diff --git "a/data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.LinearMap.End.sym.json" "b/data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.LinearMap.End.sym.json"
new file mode 100644--- /dev/null
+++ "b/data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.LinearMap.End.sym.json"
@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["Module","toModuleEnd","_proof_2"],"typeFallback":"forall (R : Type.{u_2}) {S : Type.{u_3}} (M : Type.{u_1}) [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 : Semiring.{u_2} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 : AddCommMonoid.{u_1} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16 : Module.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20 : Semiring.{u_3} S] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.23 : Module.{u_3, u_1} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.27 : SMulCommClass.{u_3, u_2, u_1} S R M (SMulZeroClass.toSMul.{u_3, u_1} S M (AddZero.toZero.{u_1} M (AddZeroClass.toAddZero.{u_1} M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_3, u_1} S M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_3, u_1} S M (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.23)))) (SMulZeroClass.toSMul.{u_2, u_1} R M (AddZero.toZero.{u_1} M (AddZeroClass.toAddZero.{u_1} M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_2, u_1} R M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_2, u_1} R M (MonoidWithZero.toMonoid.{u_2} R (Semiring.toMonoidWithZero.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13) (Module.toDistribMulAction.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16))))] (x : S) (y : S), Eq.{succ u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (OneHom.toFun.{u_3, u_1} S (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (MulOne.toOne.{u_3} S (MulOneClass.toMulOne.{u_3} S (Monoid.toMulOneClass.{u_3} S (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20))))) (MulOne.toOne.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (MulOneClass.toMulOne.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (MulZeroOneClass.toMulOneClass.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (NonAssocSemiring.toMulZeroOneClass.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (Semiring.toNonAssocSemiring.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (Module.End.instSemiring.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16)))))) (MonoidHom.toOneHom.{u_3, u_1} S (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (MulOneClass.toMulOne.{u_3} S (Monoid.toMulOneClass.{u_3} S (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20)))) (MulOneClass.toMulOne.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (MulZeroOneClass.toMulOneClass.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (NonAssocSemiring.toMulZeroOneClass.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (Semiring.toNonAssocSemiring.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (Module.End.instSemiring.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16))))) (DistribMulAction.toModuleEnd.{u_2, u_3, u_1} R S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16 (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20)) (Module.toDistribMulAction.{u_3, u_1} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.23) inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.27)) (HMul.hMul.{u_3, u_3, u_3} S S S (instHMul.{u_3} S (MulOne.toMul.{u_3} S (MulOneClass.toMulOne.{u_3} S (Monoid.toMulOneClass.{u_3} S (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20)))))) x y)) (HMul.hMul.{u_1, u_1, u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 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inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (Module.End.instSemiring.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16))))))) (OneHom.toFun.{u_3, u_1} S (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (MulOne.toOne.{u_3} S (MulOneClass.toMulOne.{u_3} S (Monoid.toMulOneClass.{u_3} S (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20))))) (MulOne.toOne.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 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(Semiring.toNonAssocSemiring.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (Module.End.instSemiring.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16)))))) (MonoidHom.toOneHom.{u_3, u_1} S (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (MulOneClass.toMulOne.{u_3} S (Monoid.toMulOneClass.{u_3} S (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20)))) (MulOneClass.toMulOne.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (MulZeroOneClass.toMulOneClass.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (NonAssocSemiring.toMulZeroOneClass.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (Semiring.toNonAssocSemiring.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (Module.End.instSemiring.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16))))) (DistribMulAction.toModuleEnd.{u_2, u_3, u_1} R S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16 (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20)) (Module.toDistribMulAction.{u_3, u_1} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.23) inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.27)) x) (OneHom.toFun.{u_3, u_1} S (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (MulOne.toOne.{u_3} S (MulOneClass.toMulOne.{u_3} S (Monoid.toMulOneClass.{u_3} S (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20))))) (MulOne.toOne.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (MulOneClass.toMulOne.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (MulZeroOneClass.toMulOneClass.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (NonAssocSemiring.toMulZeroOneClass.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (Semiring.toNonAssocSemiring.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (Module.End.instSemiring.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16)))))) (MonoidHom.toOneHom.{u_3, u_1} S (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (MulOneClass.toMulOne.{u_3} S (Monoid.toMulOneClass.{u_3} S (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20)))) (MulOneClass.toMulOne.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (MulZeroOneClass.toMulOneClass.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (NonAssocSemiring.toMulZeroOneClass.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (Semiring.toNonAssocSemiring.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (Module.End.instSemiring.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16))))) (DistribMulAction.toModuleEnd.{u_2, u_3, u_1} R S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16 (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20)) (Module.toDistribMulAction.{u_3, u_1} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.23) inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.27)) y))","typeFull":"∀ (R : Type u_2) {S : Type u_3} (M : Type u_1) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  [inst_3 : Semiring S] [inst_4 : Module S M] [inst_5 : SMulCommClass S R M] (x y : S),\n  (↑(DistribMulAction.toModuleEnd R M)).toFun (x * y) =\n    (↑(DistribMulAction.toModuleEnd R M)).toFun x * (↑(DistribMulAction.toModuleEnd R M)).toFun y","typeReadable":"∀ (R : Type u_2) {S : Type u_3} (M : Type u_1) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  [inst_3 : Semiring S] [inst_4 : Module S M] [inst_5 : SMulCommClass S R M] (x y : S),\n  (↑(DistribMulAction.toModuleEnd R M)).toFun (x * y) =\n    (↑(DistribMulAction.toModuleEnd R M)).toFun x * (↑(DistribMulAction.toModuleEnd R M)).toFun y","typeReferences":[["MulOneClass","toMulOne"],["Module"],["HMul","hMul"],["SMulZeroClass","toSMul"],["MulZeroOneClass","toMulOneClass"],["AddCommMonoid","toAddMonoid"],["OneHom","toFun"],["MulOne","toMul"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["MonoidWithZero","toMonoid"],["Monoid","toMulOneClass"],["Eq"],["NonAssocSemiring","toMulZeroOneClass"],["DistribSMul","toSMulZeroClass"],["Module","End"],["Module","End","instSemiring"],["DistribMulAction","toModuleEnd"],["MulOne","toOne"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["SMulCommClass"],["Module","toDistribMulAction"],["MonoidHom","toOneHom"],["instHMul"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["MulOneClass","toMulOne"],["Module","toDistribMulAction"],["Module","End"],["Module","End","instSemiring"],["Semiring","toNonAssocSemiring"],["DistribMulAction","toModuleEnd"],["MonoidWithZero","toMonoid"],["Monoid","toMulOneClass"],["MonoidHom","map_mul'"],["Semiring","toMonoidWithZero"],["MulZeroOneClass","toMulOneClass"],["NonAssocSemiring","toMulZeroOneClass"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","smulRight_apply_eq_zero_iff"],"typeFallback":"forall {R : Type.