=
 #align dual_number.snd_eps DualNumber.snd_eps
 -/
 
+#print DualNumber.snd_mul /-
 /-- A version of `triv_sq_zero_ext.snd_mul` with `*` instead of `•`. -/
 @[simp]
 theorem snd_mul [Semiring R] (x y : R[ε]) : snd (x * y) = fst x * snd y + snd x * fst y :=
   snd_mul _ _
 #align dual_number.snd_mul DualNumber.snd_mul
+-/
 
+#print DualNumber.eps_mul_eps /-
 @[simp]
 theorem eps_mul_eps [Semiring R] : (ε * ε : R[ε]) = 0 :=
   inr_mul_inr _ _ _
 #align dual_number.eps_mul_eps DualNumber.eps_mul_eps
+-/
 
+#print DualNumber.inr_eq_smul_eps /-
 @[simp]
 theorem inr_eq_smul_eps [MulZeroOneClass R] (r : R) : inr r = (r • ε : R[ε]) :=
   ext (MulZeroClass.mul_zero r).symm (mul_one r).symm
 #align dual_number.inr_eq_smul_eps DualNumber.inr_eq_smul_eps
+-/
 
 #print DualNumber.algHom_ext /-
 /-- For two algebra morphisms out of `R[ε]` to agree, it suffices for them to agree on `ε`. -/
@@ -112,6 +116,7 @@ theorem algHom_ext {A} [CommSemiring R] [Semiring A] [Algebra R A] ⦃f g : R[ε
 
 variable {A : Type _} [CommSemiring R] [Semiring A] [Algebra R A]
 
+#print DualNumber.lift /-
 /-- A universal property of the dual numbers, providing a unique `R[ε] →ₐ[R] A` for every element
 of `A` which squares to `0`.
 
@@ -127,12 +132,15 @@ def lift : { e : A // e * e = 0 } ≃ (R[ε] →ₐ[R] A) :=
         refine' ⟨fun h x y => h.symm ▸ smul_zero _, fun h => by simpa using h 1 1⟩)
     TrivSqZeroExt.lift
 #align dual_number.lift DualNumber.lift
+-/
 
+#print DualNumber.lift_apply_eps /-
 -- When applied to `ε`, `dual_number.lift` produces the element of `A` that squares to 0.
 @[simp]
 theorem lift_apply_eps (e : { e : A // e * e = 0 }) : lift e (ε : R[ε]) = e :=
   (TrivSqZeroExt.liftAux_apply_inr _ _ _).trans <| one_smul _ _
 #align dual_number.lift_apply_eps DualNumber.lift_apply_eps
+-/
 
 #print DualNumber.lift_eps /-
 -- Lifting `dual_number.eps` itself gives the identity.

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

@@ -65,7 +65,7 @@ scoped[DualNumber] notation "ε" => DualNumber.eps
 -- mathport name: dual_number
 scoped[DualNumber] postfix:1024 "[ε]" => DualNumber
 
-open DualNumber
+open scoped DualNumber
 
 namespace DualNumber
 

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

@@ -85,35 +85,17 @@ theorem snd_eps [Zero R] [One R] : snd ε = (1 : R) :=
 #align dual_number.snd_eps DualNumber.snd_eps
 -/
 
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 /-- A version of `triv_sq_zero_ext.snd_mul` with `*` instead of `•`. -/
 @[simp]
 theorem snd_mul [Semiring R] (x y : R[ε]) : snd (x * y) = fst x * snd y + snd x * fst y :=
   snd_mul _ _
 #align dual_number.snd_mul DualNumber.snd_mul
 
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 @[simp]
 theorem eps_mul_eps [Semiring R] : (ε * ε : R[ε]) = 0 :=
   inr_mul_inr _ _ _
 #align dual_number.eps_mul_eps DualNumber.eps_mul_eps
 
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 @[simp]
 theorem inr_eq_smul_eps [MulZeroOneClass R] (r : R) : inr r = (r • ε : R[ε]) :=
   ext (MulZeroClass.mul_zero r).symm (mul_one r).symm
@@ -130,12 +112,6 @@ theorem algHom_ext {A} [CommSemiring R] [Semiring A] [Algebra R A] ⦃f g : R[ε
 
 variable {A : Type _} [CommSemiring R] [Semiring A] [Algebra R A]
 
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-Case conversion may be inaccurate. Consider using '#align dual_number.lift DualNumber.liftₓ'. -/
 /-- A universal property of the dual numbers, providing a unique `R[ε] →ₐ[R] A` for every element
 of `A` which squares to `0`.
 
@@ -152,9 +128,6 @@ def lift : { e : A // e * e = 0 } ≃ (R[ε] →ₐ[R] A) :=
     TrivSqZeroExt.lift
 #align dual_number.lift DualNumber.lift
 
-/- warning: dual_number.lift_apply_eps -> DualNumber.lift_apply_eps is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align dual_number.lift_apply_eps DualNumber.lift_apply_epsₓ'. -/
 -- When applied to `ε`, `dual_number.lift` produces the element of `A` that squares to 0.
 @[simp]
 theorem lift_apply_eps (e : { e : A // e * e = 0 }) : lift e (ε : R[ε]) = e :=

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

@@ -153,10 +153,7 @@ def lift : { e : A // e * e = 0 } ≃ (R[ε] →ₐ[R] A) :=
 #align dual_number.lift DualNumber.lift
 
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(DualNumber.{u1} R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} R) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} R) _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))))))) (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u1, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) => AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3) e) R (DualNumber.{u1} R) A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} R) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} R) _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u2, max u1 u2} R (DualNumber.{u1} R) A ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) => AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3) e) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} R) _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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+<too large>
 Case conversion may be inaccurate. Consider using '#align dual_number.lift_apply_eps DualNumber.lift_apply_epsₓ'. -/
 -- When applied to `ε`, `dual_number.lift` produces the element of `A` that squares to 0.
 @[simp]

