diff --git "a/data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.Hom.sym.json" "b/data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.Hom.sym.json"
new file mode 100644--- /dev/null
+++ "b/data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.Hom.sym.json"
@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["AddMonoid","End","isScalarTower"],"typeFallback":"forall {R : Type.{u_1}} {S : Type.{u_2}} {A : Type.{u_4}} [inst._@.Mathlib.Algebra.Module.Hom.1890278916._hygCtx._hyg.7 : Monoid.{u_1} R] [inst._@.Mathlib.Algebra.Module.Hom.1890278916._hygCtx._hyg.10 : Monoid.{u_2} S] [inst._@.Mathlib.Algebra.Module.Hom.1890278916._hygCtx._hyg.13 : AddCommMonoid.{u_4} A] [inst._@.Mathlib.Algebra.Module.Hom.1890278916._hygCtx._hyg.16 : DistribMulAction.{u_1, u_4} R A inst._@.Mathlib.Algebra.Module.Hom.1890278916._hygCtx._hyg.7 (AddCommMonoid.toAddMonoid.{u_4} A inst._@.Mathlib.Algebra.Module.Hom.1890278916._hygCtx._hyg.13)] [inst._@.Mathlib.Algebra.Module.Hom.1890278916._hygCtx._hyg.20 : DistribMulAction.{u_2, u_4} S A inst._@.Mathlib.Algebra.Module.Hom.1890278916._hygCtx._hyg.10 (AddCommMonoid.toAddMonoid.{u_4} A inst._@.Mathlib.Algebra.Module.Hom.1890278916._hygCtx._hyg.13)] [inst._@.Mathlib.Algebra.Module.Hom.1890278916._hygCtx._hyg.24 : SMul.{u_1, u_2} R S] 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inst._@.Mathlib.Algebra.Module.Hom.1890278916._hygCtx._hyg.13))))) (DistribSMul.toSMulZeroClass.{u_2, u_4} S (AddMonoid.End.{u_4} A (AddZeroClass.toAddZero.{u_4} A (AddMonoid.toAddZeroClass.{u_4} A (AddCommMonoid.toAddMonoid.{u_4} A inst._@.Mathlib.Algebra.Module.Hom.1890278916._hygCtx._hyg.13)))) (AddMonoid.toAddZeroClass.{u_4} (AddMonoid.End.{u_4} A (AddZeroClass.toAddZero.{u_4} A (AddMonoid.toAddZeroClass.{u_4} A (AddCommMonoid.toAddMonoid.{u_4} A inst._@.Mathlib.Algebra.Module.Hom.1890278916._hygCtx._hyg.13)))) (AddMonoidWithOne.toAddMonoid.{u_4} (AddMonoid.End.{u_4} A (AddZeroClass.toAddZero.{u_4} A (AddMonoid.toAddZeroClass.{u_4} A (AddCommMonoid.toAddMonoid.{u_4} A inst._@.Mathlib.Algebra.Module.Hom.1890278916._hygCtx._hyg.13)))) (AddMonoid.End.instAddMonoidWithOne.{u_4} A inst._@.Mathlib.Algebra.Module.Hom.1890278916._hygCtx._hyg.13))) (AddMonoid.End.instDistribSMul.{u_2, u_4} S A inst._@.Mathlib.Algebra.Module.Hom.1890278916._hygCtx._hyg.13 (DistribMulAction.toDistribSMul.{u_2, u_4} S A inst._@.Mathlib.Algebra.Module.Hom.1890278916._hygCtx._hyg.10 (AddCommMonoid.toAddMonoid.{u_4} A inst._@.Mathlib.Algebra.Module.Hom.1890278916._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Hom.1890278916._hygCtx._hyg.20)))) (SMulZeroClass.toSMul.{u_1, u_4} R (AddMonoid.End.{u_4} A (AddZeroClass.toAddZero.{u_4} A (AddMonoid.toAddZeroClass.{u_4} A (AddCommMonoid.toAddMonoid.{u_4} A inst._@.Mathlib.Algebra.Module.Hom.1890278916._hygCtx._hyg.13)))) (AddZero.toZero.{u_4} (AddMonoid.End.{u_4} A (AddZeroClass.toAddZero.{u_4} A (AddMonoid.toAddZeroClass.{u_4} A (AddCommMonoid.toAddMonoid.{u_4} A inst._@.Mathlib.Algebra.Module.Hom.1890278916._hygCtx._hyg.13)))) (AddZeroClass.toAddZero.{u_4} (AddMonoid.End.{u_4} A (AddZeroClass.toAddZero.{u_4} A (AddMonoid.toAddZeroClass.{u_4} A (AddCommMonoid.toAddMonoid.{u_4} A inst._@.Mathlib.Algebra.Module.Hom.1890278916._hygCtx._hyg.13)))) (AddMonoid.toAddZeroClass.{u_4} (AddMonoid.End.{u_4} A 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(AddMonoid.End.{u_4} A (AddZeroClass.toAddZero.{u_4} A (AddMonoid.toAddZeroClass.{u_4} A (AddCommMonoid.toAddMonoid.{u_4} A inst._@.Mathlib.Algebra.Module.Hom.1890278916._hygCtx._hyg.13)))) (AddMonoid.End.instAddMonoidWithOne.{u_4} A inst._@.Mathlib.Algebra.Module.Hom.1890278916._hygCtx._hyg.13))) (AddMonoid.End.instDistribSMul.{u_1, u_4} R A inst._@.Mathlib.Algebra.Module.Hom.1890278916._hygCtx._hyg.13 (DistribMulAction.toDistribSMul.