{u_1}} {S : Type.{u_3}} {M : Type.{u_4}} {M₁ : Type.{u_5}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.13 : AddCommMonoid.{u_4} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.16 : AddCommMonoid.{u_5} M₁] [inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.19 : Module.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.23 : Module.{u_1, u_5} R M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.27 : Semiring.{u_3} S] [inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.30 : Module.{u_1, u_3} R S inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.10 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.27)))] [inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.34 : Module.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.38 : IsScalarTower.{u_1, u_3, u_4} R S M (SMulZeroClass.toSMul.{u_1, u_3} R S (AddZero.toZero.{u_3} S (AddZeroClass.toAddZero.{u_3} S (AddMonoid.toAddZeroClass.{u_3} S (AddMonoidWithOne.toAddMonoid.{u_3} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_3} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S 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inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.34)))) (SMulZeroClass.toSMul.{u_1, u_4} R M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_1, u_4} R M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_1, u_4} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.19))))] [inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.43 : IsDomain.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.27] {f : LinearMap.{u_1, u_1, u_5, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.10)) M₁ S inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} S 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inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.19) (LinearMap.smulRight.{u_1, u_3, u_4, u_5} R S M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.34 inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.38 f x) (OfNat.ofNat.{max 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inst._@.Mathlib.Algebra.Module.LinearMap.End.2971719248._hygCtx._hyg.46 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R (CommSemiring.toSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2971719248._hygCtx._hyg.43))) (DistribMulAction.toDistribSMul.{u_9, u_4} R M (MonoidWithZero.toMonoid.{u_9} R (Semiring.toMonoidWithZero.{u_9} R (CommSemiring.toSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2971719248._hygCtx._hyg.43))) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2971719248._hygCtx._hyg.13) (Module.toDistribMulAction.{u_9, u_4} R M (CommSemiring.toSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2971719248._hygCtx._hyg.43) inst._@.Mathlib.Algebra.Module.LinearMap.End.2971719248._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2971719248._hygCtx._hyg.46)) (smulCommClass_self.{u_9, u_4} R M (CommSemiring.toCommMonoid.{u_9} R 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{R : Type u_9} [inst_1 : CommSemiring R] [inst_2 : Module R M] (α : R)\n  (hα : autoParam (α ∈ Set.center R) Module.End.smulLeft_eq._auto_1), Module.End.smulLeft α hα = α • LinearMap.id","typeReadable":"∀ {M : Type u_4} [inst : AddCommMonoid M] {R : Type u_9} [inst_1 : CommSemiring R] [inst_2 : Module R M] (α : R)\n  (hα : autoParam (α ∈ Set.center R) Module.End.smulLeft_eq._auto_1), Module.End.smulLeft α hα = α • 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M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoid.toAddZeroClass.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_1, u_1, max u_2 u_3, u_3} R R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))))))) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoidHom.instFunLike.{u_2, max u_3 u_2} M (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13))) (AddZeroClass.toAddZero.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoid.toAddZeroClass.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_1, u_1, max u_2 u_3, u_3} R R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))))))) (LinearMap.applyₗ'.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) (HSMul.hSMul.{u_1, u_2, u_2} R M M (instHSMul.{u_1, u_2} R M (SMulZeroClass.toSMul.{u_1, u_2} R M (AddZero.toZero.{u_2} M (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_1, u_2} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22))))) x._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.109 x._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.111))) (HSMul.hSMul.{u_1, max u_3 u_2, max u_3 u_2} R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (instHSMul.{u_1, max u_3 u_2} R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (SMulZeroClass.toSMul.{u_1, max u_3 u_2} R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddZero.toZero.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddZeroClass.toAddZero.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoid.toAddZeroClass.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddMonoid.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))))))) (DistribSMul.toSMulZeroClass.{u_1, max u_3 u_2} R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoid.toAddZeroClass.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddMonoid.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))))) (DistribMulAction.toDistribSMul.{u_1, max u_3 u_2} R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))))) (Module.toDistribMulAction.{u_1, max u_3 u_2} R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26))))))) m x)) (HSMul.hSMul.{u_1, u_3, u_3} R M₂ M₂ (instHSMul.{u_1, u_3} R M₂ (SMulZeroClass.toSMul.{u_1, u_3} R M₂ (AddZero.toZero.{u_3} M₂ (AddZeroClass.toAddZero.{u_3} M₂ (AddMonoid.toAddZeroClass.{u_3} M₂ (AddCommMonoid.toAddMonoid.{u_3} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16)))) (DistribSMul.toSMulZeroClass.{u_1, u_3} R M₂ (AddMonoid.toAddZeroClass.{u_3} M₂ (AddCommMonoid.toAddMonoid.{u_3} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16)) (DistribMulAction.toDistribSMul.{u_1, u_3} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{u_3} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16) (Module.toDistribMulAction.{u_1, u_3} R M₂ (CommSemiring.toSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))))))) (AddCommMagma.toAdd.{u_3} M₂ (AddCommSemigroup.toAddCommMagma.{u_3} 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inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoid.toAddZeroClass.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_1, u_1, max u_2 u_3, u_3} R R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))))))) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoidHom.instFunLike.{u_2, max u_3 u_2} M (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13))) (AddZeroClass.toAddZero.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoid.toAddZeroClass.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_1, u_1, max u_2 u_3, u_3} R R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))))))) (LinearMap.applyₗ'.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) (HSMul.hSMul.{u_1, u_2, u_2} R M M (instHSMul.{u_1, u_2} R M (SMulZeroClass.toSMul.{u_1, u_2} R M (AddZero.toZero.{u_2} M (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_1, u_2} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22))))) x._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.109 x._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.111))) x))","typeFull":"∀ {R : Type u_1} {M : Type u_2} {M₂ : Type u_3} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₂] [inst_3 : Module R M] [inst_4 : Module R M₂] (x : R) (x_1 : M) (m : R) (x_2 : M →ₗ[R] M₂),\n  ((LinearMap.applyₗ' R) (x • x_1)).toFun (m • x_2) = (RingHom.id R) m • ((LinearMap.applyₗ' R) (x • x_1)).toFun x_2","typeReadable":"∀ {R : Type u_1} {M : Type u_2} {M₂ : Type u_3} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₂] [inst_3 : Module R M] [inst_4 : Module R M₂] (x : R) (x_1 : M) (m : R) (x_2 : M →ₗ[R] M₂),\n  ((LinearMap.applyₗ' R) (x • x_1)).toFun (m • x_2) = (RingHom.id R) m • ((LinearMap.applyₗ' R) (x • x_1)).toFun x_2","typeReferences":[["RingHom"],["Module"],["CommSemiring"],["RingHom","instFunLike"],["LinearMap","toAddHom"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["AddMonoidHom"],["MonoidWithZero","toMonoid"],["AddMonoidHom","instFunLike"],["instHSMul"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["AddHom","toFun"],["Eq"],["DistribSMul","toSMulZeroClass"],["LinearMap","applyₗ","_proof_1"],["LinearMap","applyₗ'"],["CommSemiring","toSemiring"],["LinearMap","module"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["LinearMap"],["AddZeroClass","toAddZero"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["AddCommMonoid","toAddCommSemigroup"],["HSMul","hSMul"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["smulCommClass_self"],["CommMonoid","toMonoid"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["AddMonoidHom"],["MonoidWithZero","toMonoid"],["DistribMulAction","toMulAction"],["AddMonoidHom","instFunLike"],["instHSMul"],["LinearMap","map_smul'"],["DistribSMul","toSMulZeroClass"],["LinearMap","applyₗ'"],["LinearMap","module"],["CommSemiring","toSemiring"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["LinearMap"],["AddZeroClass","toAddZero"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["HSMul","hSMul"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["Module","End","instRing","_proof_4"],"typeFallback":"forall {R : Type.