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

@@ -156,7 +156,7 @@ def lift : { e : A // e * e = 0 } ≃ (R[ε] →ₐ[R] A) :=
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (e : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) e e) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))))), Eq.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R 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(NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) e e) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))))) A (CoeTCₓ.coe.{succ u2, succ u2} (Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) e e) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))))) A (coeBase.{succ u2, succ u2} (Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) e e) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))))) A (coeSubtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) e e) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))))))) e)
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (e : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : DualNumber.{u1} R) => A) (DualNumber.eps.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) => AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3) e) (DualNumber.{u1} R) (fun (_x : DualNumber.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : DualNumber.{u1} R) => A) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, u1, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) => AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3) e) R (DualNumber.{u1} R) A (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} R) (AddMonoid.toZero.{u1} (DualNumber.{u1} R) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} R) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} R) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} R) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} R) _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))))))) (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u1, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) => AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3) e) R (DualNumber.{u1} R) A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} R) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} R) _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u2, max u1 u2} R (DualNumber.{u1} R) A ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) => AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3) e) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} R) _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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(Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} 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+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (e : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : DualNumber.{u1} R) => A) (DualNumber.eps.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) => AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3) e) (DualNumber.{u1} R) (fun (_x : DualNumber.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : DualNumber.{u1} R) => A) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, u1, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) => AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R 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(AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3) e) R (DualNumber.{u1} R) A (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} R) (AddMonoid.toZero.{u1} (DualNumber.{u1} R) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} R) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} R) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} R) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} R) _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))))))) (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u1, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) => AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3) e) R (DualNumber.{u1} R) A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} R) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} R) _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u2, max u1 u2} R (DualNumber.{u1} R) A ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) => AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3) e) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} R) _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 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R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3)) (DualNumber.lift.{u1, u2} R A _inst_1 _inst_2 _inst_3) e) (DualNumber.eps.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Subtype.val.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2))))) e)
 Case conversion may be inaccurate. Consider using '#align dual_number.lift_apply_eps DualNumber.lift_apply_epsₓ'. -/
 -- When applied to `ε`, `dual_number.lift` produces the element of `A` that squares to 0.
 @[simp]

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

@@ -156,7 +156,7 @@ def lift : { e : A // e * e = 0 } ≃ (R[ε] →ₐ[R] A) :=
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (e : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) e e) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))))), Eq.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R 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 but is expected to have type
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(CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} R) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} R) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} R) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} R) _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))))))) (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u1, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) => AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3) e) R (DualNumber.{u1} R) A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} R) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} R) _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u2, max u1 u2} R (DualNumber.{u1} R) A ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) => AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3) e) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} R) _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 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(TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u1) (succ u2)} (Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A 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(AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} 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+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (e : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : DualNumber.{u1} R) => A) (DualNumber.eps.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) => AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3) e) (DualNumber.{u1} R) (fun (_x : DualNumber.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : DualNumber.{u1} R) => A) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, u1, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) => AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R 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(AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3) e) R (DualNumber.{u1} R) A (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} R) (AddMonoid.toZero.{u1} (DualNumber.{u1} R) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} R) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} R) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} R) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} R) _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))))))) (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u1, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) => AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3) e) R (DualNumber.{u1} R) A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} R) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} R) _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u2, max u1 u2} R (DualNumber.{u1} R) A ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) => AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3) e) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} R) _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R 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(Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) => AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 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(CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u1) (succ u2)} (Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) (AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3)) (DualNumber.lift.{u1, u2} R A _inst_1 _inst_2 _inst_3) e) (DualNumber.eps.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Subtype.val.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2))))) e)
 Case conversion may be inaccurate. Consider using '#align dual_number.lift_apply_eps DualNumber.lift_apply_epsₓ'. -/
 -- When applied to `ε`, `dual_number.lift` produces the element of `A` that squares to 0.
 @[simp]

mathlib commit https://github.com/leanprover-community/mathlib/commit/b19481deb571022990f1baa9cbf9172e6757a479