{u_1, u_4} R A inst._@.Mathlib.Algebra.Module.Hom.1890278916._hygCtx._hyg.7 (AddCommMonoid.toAddMonoid.{u_4} A inst._@.Mathlib.Algebra.Module.Hom.1890278916._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Hom.1890278916._hygCtx._hyg.16))))","typeFull":"∀ {R : Type u_1} {S : Type u_2} {A : Type u_4} [inst : Monoid R] [inst_1 : Monoid S] [inst_2 : AddCommMonoid A]\n  [inst_3 : DistribMulAction R A] [inst_4 : DistribMulAction S A] [inst_5 : SMul R S] [IsScalarTower R S A],\n  IsScalarTower R S (AddMonoid.End A)","typeReadable":"∀ {R : Type u_1} {S : Type u_2} {A : Type u_4} [inst : Monoid R] [inst_1 : Monoid S] [inst_2 : AddCommMonoid A]\n  [inst_3 : DistribMulAction R A] [inst_4 : DistribMulAction S A] [inst_5 : SMul R S] [IsScalarTower R S A],\n  IsScalarTower R S (AddMonoid.End A)","typeReferences":[["IsScalarTower"],["DistribMulAction","toDistribSMul"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddMonoidWithOne","toAddMonoid"],["AddZeroClass","toAddZero"],["AddMonoid","End","instAddMonoidWithOne"],["AddCommMonoid"],["SMul"],["Monoid"],["AddMonoid","End"],["AddMonoid","End","instDistribSMul"],["AddZero","toZero"],["DistribMulAction"],["AddMonoid","toAddZeroClass"],["DistribSMul","toSMulZeroClass"]],"valueReferences":[["DistribMulAction","toDistribSMul"],["AddCommMonoid","toAddMonoid"],["AddMonoid","toAddZeroClass"],["AddMonoidHom","instIsScalarTower"]]},{"isProp":true,"kind":"theorem","name":["AddMonoidHom","instDomMulActModule","_proof_4"],"typeFallback":"forall {S : Type.{u_3}} {M : Type.{u_2}} {M₂ : Type.{u_1}} 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A] → DistribSMul M (AddMonoid.End A)","typeReadable":"{M : Type u_3} → {A : Type u_4} → [inst : AddCommMonoid A] → [DistribSMul M A] → DistribSMul M (AddMonoid.End A)","typeReferences":[["AddCommMonoid"],["AddMonoid","End"],["AddCommMonoid","toAddMonoid"],["AddMonoidWithOne","toAddMonoid"],["AddZeroClass","toAddZero"],["DistribSMul"],["AddMonoid","End","instAddMonoidWithOne"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["SMul","mk"],["AddMonoid","End","instDistribSMul","_proof_3"],["DistribSMul","mk"],["SMulZeroClass","mk"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["AddMonoidWithOne","toAddMonoid"],["AddMonoid","End","instAddMonoidWithOne"],["AddMonoid","End","instDistribSMul","_proof_4"],["AddMonoid","End","instDistribSMul","_aux_1"],["AddMonoid","End"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["ZeroHom","instModule","_proof_2"],"typeFallback":"forall {R : Type.{u_3}} {A : Type.{u_1}} {B : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.Hom.955123615._hygCtx._hyg.7 : Semiring.{u_3} R] [inst._@.Mathlib.Algebra.Module.Hom.955123615._hygCtx._hyg.10 : AddMonoid.{u_1} A] [inst._@.Mathlib.Algebra.Module.Hom.955123615._hygCtx._hyg.13 : AddCommMonoid.{u_2} B] [inst._@.Mathlib.Algebra.Module.Hom.955123615._hygCtx._hyg.16 : Module.{u_3, u_2} R B inst._@.Mathlib.Algebra.Module.Hom.955123615._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Hom.955123615._hygCtx._hyg.13] (x._@.Mathlib.Algebra.Module.Hom.955123615._hygCtx._hyg.46 : R) (x._@.Mathlib.Algebra.Module.Hom.955123615._hygCtx._hyg.48 : ZeroHom.{u_1, u_2} A B (AddZero.toZero.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.955123615._hygCtx._hyg.10))) (AddZero.toZero.{u_2} B (AddZeroClass.toAddZero.{u_2} B (AddMonoid.toAddZeroClass.{u_2} B (AddCommMonoid.toAddMonoid.{u_2} B inst._@.Mathlib.Algebra.Module.Hom.955123615._hygCtx._hyg.13))))) 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[inst._@.Mathlib.Algebra.Module.Hom.955123615._hygCtx._hyg.7 : Semiring.{u_3} R] [inst._@.Mathlib.Algebra.Module.Hom.955123615._hygCtx._hyg.10 : AddMonoid.{u_1} A] [inst._@.Mathlib.Algebra.Module.Hom.955123615._hygCtx._hyg.13 : AddCommMonoid.