{u_1}} {N₁ : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16 : AddCommGroup.{u_2} N₁] [inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 : Module.{u_1, u_2} R N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16)] (n : Nat) (a : LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23), Eq.{succ u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (SubNegMonoid.zsmul.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddGroup.toSubNegMonoid.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddCommGroup.toAddGroup.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (LinearMap.addCommGroup.{u_1, u_1, u_2, u_2} R R N₁ N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10))))) (Int.negSucc n) a) (Neg.neg.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (SubNegMonoid.toNeg.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddGroup.toSubNegMonoid.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddCommGroup.toAddGroup.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (LinearMap.addCommGroup.{u_1, u_1, u_2, u_2} R R N₁ N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)))))) (SubNegMonoid.zsmul.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddGroup.toSubNegMonoid.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddCommGroup.toAddGroup.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (LinearMap.addCommGroup.{u_1, u_1, u_2, u_2} R R N₁ N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10))))) (Nat.cast.{0} Int instNatCastInt (Nat.succ n)) a))","typeFull":"∀ {R : Type u_1} {N₁ : Type u_2} [inst : Semiring R] [inst_1 : AddCommGroup N₁] [inst_2 : Module R N₁] (n : ℕ)\n  (a : N₁ →ₗ[R] N₁), SubNegMonoid.zsmul (Int.negSucc n) a = -SubNegMonoid.zsmul (↑n.succ) a","typeReadable":"∀ {R : Type u_1} {N₁ : Type u_2} [inst : Semiring R] [inst_1 : AddCommGroup N₁] [inst_2 : Module R N₁] (n : ℕ)\n  (a : N₁ →ₗ[R] N₁), SubNegMonoid.zsmul (Int.negSucc n) a = -SubNegMonoid.zsmul (↑n.succ) a","typeReferences":[["Nat","cast"],["Neg","neg"],["Module"],["SubNegMonoid","zsmul"],["AddCommGroup","toAddGroup"],["SubNegMonoid","toNeg"],["Int","negSucc"],["AddCommGroup"],["LinearMap"],["Int"],["Nat"],["Semiring","toNonAssocSemiring"],["Nat","succ"],["RingHom","id"],["AddCommGroup","toAddCommMonoid"],["AddGroup","toSubNegMonoid"],["Eq"],["LinearMap","addCommGroup"],["instNatCastInt"],["Semiring"]],"valueReferences":[["Semiring","toNonAssocSemiring"],["RingHom","id"],["SubNegMonoid","zsmul_neg'"],["AddCommGroup","toAddGroup"],["AddCommGroup","toAddCommMonoid"],["AddGroup","toSubNegMonoid"],["LinearMap","addCommGroup"],["LinearMap"]]},{"isProp":true,"kind":"theorem","name":["Module","End","instMonoid","_proof_1"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 : AddCommMonoid.{u_2} M] 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inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Semigroup.mk.{u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Mul.mk.{u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Mul.mul.{u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.instMul.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19))) (fun (x._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.42 : Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (x._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.44 : Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (x._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.46 : Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) => LinearMap.ext.{u_1, u_1, u_2, u_2} R R M M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10)) (HMul.hMul.{u_2, u_2, u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (instHMul.{u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.instMul.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19)) (HMul.hMul.{u_2, u_2, u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (instHMul.{u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.instMul.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19)) x._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.42 x._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.44) x._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.46) (HMul.hMul.{u_2, u_2, u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (instHMul.{u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.instMul.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19)) x._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.42 (HMul.hMul.{u_2, u_2, u_2} 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(Module.End.instMul.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19)) x._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.44 x._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.46)) (fun (x._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.51 : M) => rfl.{succ u_2} M (DFunLike.coe.{succ u_2, succ u_2, succ u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (LinearMap.instFunLike.{u_1, u_1, u_2, u_2} R R M M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10))) (HMul.hMul.{u_2, u_2, u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (instHMul.{u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.instMul.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 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Type.{u_4}} {M₂ : Type.{u_6}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10 : CommSemiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13 : AddCommMonoid.{u_4} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.16 : AddCommMonoid.{u_6} M₂] [inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.22 : Module.{u_1, u_4} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.26 : Module.{u_1, u_6} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.16] (f : LinearMap.{u_1, u_1, u_6, u_1} R R (CommSemiring.toSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.22 (smulCommClass_self.{u_1, u_4} R M (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_4} R M (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.22)))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) (LinearMap.module.{u_1, u_1, u_1, u_6, u_4} R R R M₂ M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.22 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.22 (smulCommClass_self.{u_1, u_4} R M (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_4} R M (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.22)))) (LinearMap.instSMulCommClass.{u_1, u_1, u_1, u_1, u_6, u_4} R R R R M₂ M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.22 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10))) (DistribMulAction.toDistribSMul.{u_1, u_4} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.22)) (smulCommClass_self.{u_1, u_4} R M (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_4} R M (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.22))) (DistribMulAction.toDistribSMul.{u_1, u_4} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.22)) (smulCommClass_self.{u_1, u_4} R M (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_4} R M (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.22))) (smulCommClass_self.{u_1, u_4} R M (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_4} R M (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.22)))))) (LinearMap.{u_1, u_1, u_6, u_1} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.26 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10))) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : LinearMap.{u_1, u_1, u_6, u_1} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.26 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10))) => LinearMap.