@@ -134,7 +134,7 @@ variable {A : Type _} [CommSemiring R] [Semiring A] [Algebra R A]
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Equiv.{succ u2, max (succ u1) (succ u2)} (Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) e e) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))))) (AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (DualNumber.lift._proof_1.{u1} R _inst_1)) _inst_2 (TrivSqZeroExt.algebra.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (DualNumber.lift._proof_2.{u1} R _inst_1)) _inst_3)
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Equiv.{succ u2, max (succ u2) (succ u1)} (Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) (AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeInstSemiringMulOppositeInstAlgebraMulOppositeInstSemiringMulOppositeIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3)
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Equiv.{succ u2, max (succ u2) (succ u1)} (Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) (AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3)
 Case conversion may be inaccurate. Consider using '#align dual_number.lift DualNumber.liftₓ'. -/
 /-- A universal property of the dual numbers, providing a unique `R[ε] →ₐ[R] A` for every element
 of `A` which squares to `0`.
@@ -156,7 +156,7 @@ def lift : { e : A // e * e = 0 } ≃ (R[ε] →ₐ[R] A) :=
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (e : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) e e) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))))), Eq.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R 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 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (e : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : DualNumber.{u1} R) => A) (DualNumber.eps.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A 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(AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeInstSemiringMulOppositeInstAlgebraMulOppositeInstSemiringMulOppositeIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3) e) (DualNumber.{u1} R) (fun (_x : DualNumber.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : DualNumber.{u1} R) => A) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, u1, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) => AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeInstSemiringMulOppositeInstAlgebraMulOppositeInstSemiringMulOppositeIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3) e) R (DualNumber.{u1} R) A (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} R) (AddMonoid.toZero.{u1} (DualNumber.{u1} R) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} R) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} R) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} R) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} R) _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeInstSemiringMulOppositeInstAlgebraMulOppositeInstSemiringMulOppositeIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))))))) (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u1, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) => AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeInstSemiringMulOppositeInstAlgebraMulOppositeInstSemiringMulOppositeIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3) e) R (DualNumber.{u1} R) A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} R) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} R) _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeInstSemiringMulOppositeInstAlgebraMulOppositeInstSemiringMulOppositeIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u2, max u1 u2} R (DualNumber.{u1} R) A ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) => AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeInstSemiringMulOppositeInstAlgebraMulOppositeInstSemiringMulOppositeIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3) e) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) 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(CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} R) _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeInstSemiringMulOppositeInstAlgebraMulOppositeInstSemiringMulOppositeIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (AlgHomClass.linearMapClass.{u1, u1, u2, max u1 u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeInstSemiringMulOppositeInstAlgebraMulOppositeInstSemiringMulOppositeIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3 ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) => AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeInstSemiringMulOppositeInstAlgebraMulOppositeInstSemiringMulOppositeIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3) e) (AlgHom.algHomClass.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R 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(NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) => AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3) e) (DualNumber.{u1} R) (fun (_x : DualNumber.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : DualNumber.{u1} R) => A) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, u1, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) => AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3) e) R (DualNumber.{u1} R) A (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} R) (AddMonoid.toZero.{u1} (DualNumber.{u1} R) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} R) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} R) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} R) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} R) _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))))))) (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u1, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) => AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3) e) R (DualNumber.{u1} R) A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} R) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} R) _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u2, max u1 u2} R (DualNumber.{u1} R) A ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) => AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3) e) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) 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u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} R) _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (AlgHomClass.linearMapClass.{u1, u1, u2, max u1 u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3 ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) => AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 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 Case conversion may be inaccurate. Consider using '#align dual_number.lift_apply_eps DualNumber.lift_apply_epsₓ'. -/
 -- When applied to `ε`, `dual_number.lift` produces the element of `A` that squares to 0.
 @[simp]

mathlib commit https://github.com/leanprover-community/mathlib/commit/290a7ba01fbcab1b64757bdaa270d28f4dcede35

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 
 ! This file was ported from Lean 3 source module algebra.dual_number
-! leanprover-community/mathlib commit b8d2eaa69d69ce8f03179a5cda774fc0cde984e4
+! leanprover-community/mathlib commit 290a7ba01fbcab1b64757bdaa270d28f4dcede35
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Algebra.TrivSqZeroExt
 /-!
 # Dual numbers
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 The dual numbers over `R` are of the form `a + bε`, where `a` and `b` are typically elements of a
 commutative ring `R`, and `ε` is a symbol satisfying `ε^2 = 0`. They are a special case of
 `triv_sq_zero_ext R M` with `M = R`.

mathlib commit https://github.com/leanprover-community/mathlib/commit/1f4705ccdfe1e557fc54a0ce081a05e33d2e6240

@@ -42,15 +42,19 @@ Rather than duplicating the API of `triv_sq_zero_ext`, this file reuses the func
 
 variable {R : Type _}
 
+#print DualNumber /-
 /-- The type of dual numbers, numbers of the form $a + bε$ where $ε^2 = 0$.-/
 abbrev DualNumber (R : Type _) : Type _ :=
   TrivSqZeroExt R R
 #align dual_number DualNumber
+-/
 
+#print DualNumber.eps /-
 /-- The unit element $ε$ that squares to zero. -/
 def DualNumber.eps [Zero R] [One R] : DualNumber R :=
   TrivSqZeroExt.inr 1
 #align dual_number.eps DualNumber.eps
+-/
 
 -- mathport name: dual_number.eps
 scoped[DualNumber] notation "ε" => DualNumber.eps
@@ -64,41 +68,71 @@ namespace DualNumber
 
 open TrivSqZeroExt
 
+#print DualNumber.fst_eps /-
 @[simp]
 theorem fst_eps [Zero R] [One R] : fst ε = (0 : R) :=
   fst_inr _ _
 #align dual_number.fst_eps DualNumber.fst_eps
+-/
 
+#print DualNumber.snd_eps /-
 @[simp]
 theorem snd_eps [Zero R] [One R] : snd ε = (1 : R) :=
   snd_inr _ _
 #align dual_number.snd_eps DualNumber.snd_eps
+-/
 
+/- warning: dual_number.snd_mul -> DualNumber.snd_mul is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align dual_number.snd_mul DualNumber.snd_mulₓ'. -/
 /-- A version of `triv_sq_zero_ext.snd_mul` with `*` instead of `•`. -/
 @[simp]
 theorem snd_mul [Semiring R] (x y : R[ε]) : snd (x * y) = fst x * snd y + snd x * fst y :=
   snd_mul _ _
 #align dual_number.snd_mul DualNumber.snd_mul
 
+/- warning: dual_number.eps_mul_eps -> DualNumber.eps_mul_eps is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align dual_number.eps_mul_eps DualNumber.eps_mul_epsₓ'. -/
 @[simp]
 theorem eps_mul_eps [Semiring R] : (ε * ε : R[ε]) = 0 :=
   inr_mul_inr _ _ _
 #align dual_number.eps_mul_eps DualNumber.eps_mul_eps
 