{u_2} B] [inst._@.Mathlib.Algebra.Module.Hom.955123615._hygCtx._hyg.16 : Module.{u_3, u_2} R B inst._@.Mathlib.Algebra.Module.Hom.955123615._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Hom.955123615._hygCtx._hyg.13] (x._@.Mathlib.Algebra.Module.Hom.955123615._hygCtx._hyg.63 : R) (x._@.Mathlib.Algebra.Module.Hom.955123615._hygCtx._hyg.65 : R) (x._@.Mathlib.Algebra.Module.Hom.955123615._hygCtx._hyg.67 : ZeroHom.{u_1, u_2} A B (AddZero.toZero.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.955123615._hygCtx._hyg.10))) (AddZero.toZero.{u_2} B (AddZeroClass.toAddZero.{u_2} B (AddMonoid.toAddZeroClass.{u_2} B (AddCommMonoid.toAddMonoid.{u_2} B 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inst._@.Mathlib.Algebra.Module.Hom.955123615._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Hom.955123615._hygCtx._hyg.16)))))) x._@.Mathlib.Algebra.Module.Hom.955123615._hygCtx._hyg.65 x._@.Mathlib.Algebra.Module.Hom.955123615._hygCtx._hyg.67))","typeFull":"∀ {R : Type u_3} {A : Type u_1} {B : Type u_2} [inst : Semiring R] [inst_1 : AddMonoid A] [inst_2 : AddCommMonoid B]\n  [inst_3 : Module R B] (x x_1 : R) (x_2 : ZeroHom A B), (x + x_1) • x_2 = x • x_2 + x_1 • x_2","typeReadable":"∀ {R : Type u_3} {A : Type u_1} {B : Type u_2} [inst : Semiring R] [inst_1 : AddMonoid A] [inst_2 : AddCommMonoid B]\n  [inst_3 : Module R B] (x x_1 : R) (x_2 : ZeroHom A B), (x + x_1) • x_2 = x • x_2 + x_1 • x_2","typeReferences":[["Module"],["SemigroupAction","toSMul"],["ZeroHom"],["AddCommMonoid","toAddMonoid"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["MonoidWithZero","toMonoid"],["instHSMul"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Monoid","toSemigroup"],["Eq"],["ZeroHom","instMulActionWithZero"],["Distrib","toAdd"],["NonUnitalNonAssocSemiring","toDistrib"],["instHAdd"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["instZeroZeroHom"],["ZeroHom","instAddCommMonoid"],["Semiring","toMonoidWithZero"],["AddMonoid"],["Module","toMulActionWithZero"],["AddZeroClass","toAddZero"],["HAdd","hAdd"],["AddCommMonoid","toAddCommSemigroup"],["HSMul","hSMul"],["AddZero","toZero"],["MulAction","toSemigroupAction"],["AddMonoid","toAddZeroClass"],["Semiring"],["MulActionWithZero","toMulAction"]],"valueReferences":[["SemigroupAction","toSMul"],["ZeroHom"],["AddCommMonoid","toAddMonoid"],["ZeroHom","ext"],["DFunLike","coe"],["Semiring","toNonAssocSemiring"],["MonoidWithZero","toMonoid"],["instHSMul"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Monoid","toSemigroup"],["ZeroHom","instMulActionWithZero"],["Distrib","toAdd"],["NonUnitalNonAssocSemiring","toDistrib"],["instHAdd"],["instZeroZeroHom"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["ZeroHom","instAddCommMonoid"],["Semiring","toMonoidWithZero"],["Module","toMulActionWithZero"],["AddZeroClass","toAddZero"],["HAdd","hAdd"],["ZeroHom","funLike"],["AddCommMonoid","toAddCommSemigroup"],["HSMul","hSMul"],["MulAction","toSemigroupAction"],["AddZero","toZero"],["add_smul"],["AddMonoid","toAddZeroClass"],["MulActionWithZero","toMulAction"]]},{"isProp":true,"kind":"theorem","name":["AddMonoid","End","instDistribMulAction","_proof_4"],"typeFallback":"forall {R : Type.{u_2}} {A : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.7 : Monoid.{u_2} R] [inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13 : AddCommMonoid.{u_1} A] [inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.16 : DistribMulAction.{u_2, u_1} R A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.7 (AddCommMonoid.toAddMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13)] (a : R) (x : AddMonoid.End.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddCommMonoid.toAddMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13)))) (y : AddMonoid.End.