{u_1, u_1, u_4, max u_4 u_6} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10))) M (LinearMap.{u_1, u_1, u_6, u_4} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.22) inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_1, u_1, u_6, u_4} R R M₂ M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.22 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.22 (LinearMap.module.{u_1, u_1, u_1, u_6, u_4} R R R M₂ M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.22 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.22 (smulCommClass_self.{u_1, u_4} R M (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_4} R M (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.22))))) (LinearMap.instFunLike.{u_1, u_1, max u_6 u_1, max u_6 u_4} R R (LinearMap.{u_1, u_1, u_6, u_1} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.26 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_4, max u_4 u_6} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10))) M (LinearMap.{u_1, u_1, u_6, u_4} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.22) inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_1, u_1, u_6, u_4} R R M₂ M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.22 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.22 (LinearMap.module.{u_1, u_1, u_1, u_6, u_4} R R R M₂ M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.22 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.22 (smulCommClass_self.{u_1, u_4} R M (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_4} R M (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.22))))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R 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(CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.22 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.22 (smulCommClass_self.{u_1, u_4} R M (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.22 (smulCommClass_self.{u_1, u_4} R M (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_4} R M (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.22)))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) (LinearMap.module.{u_1, u_1, u_1, u_6, u_4} R R R M₂ M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.22 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.22 (smulCommClass_self.{u_1, 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.22 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10))) (DistribMulAction.toDistribSMul.{u_1, u_4} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1398367897._hygCtx._hyg.10) 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CommSemiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 : AddCommMonoid.{u_3} M₂] [inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 : Module.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 : Module.{u_1, u_3} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16], SMulCommClass.{u_1, u_1, max u_2 u_3} R R (LinearMap.{u_1, u_1, u_3, u_2} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (DistribMulAction.toDistribSMul.{u_1, u_2} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22)) (LinearMap.applyₗ._proof_1.{u_1, u_2} R M 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(MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22)) (LinearMap.applyₗ._proof_1.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22))","typeFull":"∀ {R : Type u_1} {M : Type u_2} {M₂ : Type u_3} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₂] [inst_3 : Module R M] [inst_4 : Module R M₂], SMulCommClass R R (M₂ →ₗ[R] M)","typeReadable":"∀ {R : Type u_1} {M : Type u_2} {M₂ : Type u_3} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₂] [inst_3 : Module R M] [inst_4 : Module R M₂], SMulCommClass R R (M₂ →ₗ[R] 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u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommSemigroup.toAddCommMagma.{max u_2 u_1} (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddCommSemigroup.{max u_2 u_1} (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))))))) (AddCommMagma.toAdd.{u_1} M₂ (AddCommSemigroup.toAddCommMagma.{u_1} M₂ (AddCommMonoid.toAddCommSemigroup.{u_1} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16))) (fun (f : LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) => DFunLike.coe.{max (succ u_2) (succ u_1), succ u_2, succ u_1} (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M₂) (LinearMap.instFunLike.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) f (HSMul.hSMul.{u_3, u_2, u_2} R M M (instHSMul.{u_3, u_2} R M (SMulZeroClass.toSMul.{u_3, u_2} R M (AddZero.toZero.{u_2} M (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_3, u_2} R M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_3, u_2} R M (MonoidWithZero.toMonoid.{u_3} R (Semiring.toMonoidWithZero.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_2} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22))))) x._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.109 x._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.111)) (LinearMap.applyₗ._proof_5.{u_3, u_2, u_1} R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 x._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.109 x._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.111)) (LinearMap.applyₗ._proof_6.{u_3, u_2, u_1} R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 x._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.109 x._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.111)) (HSMul.hSMul.{u_3, max u_2 u_1, max u_2 u_1} R (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (instHSMul.{u_3, max u_2 u_1} R (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (SMulZeroClass.toSMul.{u_3, max u_2 u_1} R (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddZero.toZero.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddZeroClass.toAddZero.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoid.toAddZeroClass.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddMonoid.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_3, u_3, max u_2 u_1, u_1} R R (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))))))) (DistribSMul.toSMulZeroClass.{u_3, max u_2 u_1} R (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoid.toAddZeroClass.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddMonoid.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_3, u_3, max u_2 u_1, u_1} R R (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))))) (DistribMulAction.toDistribSMul.{u_3, max u_2 u_1} R (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (MonoidWithZero.toMonoid.{u_3} R (Semiring.toMonoidWithZero.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_3, u_3, max u_2 u_1, u_1} R R (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))))) (Module.toDistribMulAction.{u_3, max u_2 u_1} R (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_3, u_3, max u_2 u_1, u_1} R R (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) (LinearMap.module.{u_3, u_3, u_3, max u_2 u_1, u_1} R R R (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26))))))) (DFunLike.coe.{succ u_3, succ u_3, succ u_3} (RingHom.{u_3, u_3} R R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)) (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) R (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : R) => R) (RingHom.instFunLike.{u_3, u_3} R R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)) (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) x._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.109) (LinearMap.mk.{u_3, u_3, max u_2 u_1, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (AddHom.mk.{max u_2 u_1, u_1} (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (AddCommMagma.toAdd.{max u_2 u_1} (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommSemigroup.toAddCommMagma.{max u_2 u_1} (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddCommSemigroup.{max u_2 u_1} (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 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(Module.End.instMul.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19)) x._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.42 (HMul.hMul.{u_2, u_2, u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (instHMul.{u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.instMul.