+/- warning: dual_number.inr_eq_smul_eps -> DualNumber.inr_eq_smul_eps is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align dual_number.inr_eq_smul_eps DualNumber.inr_eq_smul_epsₓ'. -/
 @[simp]
 theorem inr_eq_smul_eps [MulZeroOneClass R] (r : R) : inr r = (r • ε : R[ε]) :=
   ext (MulZeroClass.mul_zero r).symm (mul_one r).symm
 #align dual_number.inr_eq_smul_eps DualNumber.inr_eq_smul_eps
 
+#print DualNumber.algHom_ext /-
 /-- For two algebra morphisms out of `R[ε]` to agree, it suffices for them to agree on `ε`. -/
 @[ext]
 theorem algHom_ext {A} [CommSemiring R] [Semiring A] [Algebra R A] ⦃f g : R[ε] →ₐ[R] A⦄
     (h : f ε = g ε) : f = g :=
   algHom_ext' <| LinearMap.ext_ring <| h
 #align dual_number.alg_hom_ext DualNumber.algHom_ext
+-/
 
 variable {A : Type _} [CommSemiring R] [Semiring A] [Algebra R A]
 
+/- warning: dual_number.lift -> DualNumber.lift is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align dual_number.lift DualNumber.liftₓ'. -/
 /-- A universal property of the dual numbers, providing a unique `R[ε] →ₐ[R] A` for every element
 of `A` which squares to `0`.
 
@@ -115,17 +149,25 @@ def lift : { e : A // e * e = 0 } ≃ (R[ε] →ₐ[R] A) :=
     TrivSqZeroExt.lift
 #align dual_number.lift DualNumber.lift
 
+/- warning: dual_number.lift_apply_eps -> DualNumber.lift_apply_eps is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeInstSemiringMulOppositeInstAlgebraMulOppositeInstSemiringMulOppositeIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3) e) (DualNumber.{u1} R) (fun (_x : DualNumber.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : DualNumber.{u1} R) => A) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, u1, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) => AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeInstSemiringMulOppositeInstAlgebraMulOppositeInstSemiringMulOppositeIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3) e) R (DualNumber.{u1} R) A (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} R) (AddMonoid.toZero.{u1} (DualNumber.{u1} R) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} R) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} R) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} R) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} R) _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeInstSemiringMulOppositeInstAlgebraMulOppositeInstSemiringMulOppositeIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))))))) (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u1, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) => AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeInstSemiringMulOppositeInstAlgebraMulOppositeInstSemiringMulOppositeIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3) e) R (DualNumber.{u1} R) A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} R) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} R) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} R) _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeInstSemiringMulOppositeInstAlgebraMulOppositeInstSemiringMulOppositeIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u2, max u1 u2} R (DualNumber.{u1} R) A ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) => AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeInstSemiringMulOppositeInstAlgebraMulOppositeInstSemiringMulOppositeIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3) e) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} R) 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(CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} R) _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeInstSemiringMulOppositeInstAlgebraMulOppositeInstSemiringMulOppositeIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (AlgHomClass.linearMapClass.{u1, u1, u2, max u1 u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeInstSemiringMulOppositeInstAlgebraMulOppositeInstSemiringMulOppositeIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommSemiring.toCommSemigroup.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)))) _inst_3 ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{succ u2} A (fun (e : A) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) e e) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))))) => AlgHom.{u1, u1, u2} R (DualNumber.{u1} R) A _inst_1 (TrivSqZeroExt.semiring.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SMulCommClass.opposite_mid.{u1, u1} R R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (IsScalarTower.right.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_2 (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeInstSemiringMulOppositeInstAlgebraMulOppositeInstSemiringMulOppositeIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R 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+Case conversion may be inaccurate. Consider using '#align dual_number.lift_apply_eps DualNumber.lift_apply_epsₓ'. -/
 -- When applied to `ε`, `dual_number.lift` produces the element of `A` that squares to 0.
 @[simp]
 theorem lift_apply_eps (e : { e : A // e * e = 0 }) : lift e (ε : R[ε]) = e :=
   (TrivSqZeroExt.liftAux_apply_inr _ _ _).trans <| one_smul _ _
 #align dual_number.lift_apply_eps DualNumber.lift_apply_eps
 
+#print DualNumber.lift_eps /-
 -- Lifting `dual_number.eps` itself gives the identity.
 @[simp]
 theorem lift_eps : lift ⟨ε, eps_mul_eps⟩ = AlgHom.id R R[ε] :=
   algHom_ext <| lift_apply_eps _
 #align dual_number.lift_eps DualNumber.lift_eps
+-/
 
 end DualNumber
 

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

@@ -87,7 +87,7 @@ theorem eps_mul_eps [Semiring R] : (ε * ε : R[ε]) = 0 :=
 
 @[simp]
 theorem inr_eq_smul_eps [MulZeroOneClass R] (r : R) : inr r = (r • ε : R[ε]) :=
-  ext (mul_zero r).symm (mul_one r).symm
+  ext (MulZeroClass.mul_zero r).symm (mul_one r).symm
 #align dual_number.inr_eq_smul_eps DualNumber.inr_eq_smul_eps
 
 /-- For two algebra morphisms out of `R[ε]` to agree, it suffices for them to agree on `ε`. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/22131150f88a2d125713ffa0f4693e3355b1eb49

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 
 ! This file was ported from Lean 3 source module algebra.dual_number
-! leanprover-community/mathlib commit 3d7987cda72abc473c7cdbbb075170e9ac620042
+! leanprover-community/mathlib commit b8d2eaa69d69ce8f03179a5cda774fc0cde984e4
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -76,7 +76,7 @@ theorem snd_eps [Zero R] [One R] : snd ε = (1 : R) :=
 
 /-- A version of `triv_sq_zero_ext.snd_mul` with `*` instead of `•`. -/
 @[simp]
-theorem snd_mul [Semiring R] (x y : R[ε]) : snd (x * y) = fst x * snd y + fst y * snd x :=
+theorem snd_mul [Semiring R] (x y : R[ε]) : snd (x * y) = fst x * snd y + snd x * fst y :=
   snd_mul _ _
 #align dual_number.snd_mul DualNumber.snd_mul
 

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

Adds a representation for Complex numbers and DualNumber so they can be used in #eval statements.