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddCommMonoid.toAddMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13)))), Eq.{succ u_1} (AddMonoid.End.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddCommMonoid.toAddMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13)))) (HSMul.hSMul.{u_2, u_1, u_1} R (AddMonoid.End.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddCommMonoid.toAddMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13)))) (AddMonoid.End.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddCommMonoid.toAddMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13)))) (instHSMul.{u_2, u_1} R (AddMonoid.End.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddCommMonoid.toAddMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13)))) (SemigroupAction.toSMul.{u_2, u_1} R (AddMonoid.End.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddCommMonoid.toAddMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13)))) (Monoid.toSemigroup.{u_2} R inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.7) (MulAction.toSemigroupAction.{u_2, u_1} R (AddMonoid.End.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddCommMonoid.toAddMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13)))) inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.7 (MulAction.mk.{u_2, u_1} R (AddMonoid.End.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddCommMonoid.toAddMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13)))) inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.7 (SemigroupAction.mk.{u_2, u_1} R (AddMonoid.End.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddCommMonoid.toAddMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13)))) (Monoid.toSemigroup.{u_2} R inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.7) (SMulZeroClass.toSMul.{u_2, u_1} R (AddMonoid.End.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddCommMonoid.toAddMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13)))) (AddZero.toZero.{u_1} (AddMonoid.End.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddCommMonoid.toAddMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13)))) (AddZeroClass.toAddZero.{u_1} (AddMonoid.End.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddCommMonoid.toAddMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13)))) (AddMonoid.toAddZeroClass.{u_1} (AddMonoid.End.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddCommMonoid.toAddMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13)))) (AddMonoidWithOne.toAddMonoid.{u_1} (AddMonoid.End.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddCommMonoid.toAddMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13)))) (AddMonoid.End.instAddMonoidWithOne.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13))))) (DistribSMul.toSMulZeroClass.{u_2, u_1} R (AddMonoid.End.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddCommMonoid.toAddMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13)))) (AddMonoid.toAddZeroClass.{u_1} (AddMonoid.End.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddCommMonoid.toAddMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13)))) (AddMonoidWithOne.toAddMonoid.{u_1} (AddMonoid.End.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddCommMonoid.toAddMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13)))) (AddMonoid.End.instAddMonoidWithOne.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13))) (AddMonoid.End.instDistribSMul.{u_2, u_1} R A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13 (DistribMulAction.toDistribSMul.{u_2, u_1} R A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.7 (AddCommMonoid.toAddMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.16)))) (AddMonoid.End.instDistribMulAction._proof_1.{u_1, u_2} R A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.16)) (AddMonoid.End.instDistribMulAction._proof_2.