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19)) x._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.44 x._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.46))","typeFull":"∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  (x x_1 x_2 : Module.End R M), x * x_1 * x_2 = x * (x_1 * x_2)","typeReadable":"∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  (x x_1 x_2 : Module.End R M), x * x_1 * x_2 = x * (x_1 * x_2)","typeReferences":[["Module","End"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Module"],["instHMul"],["HMul","hMul"],["LinearMap"],["Eq"],["Module","End","instMul"],["Semiring"]],"valueReferences":[["rfl"],["Module","End"],["Semiring","toNonAssocSemiring"],["LinearMap","instFunLike"],["RingHom","id"],["LinearMap","ext"],["instHMul"],["HMul","hMul"],["LinearMap"],["DFunLike","coe"],["Module","End","instMul"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","compRight_apply"],"typeFallback":"forall {R : Type.{u_1}} (S : Type.{u_3}) {M : Type.{u_4}} {M₁ : Type.{u_5}} {M₂ : Type.{u_6}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.13 : Semiring.{u_3} S] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.16 : AddCommMonoid.{u_4} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.19 : AddCommMonoid.{u_5} M₁] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.22 : AddCommMonoid.{u_6} M₂] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.25 : Module.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.29 : Module.{u_1, u_5} R M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.33 : Module.{u_1, u_6} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.37 : Module.{u_3, u_5} S M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.41 : Module.{u_3, u_6} S M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.45 : SMulCommClass.{u_1, u_3, u_5} R S M₁ (SMulZeroClass.toSMul.{u_1, u_5} R M₁ (AddZero.toZero.{u_5} M₁ (AddZeroClass.toAddZero.{u_5} M₁ (AddMonoid.toAddZeroClass.{u_5} M₁ (AddCommMonoid.toAddMonoid.{u_5} M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.19)))) (DistribSMul.toSMulZeroClass.{u_1, u_5} R M₁ (AddMonoid.toAddZeroClass.{u_5} M₁ (AddCommMonoid.toAddMonoid.{u_5} M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.19)) (DistribMulAction.toDistribSMul.{u_1, u_5} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_5} M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.19) (Module.toDistribMulAction.{u_1, u_5} R M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.29)))) (SMulZeroClass.toSMul.{u_3, u_5} S M₁ (AddZero.toZero.{u_5} M₁ (AddZeroClass.toAddZero.{u_5} M₁ (AddMonoid.toAddZeroClass.{u_5} M₁ (AddCommMonoid.toAddMonoid.{u_5} M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.19)))) (DistribSMul.toSMulZeroClass.{u_3, u_5} S M₁ (AddMonoid.toAddZeroClass.{u_5} M₁ (AddCommMonoid.toAddMonoid.{u_5} M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.19)) (DistribMulAction.toDistribSMul.{u_3, u_5} S M₁ (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.13)) (AddCommMonoid.toAddMonoid.{u_5} M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.19) (Module.toDistribMulAction.{u_3, u_5} S M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.37))))] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.50 : SMulCommClass.{u_1, u_3, u_6} R S M₂ (SMulZeroClass.toSMul.{u_1, u_6} R M₂ (AddZero.toZero.{u_6} M₂ (AddZeroClass.toAddZero.{u_6} M₂ (AddMonoid.toAddZeroClass.{u_6} M₂ (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.22)))) (DistribSMul.toSMulZeroClass.{u_1, u_6} R M₂ (AddMonoid.toAddZeroClass.{u_6} M₂ (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.22)) (DistribMulAction.toDistribSMul.{u_1, u_6} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.22) (Module.toDistribMulAction.{u_1, u_6} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.33)))) (SMulZeroClass.toSMul.{u_3, u_6} S M₂ (AddZero.toZero.{u_6} M₂ (AddZeroClass.toAddZero.{u_6} M₂ (AddMonoid.toAddZeroClass.{u_6} M₂ (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.22)))) (DistribSMul.toSMulZeroClass.{u_3, u_6} S M₂ (AddMonoid.toAddZeroClass.{u_6} M₂ (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.22)) (DistribMulAction.toDistribSMul.{u_3, u_6} S M₂ (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.13)) (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.22) (Module.toDistribMulAction.{u_3, u_6} S M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.41))))] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.55 : LinearMap.CompatibleSMul.{u_5, u_6, u_3, u_1} M₁ M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.22 S R inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 (SMulZeroClass.toSMul.{u_3, u_5} S M₁ (AddZero.toZero.{u_5} M₁ (AddZeroClass.toAddZero.{u_5} M₁ (AddMonoid.toAddZeroClass.{u_5} M₁ (AddCommMonoid.toAddMonoid.{u_5} M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.19)))) (DistribSMul.toSMulZeroClass.{u_3, u_5} S M₁ (AddMonoid.toAddZeroClass.{u_5} M₁ (AddCommMonoid.toAddMonoid.{u_5} M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.19)) (DistribMulAction.toDistribSMul.{u_3, u_5} S M₁ (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.13)) (AddCommMonoid.toAddMonoid.{u_5} M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.19) (Module.toDistribMulAction.{u_3, u_5} S M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.37)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.29 (SMulZeroClass.toSMul.{u_3, u_6} S M₂ (AddZero.toZero.{u_6} M₂ (AddZeroClass.toAddZero.{u_6} M₂ (AddMonoid.toAddZeroClass.{u_6} M₂ (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.22)))) (DistribSMul.toSMulZeroClass.{u_3, u_6} S M₂ (AddMonoid.toAddZeroClass.{u_6} M₂ (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.22)) (DistribMulAction.toDistribSMul.{u_3, u_6} S M₂ (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.13)) (AddCommMonoid.toAddMonoid.{u_6} M₂ 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(RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10)) M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.29) (LinearMap.{u_1, u_1, u_4, u_6} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.33) (LinearMap.addCommMonoid.{u_1, u_1, u_4, u_5} R R M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.29 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10))) (LinearMap.addCommMonoid.{u_1, u_1, u_4, u_6} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10))) (LinearMap.module.{u_1, u_1, u_3, u_4, u_5} R R S M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.29 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.37 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.45) (LinearMap.module.{u_1, u_1, u_3, u_4, u_6} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.50)) (LinearMap.{u_1, u_1, u_4, u_5} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10)) M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.29) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : LinearMap.{u_1, u_1, u_4, u_5} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10)) M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.29) => LinearMap.{u_1, u_1, u_4, u_6} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.33) (LinearMap.instFunLike.{u_3, u_3, max u_5 u_4, max u_6 u_4} S S (LinearMap.{u_1, u_1, u_4, u_5} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10)) M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.29) (LinearMap.{u_1, u_1, u_4, u_6} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.33) inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_1, u_1, u_4, u_5} R R M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.29 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10))) (LinearMap.addCommMonoid.{u_1, u_1, u_4, u_6} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10))) (LinearMap.module.{u_1, u_1, u_3, u_4, u_5} R R S M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.29 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.37 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.45) (LinearMap.module.{u_1, u_1, u_3, u_4, u_6} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.50) (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.13))) (LinearMap.compRight.{u_1, u_3, u_4, u_5, u_6} R S M M₁ M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.29 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.37 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.45 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.55 f) g) (LinearMap.comp.