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

@@ -189,4 +189,10 @@ theorem lift_inlAlgHom_eps :
   lift.apply_symm_apply <| AlgHom.id R A[ε]
 #align dual_number.lift_eps DualNumber.lift_inlAlgHom_epsₓ
 
+/-- Show DualNumber with values x and y as an "x + y*ε" string -/
+instance instRepr [Repr R] : Repr (DualNumber R) where
+  reprPrec f p :=
+    (if p > 65 then (Std.Format.bracket "(" . ")") else (·)) <|
+      reprPrec f.fst 65 ++ " + " ++ reprPrec f.snd 70 ++ "*ε"
+
 end DualNumber

Defined inverses for TrivEqExtZero in a way that is consitent with DualNumbers.

Note that $(a + b\epsilon)^{-1} = \frac{1(a - b\epsilon)}{(a + b\epsilon)(a - b\epsilon)} = \frac{a - b\epsilon}{a^2}$ Which becomes $\frac{1}{a} - \frac{b}{a^2}\epsilon$. We want to be able have left multiplicative inverses $x x^{-1} = 0$ So we write $\frac{b}{a^2} = a^{-1} \cdot b \cdot a^{-1}$

Also included a proof that $x \cdot x^{-1} = 1$ when $\text{fst } x \neq 0$

Co-authored-by: Frederick Pu <frederick.pu@mail.utoronto.ca>

@@ -83,6 +83,10 @@ theorem eps_mul_eps [Semiring R] : (ε * ε : R[ε]) = 0 :=
   inr_mul_inr _ _ _
 #align dual_number.eps_mul_eps DualNumber.eps_mul_eps
 
+@[simp]
+theorem inv_eps [DivisionRing R] : (ε : R[ε])⁻¹ = 0 :=
+  TrivSqZeroExt.inv_inr 1
+
 @[simp]
 theorem inr_eq_smul_eps [MulZeroOneClass R] (r : R) : inr r = (r • ε : R[ε]) :=
   ext (mul_zero r).symm (mul_one r).symm

This prepares for the introduction of a non-dependent synonym of FunLike, which helps a lot with keeping #8386 readable.

This is entirely search-and-replace in 680197f combined with manual fixes in 4145626, e900597 and b8428f8. The commands that generated this change:

sed -i 's/\bFunLike\b/DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoFunLike\b/toDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/import Mathlib.Data.DFunLike/import Mathlib.Data.FunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bHom_FunLike\b/Hom_DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean     
sed -i 's/\binstFunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bfunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoo many metavariables to apply `fun_like.has_coe_to_fun`/too many metavariables to apply `DFunLike.hasCoeToFun`/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean

Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

@@ -108,7 +108,7 @@ nonrec theorem algHom_ext' ⦃f g : A[ε] →ₐ[R] B⦄
   algHom_ext' hinl (by
     ext a
     show f (inr a) = g (inr a)
-    simpa only [inr_eq_smul_eps] using FunLike.congr_fun hinr a)
+    simpa only [inr_eq_smul_eps] using DFunLike.congr_fun hinr a)
 
 /-- For two `R`-algebra morphisms out of `R[ε]` to agree, it suffices for them to agree on `ε`. -/
 @[ext 1200]

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

@@ -141,7 +141,7 @@ def lift :
       (fg.val.1, fg.val.2 1),
       fg.prop.1 _ _,
       fun a => show fg.val.2 1 * fg.val.1 a = fg.val.1 a * fg.val.2 1 by
-        rw [←fg.prop.2.1, ←fg.prop.2.2, smul_eq_mul, op_smul_eq_mul, mul_one, one_mul]⟩
+        rw [← fg.prop.2.1, ← fg.prop.2.2, smul_eq_mul, op_smul_eq_mul, mul_one, one_mul]⟩
     left_inv := fun fe => Subtype.ext <| Prod.ext rfl <|
       show fe.val.1 1 * fe.val.2 = fe.val.2 by
         rw [map_one, one_mul]
@@ -164,12 +164,12 @@ theorem lift_apply_apply (fe : {_fe : (A →ₐ[R] B) × B // _}) (a : A[ε]) :
 /-- Scaling on the left is sent by `DualNumber.lift` to multiplication on the left -/
 @[simp] theorem lift_smul (fe : {fe : (A →ₐ[R] B) × B // _}) (a : A) (ad : A[ε]) :
     lift fe (a • ad) = fe.val.1 a * lift fe ad := by
-  rw [←inl_mul_eq_smul, map_mul, lift_apply_inl]
+  rw [← inl_mul_eq_smul, map_mul, lift_apply_inl]
 
 /-- Scaling on the right is sent by `DualNumber.lift` to multiplication on the right -/
 @[simp] theorem lift_op_smul (fe : {fe : (A →ₐ[R] B) × B // _}) (a : A) (ad : A[ε]) :
     lift fe (MulOpposite.op a • ad) = lift fe ad * fe.val.1 a := by
-  rw [←mul_inl_eq_op_smul, map_mul, lift_apply_inl]
+  rw [← mul_inl_eq_op_smul, map_mul, lift_apply_inl]
 
 /-- When applied to `ε`, `DualNumber.lift` produces the element of `B` that squares to 0. -/
 @[simp] theorem lift_apply_eps

The current universal properties of TrivSqZeroExt and DualNumber work only when the underlying ring is commutative. This is not the case for things like the dual quaternions.