{u_1, u_2} R A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.16))))) a (HAdd.hAdd.{u_1, u_1, u_1} (AddMonoid.End.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddCommMonoid.toAddMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13)))) (AddMonoid.End.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddCommMonoid.toAddMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13)))) (AddMonoid.End.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddCommMonoid.toAddMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13)))) (instHAdd.{u_1} (AddMonoid.End.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddCommMonoid.toAddMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13)))) (AddSemigroup.toAdd.{u_1} (AddMonoid.End.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddCommMonoid.toAddMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13)))) (AddMonoid.toAddSemigroup.{u_1} (AddMonoid.End.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddCommMonoid.toAddMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13)))) (AddMonoidWithOne.toAddMonoid.{u_1} (AddMonoid.End.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddCommMonoid.toAddMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13)))) (AddMonoid.End.instAddMonoidWithOne.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13))))) x y)) (HAdd.hAdd.{u_1, u_1, u_1} (AddMonoid.End.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddCommMonoid.toAddMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13)))) (AddMonoid.End.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddCommMonoid.toAddMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13)))) (AddMonoid.End.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddCommMonoid.toAddMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Hom.91091314._hygCtx._hyg.13)))) (instHAdd.{u_1} (AddMonoid.End.{u_1} A (AddZeroClass.toAddZero.{u_1} A 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(AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.Hom.401569664._hygCtx._hyg.13))) (AddZeroClass.toAddZero.{u_3} M₂ (AddMonoid.toAddZeroClass.{u_3} M₂ (AddCommMonoid.toAddMonoid.{u_3} M₂ inst._@.Mathlib.Algebra.Module.Hom.401569664._hygCtx._hyg.16)))) (AddMonoidHom.instAddCommMonoid.{u_2, u_3} M M₂ (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.Hom.401569664._hygCtx._hyg.13)) inst._@.Mathlib.Algebra.Module.Hom.401569664._hygCtx._hyg.16)) (DomMulAct.instDistribMulActionAddMonoidHom.{u_2, u_1, u_3} M S M₂ (MonoidWithZero.toMonoid.{u_1} S (Semiring.toMonoidWithZero.{u_1} S inst._@.Mathlib.Algebra.Module.Hom.401569664._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.Hom.401569664._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_2} S M inst._@.Mathlib.Algebra.Module.Hom.401569664._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Hom.401569664._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Hom.401569664._hygCtx._hyg.19) inst._@.Mathlib.Algebra.Module.Hom.401569664._hygCtx._hyg.16))))) (HAdd.hAdd.{u_1, u_1, u_1} (DomMulAct.{u_1} S) (DomMulAct.{u_1} S) (DomMulAct.{u_1} S) (instHAdd.{u_1} (DomMulAct.{u_1} S) (Distrib.toAdd.{u_1} (DomMulAct.{u_1} S) (NonUnitalNonAssocSemiring.toDistrib.{u_1} (DomMulAct.{u_1} S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} (DomMulAct.{u_1} S) (Semiring.toNonAssocSemiring.{u_1} (DomMulAct.{u_1} S) (DomMulAct.instSemiringOfMulOpposite.{u_1} S (MulOpposite.instSemiring.{u_1} S inst._@.Mathlib.Algebra.Module.Hom.401569664._hygCtx._hyg.10))))))) s s') f) (HAdd.hAdd.{max u_2 u_3, max u_2 u_3, max u_2 u_3} (AddMonoidHom.{u_2, u_3} M M₂ (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.Hom.401569664._hygCtx._hyg.13))) (AddZeroClass.toAddZero.