{u_1, u_1, u_1, u_4, u_5, u_6} R R R M M₁ M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.29 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3116271632._hygCtx._hyg.10))) f g)","typeFull":"∀ {R : Type u_1} (S : Type u_3) {M : Type u_4} {M₁ : Type u_5} {M₂ : Type u_6} [inst : Semiring R] [inst_1 : Semiring S]\n  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₁] [inst_4 : AddCommMonoid M₂] [inst_5 : Module R M]\n  [inst_6 : Module R M₁] [inst_7 : Module R M₂] [inst_8 : Module S M₁] [inst_9 : Module S M₂]\n  [inst_10 : SMulCommClass R S M₁] [inst_11 : SMulCommClass R S M₂] [inst_12 : LinearMap.CompatibleSMul M₁ M₂ S R]\n  (f : M₁ →ₗ[R] M₂) (g : M →ₗ[R] M₁), (LinearMap.compRight S f) g = f ∘ₗ g","typeReadable":"∀ {R : Type u_1} (S : Type u_3) {M : Type u_4} {M₁ : Type u_5} {M₂ : Type u_6} [inst : Semiring R] [inst_1 : Semiring S]\n  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₁] [inst_4 : AddCommMonoid M₂] [inst_5 : Module R M]\n  [inst_6 : Module R M₁] [inst_7 : Module R M₂] [inst_8 : Module S M₁] [inst_9 : Module S M₂]\n  [inst_10 : SMulCommClass R S M₁] [inst_11 : SMulCommClass R S M₂] [inst_12 : LinearMap.CompatibleSMul M₁ M₂ S R]\n  (f : M₁ →ₗ[R] M₂) (g : M →ₗ[R] M₁), (LinearMap.compRight S f) g = f ∘ₗ g","typeReferences":[["LinearMap","CompatibleSMul"],["LinearMap","instFunLike"],["RingHomCompTriple","ids"],["Module"],["LinearMap","comp"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["Eq"],["DistribSMul","toSMulZeroClass"],["LinearMap","module"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["LinearMap"],["LinearMap","addCommMonoid"],["SMulCommClass"],["Module","toDistribMulAction"],["LinearMap","compRight"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["LinearMap","addCommMonoid"],["rfl"],["Semiring","toNonAssocSemiring"],["LinearMap","instFunLike"],["RingHom","id"],["LinearMap","compRight"],["LinearMap","module"],["LinearMap"],["DFunLike","coe"]]},{"isProp":true,"kind":"theorem","name":["Module","End","isUnit_inv_apply_apply_of_isUnit"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_4}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.24468697._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.24468697._hygCtx._hyg.13 : AddCommMonoid.{u_4} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.24468697._hygCtx._hyg.19 : Module.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.24468697._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.24468697._hygCtx._hyg.13] {f : Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.24468697._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.24468697._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.24468697._hygCtx._hyg.19} (h : IsUnit.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.24468697._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.24468697._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.24468697._hygCtx._hyg.19) (Module.End.instMonoid.{u_1, u_4} R M 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u_1, u_6, u_1} R R R M₂ R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.26 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10)) (smulCommClass_self.{u_1, u_1} R R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_1} R R (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10))))) (Module.toDistribMulAction.{u_1, u_1} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10)))) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10)))))) (LinearMap.module.{u_1, u_1, u_1, u_4, max u_4 u_6} R R R M (LinearMap.{u_1, u_1, u_6, u_4} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_1, u_1, u_6, u_4} R R M₂ M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22 (LinearMap.module.{u_1, u_1, u_1, u_6, u_4} R R R M₂ M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22 (smulCommClass_self.{u_1, u_4} R M (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_4} R M (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22)))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (LinearMap.module.{u_1, u_1, u_1, u_6, u_4} R R R M₂ M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22 (smulCommClass_self.{u_1, u_4} R M (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_4} R M (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22)))) (LinearMap.instSMulCommClass.{u_1, u_1, u_1, u_1, u_6, u_4} R R R R M₂ M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10))) (DistribMulAction.toDistribSMul.{u_1, u_4} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22)) (smulCommClass_self.{u_1, u_4} R M (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_4} R M (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22))) (DistribMulAction.toDistribSMul.{u_1, u_4} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22)) (smulCommClass_self.{u_1, u_4} R M (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_4} R M (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22))) (smulCommClass_self.{u_1, u_4} R M (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_4} R M (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22)))))) (LinearMap.{u_1, u_1, u_6, u_1} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.26 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10))) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : LinearMap.{u_1, u_1, u_6, u_1} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.26 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10))) => LinearMap.{u_1, u_1, u_4, max u_4 u_6} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10))) M (LinearMap.{u_1, u_1, u_6, u_4} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_1, u_1, u_6, u_4} R R M₂ M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22 (LinearMap.module.{u_1, u_1, u_1, u_6, u_4} R R R M₂ M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22 (smulCommClass_self.{u_1, u_4} R M (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_4} R M (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22))))) 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inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_1, u_1, u_6, u_4} R R M₂ M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22 (smulCommClass_self.{u_1, u_4} R M (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_4} R M (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22))))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R 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(CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22 (smulCommClass_self.{u_1, u_4} R M (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) 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inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.26 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R 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R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22 (LinearMap.module.{u_1, u_1, u_1, u_6, u_4} R R R M₂ M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) 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inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10))) (DistribMulAction.toDistribSMul.{u_1, u_4} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) 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(CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22))) (smulCommClass_self.{u_1, u_4} R M (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_4} R M (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22))))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10)))) (LinearMap.smulRightₗ.{u_1, u_4, u_6} R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.26) f) x) (LinearMap.smulRight.{u_1, u_1, u_4, u_6} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.26 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22 (IsScalarTower.left.{u_1, u_4} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10))) (DistribMulAction.toMulAction.{u_1, u_4} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2466529850._hygCtx._hyg.22))) f x)","typeFull":"∀ {R : Type u_1} {M : Type u_4} {M₂ : Type u_6} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₂] [inst_3 : Module R M] [inst_4 : Module R M₂] (f : M₂ →ₗ[R] R) (x : M),\n  (LinearMap.smulRightₗ f) x = f.smulRight x","typeReadable":"∀ {R : Type u_1} {M : Type u_4} {M₂ : Type u_6} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₂] [inst_3 : Module R M] [inst_4 : Module R M₂] (f : M₂ →ₗ[R] R) (x : M),\n  (LinearMap.smulRightₗ f) x = f.smulRight x","typeReferences":[["smulCommClass_self"],["CommMonoid","toMonoid"],["LinearMap","instFunLike"],["Module"],["CommSemiring"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["DistribMulAction","toMulAction"],["LinearMap","instSMulCommClass"],["Eq"],["Semiring","toModule"],["LinearMap","smulRight"],["IsScalarTower","left"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["CommSemiring","toSemiring"],["LinearMap","module"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["LinearMap"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["LinearMap","smulRightₗ"]],"valueReferences":[["rfl"],["smulCommClass_self"],["LinearMap","instFunLike"],["CommMonoid","toMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["CommSemiring","toSemiring"],["LinearMap","module"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddCommMonoid","toAddMonoid"],["LinearMap"],["DFunLike","coe"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["DistribMulAction","toMulAction"],["LinearMap","instSMulCommClass"],["Semiring","toModule"],["LinearMap","smulRightₗ"]]},{"isProp":true,"kind":"theorem","name":["RingEquiv","moduleEndSelf","_proof_4"],"typeFallback":"forall 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inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) (instHAdd.