This generalizes both sets of results to the non-commutative case. Unfortunately the new TrivSqZeroExt version is rather involved, so this keeps the old statement as a special case.

The new DualNumber version is less bad, so I just discarded the commutative special case.

For dual numbers, the generalization is from R[ε] →ₐ[R] B to A[ε] →ₐ[R] B, where R is commutative but A may not be. Some variable names had to be shuffled to make the new statement look nice.

@@ -11,8 +11,8 @@ import Mathlib.Algebra.TrivSqZeroExt
 # Dual numbers
 
 The dual numbers over `R` are of the form `a + bε`, where `a` and `b` are typically elements of a
-commutative ring `R`, and `ε` is a symbol satisfying `ε^2 = 0`. They are a special case of
-`TrivSqZeroExt R M` with `M = R`.
+commutative ring `R`, and `ε` is a symbol satisfying `ε^2 = 0` that commutes with every other
+element. They are a special case of `TrivSqZeroExt R M` with `M = R`.
 
 ## Notation
 
@@ -37,7 +37,7 @@ Rather than duplicating the API of `TrivSqZeroExt`, this file reuses the functio
 -/
 
 
-variable {R : Type*}
+variable {R A B : Type*}
 
 /-- The type of dual numbers, numbers of the form $a + bε$ where $ε^2 = 0$.
 `R[ε]` is notation for `DualNumber R`. -/
@@ -95,40 +95,94 @@ theorem commute_eps_left [Semiring R] (x : DualNumber R) : Commute ε x := by
 /-- `ε` commutes with every element of the algebra. -/
 theorem commute_eps_right [Semiring R] (x : DualNumber R) : Commute x ε := (commute_eps_left x).symm
 
-/-- For two algebra morphisms out of `R[ε]` to agree, it suffices for them to agree on `ε`. -/
-@[ext]
-theorem algHom_ext {A} [CommSemiring R] [Semiring A] [Algebra R A] ⦃f g : R[ε] →ₐ[R] A⦄
-    (h : f ε = g ε) : f = g :=
-  algHom_ext' <| LinearMap.ext_ring <| h
+variable {A : Type*} [CommSemiring R] [Semiring A] [Semiring B] [Algebra R A] [Algebra R B]
+
+/-- For two `R`-algebra morphisms out of `A[ε]` to agree, it suffices for them to agree on the
+elements of `A` and the `A`-multiples of `ε`. -/
+@[ext 1100]
+nonrec theorem algHom_ext' ⦃f g : A[ε] →ₐ[R] B⦄
+    (hinl : f.comp (inlAlgHom _ _ _) = g.comp (inlAlgHom _ _ _))
+    (hinr : f.toLinearMap ∘ₗ (LinearMap.toSpanSingleton A A[ε] ε).restrictScalars R =
+        g.toLinearMap ∘ₗ (LinearMap.toSpanSingleton A A[ε] ε).restrictScalars R) :
+      f = g :=
+  algHom_ext' hinl (by
+    ext a
+    show f (inr a) = g (inr a)
+    simpa only [inr_eq_smul_eps] using FunLike.congr_fun hinr a)
+
+/-- For two `R`-algebra morphisms out of `R[ε]` to agree, it suffices for them to agree on `ε`. -/
+@[ext 1200]
+nonrec theorem algHom_ext ⦃f g : R[ε] →ₐ[R] A⦄ (hε : f ε = g ε) : f = g := by
+  ext
+  dsimp
+  simp only [one_smul, hε]
 #align dual_number.alg_hom_ext DualNumber.algHom_ext
 
-variable {A : Type*} [CommSemiring R] [Semiring A] [Algebra R A]
-
-/-- A universal property of the dual numbers, providing a unique `R[ε] →ₐ[R] A` for every element
-of `A` which squares to `0`.
-
-This isomorphism is named to match the very similar `Complex.lift`. -/
-@[simps!]
-def lift : { e : A // e * e = 0 } ≃ (R[ε] →ₐ[R] A) :=
-  Equiv.trans
-    (show { e : A // e * e = 0 } ≃ { f : R →ₗ[R] A // ∀ x y, f x * f y = 0 } from
-      (LinearMap.ringLmapEquivSelf R ℕ A).symm.toEquiv.subtypeEquiv fun a => by
-        dsimp
-        simp_rw [smul_mul_smul]
-        refine' ⟨fun h x y => h.symm ▸ smul_zero _, fun h => by simpa using h 1 1⟩)
-    TrivSqZeroExt.lift
+/-- A universal property of the dual numbers, providing a unique `A[ε] →ₐ[R] B` for every map
+`f : A →ₐ[R] B` and a choice of element `e : B` which squares to `0` and commutes with the range of
+`f`.
+
+This isomorphism is named to match the similar `Complex.lift`.
+Note that when `f : R →ₐ[R] B := Algebra.ofId R B`, the commutativity assumption is automatic, and
+we are free to choose any element `e : B`. -/
+def lift :
+    {fe : (A →ₐ[R] B) × B // fe.2 * fe.2 = 0 ∧ ∀ a, Commute fe.2 (fe.1 a)} ≃ (A[ε] →ₐ[R] B) := by
+  refine Equiv.trans ?_ TrivSqZeroExt.liftEquiv
+  exact {
+    toFun := fun fe => ⟨
+      (fe.val.1, MulOpposite.op fe.val.2 • fe.val.1.toLinearMap),
+      fun x y => show (fe.val.1 x * fe.val.2) * (fe.val.1 y * fe.val.2) = 0 by
+        rw [(fe.prop.2 _).mul_mul_mul_comm, fe.prop.1, mul_zero],
+      fun r x => show fe.val.1 (r * x) * fe.val.2 = fe.val.1 r * (fe.val.1 x * fe.val.2) by
+        rw [map_mul, mul_assoc],
+      fun r x => show fe.val.1 (x * r) * fe.val.2 = (fe.val.1 x * fe.val.2) * fe.val.1 r by
+        rw [map_mul, (fe.prop.2 _).right_comm]⟩
+    invFun := fun fg => ⟨
+      (fg.val.1, fg.val.2 1),
+      fg.prop.1 _ _,
+      fun a => show fg.val.2 1 * fg.val.1 a = fg.val.1 a * fg.val.2 1 by
+        rw [←fg.prop.2.1, ←fg.prop.2.2, smul_eq_mul, op_smul_eq_mul, mul_one, one_mul]⟩
+    left_inv := fun fe => Subtype.ext <| Prod.ext rfl <|
+      show fe.val.1 1 * fe.val.2 = fe.val.2 by
+        rw [map_one, one_mul]
+    right_inv := fun fg => Subtype.ext <| Prod.ext rfl <| LinearMap.ext fun x =>
+      show fg.val.1 x * fg.val.2 1 = fg.val.2 x by
+        rw [← fg.prop.2.1, smul_eq_mul, mul_one] }
 #align dual_number.lift DualNumber.lift
 