{u_3} M₂ 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inst._@.Mathlib.Algebra.Module.Hom.401569664._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_2} S M inst._@.Mathlib.Algebra.Module.Hom.401569664._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Hom.401569664._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Hom.401569664._hygCtx._hyg.19) inst._@.Mathlib.Algebra.Module.Hom.401569664._hygCtx._hyg.16))))) s f) (HSMul.hSMul.{u_1, max u_2 u_3, max u_2 u_3} (DomMulAct.{u_1} S) (AddMonoidHom.{u_2, u_3} M M₂ (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.Hom.401569664._hygCtx._hyg.13))) (AddZeroClass.toAddZero.{u_3} M₂ (AddMonoid.toAddZeroClass.{u_3} M₂ (AddCommMonoid.toAddMonoid.{u_3} M₂ inst._@.Mathlib.Algebra.Module.Hom.401569664._hygCtx._hyg.16)))) (AddMonoidHom.{u_2, u_3} M M₂ (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.Hom.401569664._hygCtx._hyg.13))) (AddZeroClass.toAddZero.{u_3} M₂ (AddMonoid.toAddZeroClass.{u_3} M₂ (AddCommMonoid.toAddMonoid.{u_3} M₂ inst._@.Mathlib.Algebra.Module.Hom.401569664._hygCtx._hyg.16)))) (instHSMul.{u_1, max u_2 u_3} (DomMulAct.{u_1} S) (AddMonoidHom.{u_2, u_3} M M₂ (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.Hom.401569664._hygCtx._hyg.13))) (AddZeroClass.toAddZero.{u_3} M₂ (AddMonoid.toAddZeroClass.{u_3} M₂ (AddCommMonoid.toAddMonoid.{u_3} M₂ inst._@.Mathlib.Algebra.Module.Hom.401569664._hygCtx._hyg.16)))) (SemigroupAction.toSMul.{u_1, max u_3 u_2} (DomMulAct.{u_1} S) (AddMonoidHom.{u_2, u_3} M M₂ (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.Hom.401569664._hygCtx._hyg.13))) (AddZeroClass.toAddZero.{u_3} M₂ (AddMonoid.toAddZeroClass.{u_3} M₂ (AddCommMonoid.toAddMonoid.{u_3} M₂ 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u_3 u_2} (DomMulAct.{u_1} S) (AddMonoidHom.{u_2, u_3} M M₂ (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.Hom.401569664._hygCtx._hyg.13))) (AddZeroClass.toAddZero.{u_3} M₂ (AddMonoid.toAddZeroClass.{u_3} M₂ (AddCommMonoid.toAddMonoid.{u_3} M₂ inst._@.Mathlib.Algebra.Module.Hom.401569664._hygCtx._hyg.16)))) (DomMulAct.instMonoidOfMulOpposite.{u_1} S (MulOpposite.instMonoid.{u_1} S (MonoidWithZero.toMonoid.{u_1} S (Semiring.toMonoidWithZero.{u_1} S inst._@.Mathlib.Algebra.Module.Hom.401569664._hygCtx._hyg.10)))) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (AddMonoidHom.{u_2, u_3} M M₂ (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.Hom.401569664._hygCtx._hyg.13))) (AddZeroClass.toAddZero.{u_3} M₂ (AddMonoid.toAddZeroClass.{u_3} M₂ (AddCommMonoid.toAddMonoid.{u_3} M₂ 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AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₂] [inst_3 : Module S M] (s s' : Sᵈᵐᵃ) (f : M →+ M₂), (s + s') • f = s • f + s' • f","typeReadable":"∀ {S : Type u_1} {M : Type u_2} {M₂ : Type u_3} [inst : Semiring S] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₂] [inst_3 : Module S M] (s s' : Sᵈᵐᵃ) (f : M →+ M₂), (s + s') • f = s • f + s' • 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AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₂] [inst_3 : Module S M] (s s' : Sᵈᵐᵃ) (f : M →+ M₂) (m : M),\n  ((s + s') • f) m = (s • f + s' • f) m","typeReadable":"∀ {S : Type u_3} {M : Type u_2} {M₂ : Type u_1} [inst : Semiring S] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₂] [inst_3 : Module S M] (s s' : Sᵈᵐᵃ) (f : M →+ M₂) (m : M),\n  ((s + s') • f) m = (s • f + s' • f) 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(DistribMulAction.toDistribSMul.{u_1, u_3} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.Hom.863986199._hygCtx._hyg.7)) (AddCommMonoid.toAddMonoid.{u_3} M inst._@.Mathlib.Algebra.Module.Hom.863986199._hygCtx._hyg.10) (Module.toDistribMulAction.