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) (LinearMap.instAdd.{u_1, u_1, u_2, u_2} R R M M 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inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) (instHAdd.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) (LinearMap.instAdd.{u_1, u_1, u_2, u_2} R R M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)))) (LinearMap.comp.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) (Module.End.instMul._proof_1.{u_1} R 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x_2","typeReferences":[["Module","End"],["Module"],["instHAdd"],["LinearMap","comp"],["LinearMap"],["HAdd","hAdd"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Module","End","instMul","_proof_1"],["LinearMap","instAdd"],["Eq"],["Semiring"]],"valueReferences":[["Semiring","toNonAssocSemiring"],["RingHom","id"],["Module","End","instMul","_proof_1"],["LinearMap","comp_add"]]},{"isProp":true,"kind":"theorem","name":["DistribSMul","toLinearMap_apply"],"typeFallback":"forall (R : Type.{u_1}) {S : Type.{u_3}} (M : Type.{u_4}) [inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13 : AddCommMonoid.{u_4} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.16 : Module.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.23 : DistribSMul.{u_3, u_4} S M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13))] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.27 : SMulCommClass.{u_3, u_1, u_4} S R M (SMulZeroClass.toSMul.{u_3, u_4} S M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_3, u_4} S M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13)) inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.23)) (SMulZeroClass.toSMul.{u_1, u_4} R M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_1, u_4} R M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_1, u_4} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.16))))] (s : S) (a._@._internal._hyg.0 : M), Eq.{succ u_4} M (DFunLike.coe.{succ u_4, succ u_4, succ u_4} (LinearMap.{u_1, u_1, u_4, u_4} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.16) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (LinearMap.instFunLike.{u_1, u_1, u_4, u_4} R R M M inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.16 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.10))) (DistribSMul.toLinearMap.{u_1, u_3, u_4} R S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.27 s) a._@._internal._hyg.0) (HSMul.hSMul.{u_3, u_4, u_4} S M M (instHSMul.{u_3, u_4} S M (SMulZeroClass.toSMul.{u_3, u_4} S M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_3, u_4} S M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13)) inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.23))) s a._@._internal._hyg.0)","typeFull":"∀ (R : Type u_1) {S : Type u_3} (M : Type u_4) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  [inst_3 : DistribSMul S M] [inst_4 : SMulCommClass S R M] (s : S) (a : M), (DistribSMul.toLinearMap R M s) a = s • a","typeReadable":"∀ (R : Type u_1) {S : Type u_3} (M : Type u_4) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  [inst_3 : DistribSMul S M] [inst_4 : SMulCommClass S R M] (s : S) (a : M), (DistribSMul.toLinearMap R M s) a = s • 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[inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 : AddCommMonoid.{u_4} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16 : Module.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20 : Semiring.{u_3} S] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.23 : Module.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.27 : SMulCommClass.{u_3, u_1, u_4} S R M (SMulZeroClass.toSMul.{u_3, u_4} S M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M 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(CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22))))) (LinearMap.mk.{u_3, u_3, u_1, max u_1 u_2} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) (AddCommMagma.toAdd.{u_1} M (AddCommSemigroup.toAddCommMagma.{u_1} M (AddCommMonoid.toAddCommSemigroup.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13))) (AddCommMagma.toAdd.{max u_1 u_2} (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))))))) (LinearMap.smulRight.{u_3, u_3, u_1, u_2} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddCommMagma.toAdd.{max u_3 u_2} (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddCommSemigroup.toAddCommMagma.{max u_3 u_2} (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddCommMonoid.toAddCommSemigroup.{max u_3 u_2} (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_3} R R M₂ R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))))))) f f')) (fun (m : M) (m' : M) => LinearMap.smulRightₗ._proof_1.{u_1, u_2, u_3} R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (HAdd.hAdd.{max u_3 u_2, max u_3 u_2, max u_3 u_2} (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R 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(CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddCommSemigroup.toAddCommMagma.{max u_3 u_2} (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddCommMonoid.toAddCommSemigroup.{max u_3 u_2} (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_3} R R M₂ R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))))))) f f') m m')) (fun (c : R) (m : M) => LinearMap.smulRightₗ._proof_2.{u_1, u_2, u_3} R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (HAdd.hAdd.{max u_3 u_2, max u_3 u_2, max u_3 u_2} (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (instHAdd.{max u_3 u_2} (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddCommMagma.toAdd.{max u_3 u_2} (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddCommSemigroup.toAddCommMagma.{max u_3 u_2} (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddCommMonoid.toAddCommSemigroup.{max u_3 u_2} (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_3} R R M₂ R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))))))) f f') c m)) (HAdd.hAdd.{max u_1 u_2, max u_1 u_2, max u_1 u_2} (LinearMap.{u_3, u_3, u_1, max u_1 u_2} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M₂ M (CommSemiring.toSemiring.{u_3} R 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R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22))))) (instHAdd.{max 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22))))) (AddCommMagma.toAdd.{max u_1 u_2} (LinearMap.{u_3, u_3, u_1, max u_1 u_2} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22))))) (AddCommSemigroup.toAddCommMagma.{max u_1 u_2} (LinearMap.{u_3, u_3, u_1, max u_1 u_2} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M (LinearMap.{u_3, u_3, u_2, u_1} R R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22))))) (LinearMap.addCommMonoid.{u_3, u_3, u_1, max u_1 u_2} R R M (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22)))) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))))))) (LinearMap.mk.{u_3, u_3, u_1, max u_1 u_2} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22)))) (AddHom.mk.{u_1, max u_1 u_2} M (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) (AddCommMagma.toAdd.{u_1} M (AddCommSemigroup.toAddCommMagma.{u_1} M (AddCommMonoid.toAddCommSemigroup.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13))) (AddCommMagma.toAdd.{max u_1 u_2} (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) (AddCommSemigroup.toAddCommMagma.{max u_1 u_2} (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) (AddCommMonoid.toAddCommSemigroup.{max u_1 u_2} (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))))))) (LinearMap.smulRight.{u_3, u_3, u_1, u_2} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (IsScalarTower.left.{u_3, u_1} R M (MonoidWithZero.toMonoid.{u_3} R (Semiring.toMonoidWithZero.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (DistribMulAction.toMulAction.{u_3, u_1} R M (MonoidWithZero.toMonoid.{u_3} R (Semiring.toMonoidWithZero.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22))) f) (fun (m : M) (m' : M) => LinearMap.smulRightₗ._proof_1.