-/-- When applied to `ε`, `DualNumber.lift` produces the element of `A` that squares to 0. -/
--- @[simp] -- Porting note: simp can prove this
-theorem lift_apply_eps (e : { e : A // e * e = 0 }) : @lift R _ _ _ _ e (ε : R[ε]) = e := by
-  simp only [lift_apply_apply, fst_eps, map_zero, snd_eps, one_smul, zero_add]
+theorem lift_apply_apply (fe : {_fe : (A →ₐ[R] B) × B // _}) (a : A[ε]) :
+    lift fe a = fe.val.1 a.fst + fe.val.1 a.snd * fe.val.2 := rfl
+
+@[simp] theorem coe_lift_symm_apply (F : A[ε] →ₐ[R] B) :
+    (lift.symm F).val = (F.comp (inlAlgHom _ _ _), F ε) := rfl
+
+/-- When applied to `inl`, `DualNumber.lift` applies the map `f : A →ₐ[R] B`. -/
+@[simp] theorem lift_apply_inl (fe : {fe : (A →ₐ[R] B) × B // _}) (a : A) :
+    lift fe (inl a : A[ε]) = fe.val.1 a := by
+  rw [lift_apply_apply, fst_inl, snd_inl, map_zero, zero_mul, add_zero]
+
+/-- Scaling on the left is sent by `DualNumber.lift` to multiplication on the left -/
+@[simp] theorem lift_smul (fe : {fe : (A →ₐ[R] B) × B // _}) (a : A) (ad : A[ε]) :
+    lift fe (a • ad) = fe.val.1 a * lift fe ad := by
+  rw [←inl_mul_eq_smul, map_mul, lift_apply_inl]
+
+/-- Scaling on the right is sent by `DualNumber.lift` to multiplication on the right -/
+@[simp] theorem lift_op_smul (fe : {fe : (A →ₐ[R] B) × B // _}) (a : A) (ad : A[ε]) :
+    lift fe (MulOpposite.op a • ad) = lift fe ad * fe.val.1 a := by
+  rw [←mul_inl_eq_op_smul, map_mul, lift_apply_inl]
+
+/-- When applied to `ε`, `DualNumber.lift` produces the element of `B` that squares to 0. -/
+@[simp] theorem lift_apply_eps
+    (fe : {fe : (A →ₐ[R] B) × B // fe.2 * fe.2 = 0 ∧ ∀ a, Commute fe.2 (fe.1 a)}) :
+    lift fe (ε : A[ε]) = fe.val.2 := by
+  simp only [lift_apply_apply, fst_eps, map_zero, snd_eps, map_one, one_mul, zero_add]
 #align dual_number.lift_apply_eps DualNumber.lift_apply_eps
 
 /-- Lifting `DualNumber.eps` itself gives the identity. -/
 @[simp]
-theorem lift_eps : lift ⟨ε, eps_mul_eps⟩ = AlgHom.id R R[ε] :=
-  algHom_ext <| lift_apply_eps _
-#align dual_number.lift_eps DualNumber.lift_eps
+theorem lift_inlAlgHom_eps :
+    lift ⟨(inlAlgHom _ _ _, ε), eps_mul_eps, fun _ => commute_eps_left _⟩ = AlgHom.id R A[ε] :=
+  lift.apply_symm_apply <| AlgHom.id R A[ε]
+#align dual_number.lift_eps DualNumber.lift_inlAlgHom_epsₓ
 
 end DualNumber

@@ -119,13 +119,13 @@ def lift : { e : A // e * e = 0 } ≃ (R[ε] →ₐ[R] A) :=
     TrivSqZeroExt.lift
 #align dual_number.lift DualNumber.lift
 
--- When applied to `ε`, `DualNumber.lift` produces the element of `A` that squares to 0.
+/-- When applied to `ε`, `DualNumber.lift` produces the element of `A` that squares to 0. -/
 -- @[simp] -- Porting note: simp can prove this
 theorem lift_apply_eps (e : { e : A // e * e = 0 }) : @lift R _ _ _ _ e (ε : R[ε]) = e := by
   simp only [lift_apply_apply, fst_eps, map_zero, snd_eps, one_smul, zero_add]
 #align dual_number.lift_apply_eps DualNumber.lift_apply_eps
 