{u_1, u_3} R M inst._@.Mathlib.Algebra.Module.Hom.863986199._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Hom.863986199._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Hom.863986199._hygCtx._hyg.13)))","typeFull":"∀ {R : Type u_1} {M : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],\n  ⇑AddMonoidHom.smul = DistribSMul.toAddMonoidHom M","typeReadable":"∀ {R : Type u_1} {M : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],\n  ⇑AddMonoidHom.smul = DistribSMul.toAddMonoidHom 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{R : Type.{u_1}} {S : Type.{u_2}} {A : Type.{u_4}} [inst._@.Mathlib.Algebra.Module.Hom.650943430._hygCtx._hyg.7 : Monoid.{u_1} R] [inst._@.Mathlib.Algebra.Module.Hom.650943430._hygCtx._hyg.10 : Monoid.{u_2} S] [inst._@.Mathlib.Algebra.Module.Hom.650943430._hygCtx._hyg.13 : AddCommMonoid.{u_4} A] [inst._@.Mathlib.Algebra.Module.Hom.650943430._hygCtx._hyg.16 : DistribMulAction.{u_1, u_4} R A inst._@.Mathlib.Algebra.Module.Hom.650943430._hygCtx._hyg.7 (AddCommMonoid.toAddMonoid.{u_4} A inst._@.Mathlib.Algebra.Module.Hom.650943430._hygCtx._hyg.13)] [inst._@.Mathlib.Algebra.Module.Hom.650943430._hygCtx._hyg.20 : DistribMulAction.{u_2, u_4} S A inst._@.Mathlib.Algebra.Module.Hom.650943430._hygCtx._hyg.10 (AddCommMonoid.toAddMonoid.{u_4} A inst._@.Mathlib.Algebra.Module.Hom.650943430._hygCtx._hyg.13)] [inst._@.Mathlib.Algebra.Module.Hom.650943430._hygCtx._hyg.24 : SMulCommClass.{u_1, u_2, u_4} R S A (SMulZeroClass.toSMul.{u_1, u_4} R A (AddZero.toZero.{u_4} A (AddZeroClass.toAddZero.{u_4} A 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A)","typeReferences":[["DistribMulAction","toDistribSMul"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["AddMonoidWithOne","toAddMonoid"],["AddMonoid","End","instAddMonoidWithOne"],["SMulCommClass"],["AddCommMonoid"],["Monoid"],["AddMonoid","End"],["AddMonoid","End","instDistribSMul"],["AddZero","toZero"],["DistribMulAction"],["AddMonoid","toAddZeroClass"],["DistribSMul","toSMulZeroClass"]],"valueReferences":[["DistribMulAction","toDistribSMul"],["AddCommMonoid","toAddMonoid"],["AddMonoidHom","instSMulCommClass"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["AddMonoidHom","instDomMulActModule","_proof_2"],"typeFallback":"forall {S : Type.{u_3}} {M : Type.{u_1}} {M₂ : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.Hom.401569664._hygCtx._hyg.10 : Semiring.{u_3} S] [inst._@.Mathlib.Algebra.Module.Hom.401569664._hygCtx._hyg.13 : AddCommMonoid.{u_1} M] [inst._@.Mathlib.Algebra.Module.Hom.401569664._hygCtx._hyg.16 : 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u_1} {M : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (r s : R) (x : M),\n  r • x + s • x = (r + s) • x","typeReadable":"∀ {R : Type u_1} {M : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (r s : R) (x : M),\n  r • x + s • x = (r + s) • 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0","typeReferences":[["SemigroupAction","mk"],["SemigroupAction","toSMul"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddMonoidWithOne","toAddMonoid"],["AddCommMonoid"],["instHSMul"],["Zero","toOfNat0"],["Monoid","toSemigroup"],["AddMonoid","End","instDistribSMul"],["Eq"],["DistribMulAction"],["DistribSMul","toSMulZeroClass"],["AddMonoid","End","instDistribMulAction","_proof_2"],["DistribMulAction","toDistribSMul"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["AddMonoid","End","instAddMonoidWithOne"],["HSMul","hSMul"],["Monoid"],["AddMonoid","End"],["MulAction","toSemigroupAction"],["AddZero","toZero"],["AddMonoid","End","instDistribMulAction","_proof_1"],["AddMonoid","toAddZeroClass"],["MulAction","mk"]],"valueReferences":[["AddMonoidHom","instDistribMulAction","_proof_3"],["AddCommMonoid","toAddMonoid"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["ZeroHom","instModule","_proof_1"],"typeFallback":"forall {R : Type.{u_3}} {A : 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