--- Lifting `DualNumber.eps` itself gives the identity.
+/-- Lifting `DualNumber.eps` itself gives the identity. -/
 @[simp]
 theorem lift_eps : lift ⟨ε, eps_mul_eps⟩ = AlgHom.id R R[ε] :=
   algHom_ext <| lift_apply_eps _

@@ -39,20 +39,21 @@ Rather than duplicating the API of `TrivSqZeroExt`, this file reuses the functio
 
 variable {R : Type*}
 
-/-- The type of dual numbers, numbers of the form $a + bε$ where $ε^2 = 0$.-/
+/-- The type of dual numbers, numbers of the form $a + bε$ where $ε^2 = 0$.
+`R[ε]` is notation for `DualNumber R`. -/
 abbrev DualNumber (R : Type*) : Type _ :=
   TrivSqZeroExt R R
 #align dual_number DualNumber
 
-/-- The unit element $ε$ that squares to zero. -/
+/-- The unit element $ε$ that squares to zero, with notation `ε`. -/
 def DualNumber.eps [Zero R] [One R] : DualNumber R :=
   TrivSqZeroExt.inr 1
 #align dual_number.eps DualNumber.eps
 
--- mathport name: dual_number.eps
+@[inherit_doc]
 scoped[DualNumber] notation "ε" => DualNumber.eps
 
--- mathport name: dual_number
+@[inherit_doc]
 scoped[DualNumber] postfix:1024 "[ε]" => DualNumber
 
 open DualNumber

This doesn't generalize to TrivSqZeroExt, as we do not have a notion of Commute for smul.

@@ -87,6 +87,13 @@ theorem inr_eq_smul_eps [MulZeroOneClass R] (r : R) : inr r = (r • ε : R[ε])
   ext (mul_zero r).symm (mul_one r).symm
 #align dual_number.inr_eq_smul_eps DualNumber.inr_eq_smul_eps
 
+/-- `ε` commutes with every element of the algebra. -/
+theorem commute_eps_left [Semiring R] (x : DualNumber R) : Commute ε x := by
+  ext <;> simp
+
+/-- `ε` commutes with every element of the algebra. -/
+theorem commute_eps_right [Semiring R] (x : DualNumber R) : Commute x ε := (commute_eps_left x).symm
+
 /-- For two algebra morphisms out of `R[ε]` to agree, it suffices for them to agree on `ε`. -/
 @[ext]
 theorem algHom_ext {A} [CommSemiring R] [Semiring A] [Algebra R A] ⦃f g : R[ε] →ₐ[R] A⦄

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

@@ -84,7 +84,7 @@ theorem eps_mul_eps [Semiring R] : (ε * ε : R[ε]) = 0 :=
 
 @[simp]
 theorem inr_eq_smul_eps [MulZeroOneClass R] (r : R) : inr r = (r • ε : R[ε]) :=
-  ext (MulZeroClass.mul_zero r).symm (mul_one r).symm
+  ext (mul_zero r).symm (mul_one r).symm
 #align dual_number.inr_eq_smul_eps DualNumber.inr_eq_smul_eps
 
 /-- For two algebra morphisms out of `R[ε]` to agree, it suffices for them to agree on `ε`. -/

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

This has nice performance benefits.

@@ -37,10 +37,10 @@ Rather than duplicating the API of `TrivSqZeroExt`, this file reuses the functio
 -/
 
 
-variable {R : Type _}
+variable {R : Type*}
 
 /-- The type of dual numbers, numbers of the form $a + bε$ where $ε^2 = 0$.-/
-abbrev DualNumber (R : Type _) : Type _ :=
+abbrev DualNumber (R : Type*) : Type _ :=
   TrivSqZeroExt R R
 #align dual_number DualNumber
 
@@ -94,7 +94,7 @@ theorem algHom_ext {A} [CommSemiring R] [Semiring A] [Algebra R A] ⦃f g : R[ε
   algHom_ext' <| LinearMap.ext_ring <| h
 #align dual_number.alg_hom_ext DualNumber.algHom_ext
 
-variable {A : Type _} [CommSemiring R] [Semiring A] [Algebra R A]
+variable {A : Type*} [CommSemiring R] [Semiring A] [Algebra R A]
 
 /-- A universal property of the dual numbers, providing a unique `R[ε] →ₐ[R] A` for every element
 of `A` which squares to `0`.

• depends on: #5966

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

@@ -2,14 +2,11 @@
 Copyright (c) 2021 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
-
-! This file was ported from Lean 3 source module algebra.dual_number
-! leanprover-community/mathlib commit b8d2eaa69d69ce8f03179a5cda774fc0cde984e4
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.TrivSqZeroExt
 
+#align_import algebra.dual_number from "leanprover-community/mathlib"@"b8d2eaa69d69ce8f03179a5cda774fc0cde984e4"
+
 /-!
 # Dual numbers
 

• Run a non-interactive version of fix-comments.py on all files.
• Go through the diff and manually add/discard/edit chunks.

@@ -102,7 +102,7 @@ variable {A : Type _} [CommSemiring R] [Semiring A] [Algebra R A]
 /-- A universal property of the dual numbers, providing a unique `R[ε] →ₐ[R] A` for every element
 of `A` which squares to `0`.
 
-This isomorphism is named to match the very similar `complex.lift`. -/
+This isomorphism is named to match the very similar `Complex.lift`. -/
 @[simps!]
 def lift : { e : A // e * e = 0 } ≃ (R[ε] →ₐ[R] A) :=
   Equiv.trans

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