{u_1, u_2, u_3} R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 f m m')) (fun (c : R) (m : M) => LinearMap.smulRightₗ._proof_2.{u_1, u_2, u_3} R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 f c m)) (LinearMap.mk.{u_3, u_3, u_1, max u_1 u_2} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22)))) (AddHom.mk.{u_1, max u_1 u_2} M (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) (AddCommMagma.toAdd.{u_1} M (AddCommSemigroup.toAddCommMagma.{u_1} M (AddCommMonoid.toAddCommSemigroup.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13))) (AddCommMagma.toAdd.{max u_1 u_2} (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) (AddCommSemigroup.toAddCommMagma.{max u_1 u_2} (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) (AddCommMonoid.toAddCommSemigroup.{max u_1 u_2} (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))))))) (LinearMap.smulRight.{u_3, u_3, u_1, u_2} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (IsScalarTower.left.{u_3, u_1} R M (MonoidWithZero.toMonoid.{u_3} R (Semiring.toMonoidWithZero.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (DistribMulAction.toMulAction.{u_3, u_1} R M (MonoidWithZero.toMonoid.{u_3} R (Semiring.toMonoidWithZero.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22))) f') (fun (m : M) (m' : M) => LinearMap.smulRightₗ._proof_1.{u_1, u_2, u_3} R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 f' m m')) (fun (c : R) (m : M) => LinearMap.smulRightₗ._proof_2.{u_1, u_2, u_3} R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 f' c m)))","typeFull":"∀ {R : Type u_3} {M : Type u_1} {M₂ : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₂] [inst_3 : Module R M] [inst_4 : Module R M₂] (f f' : M₂ →ₗ[R] R),\n  { toFun := (f + f').smulRight, map_add' := ⋯, map_smul' := ⋯ } =\n    { toFun := f.smulRight, map_add' := ⋯, map_smul' := ⋯ } + { toFun := f'.smulRight, map_add' := ⋯, map_smul' := ⋯ }","typeReadable":"∀ {R : Type u_3} {M : Type u_1} {M₂ : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₂] [inst_3 : Module R M] [inst_4 : Module R M₂] (f f' : M₂ →ₗ[R] R),\n  { toFun := (f + f').smulRight, map_add' := ⋯, map_smul' := ⋯ } =\n    { toFun := f.smulRight, map_add' := ⋯, map_smul' := ⋯ } + { toFun := f'.smulRight, map_add' := ⋯, map_smul' := ⋯ }","typeReferences":[["smulCommClass_self"],["CommMonoid","toMonoid"],["Module"],["LinearMap","mk"],["CommSemiring"],["AddHom","mk"],["AddCommMonoid","toAddMonoid"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["DistribMulAction","toMulAction"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Eq"],["Semiring","toModule"],["LinearMap","smulRight"],["IsScalarTower","left"],["instHAdd"],["LinearMap","module"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["CommSemiring","toSemiring"],["LinearMap","smulRightₗ","_proof_2"],["Semiring","toMonoidWithZero"],["LinearMap"],["CommSemiring","toCommMonoid"],["HAdd","hAdd"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["AddCommMonoid","toAddCommSemigroup"],["LinearMap","smulRightₗ","_proof_1"]],"valueReferences":[["smulCommClass_self"],["LinearMap","instFunLike"],["CommMonoid","toMonoid"],["LinearMap","mk"],["AddHom","mk"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["LinearMap","ext"],["MonoidWithZero","toMonoid"],["DistribMulAction","toMulAction"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Semiring","toModule"],["LinearMap","smulRight"],["IsScalarTower","left"],["instHAdd"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["LinearMap","module"],["CommSemiring","toSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["LinearMap","smulRightₗ","_proof_2"],["Semiring","toMonoidWithZero"],["LinearMap"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["HAdd","hAdd"],["Module","toDistribMulAction"],["AddCommMonoid","toAddCommSemigroup"],["LinearMap","smulRightₗ","_proof_1"],["add_smul"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","compRight","_proof_1"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_2}} {M₁ : Type.{u_3}} {M₂ : Type.{u_4}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 : AddCommMonoid.{u_3} M₁] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 : AddCommMonoid.{u_4} M₂] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 : Module.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29 : Module.{u_1, u_3} R M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.33 : Module.{u_1, u_4} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22] (f : LinearMap.{u_1, u_1, u_3, u_4} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M₁ M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.33) (x._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.111 : LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29) (x._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.113 : LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29), Eq.{max (succ u_4) (succ u_2)} (LinearMap.{u_1, u_1, u_2, u_4} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.33) (LinearMap.comp.{u_1, u_1, u_1, u_2, u_3, u_4} R R R M M₁ M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10))))))) x._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.111 x._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.113)) (HAdd.hAdd.{max u_2 u_4, max u_2 u_4, max u_2 u_4} (LinearMap.{u_1, u_1, u_2, u_4} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.33) (LinearMap.{u_1, u_1, u_2, u_4} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.33) (LinearMap.{u_1, u_1, u_2, u_4} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.33) (instHAdd.{max u_2 u_4} (LinearMap.{u_1, u_1, u_2, u_4} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 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inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.33) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_4} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10))))))) (LinearMap.comp.{u_1, u_1, u_1, u_2, u_3, u_4} R R R M M₁ M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R 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(Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) (Module.End.instMul._proof_1.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10) f x._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.113))","typeFull":"∀ {R : Type u_1} {M : Type u_2} {M₁ : Type u_3} {M₂ : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₁] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R M₁]\n  [inst_6 : Module R M₂] (f : M₁ →ₗ[R] M₂) (x x_1 : M →ₗ[R] M₁), f ∘ₗ (x + x_1) = f ∘ₗ x + f ∘ₗ x_1","typeReadable":"∀ {R : Type u_1} {M : Type u_2} {M₁ : Type u_3} {M₂ : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₁] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R M₁]\n  [inst_6 : Module R M₂] (f : M₁ →ₗ[R] M₂) (x x_1 : M →ₗ[R] M₁), f ∘ₗ (x + x_1) = f ∘ₗ x + f ∘ₗ 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[inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 : AddCommMonoid.{u_3} M₂] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 : Module.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 : Module.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22] (v : M) (f : LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) (g : LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33), Eq.{succ u_3} M₂ (DFunLike.coe.{max (succ u_3) (succ u_2), succ u_2, succ u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M₂) (LinearMap.instFunLike.{u_1, u_1, u_2, u_3} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) (HAdd.hAdd.{max u_3 u_2, max u_3 u_2, max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) (LinearMap.{u_1, 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inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) (instHAdd.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) (LinearMap.instAdd.{u_1, u_1, u_2, u_3} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 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inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) g v))","typeFull":"∀ {R : Type u_1} {M : Type u_2} {M₂ : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₂] [inst_3 : Module R M] [inst_4 : Module R M₂] (v : M) (f g : M →ₗ[R] M₂),\n  (f + g) v = f v + g v","typeReadable":"∀ {R : Type u_1} {M : Type u_2} {M₂ : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₂] [inst_3 : Module R M] [inst_4 : Module R M₂] (v : M) (f g : M →ₗ[R] M₂),\n  (f + g) v = f v + g v","typeReferences":[["LinearMap","instFunLike"],["Module"],["instHAdd"],["LinearMap"],["DFunLike","coe"],["HAdd","hAdd"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["AddCommMonoid","toAddCommSemigroup"],["RingHom","id"],["LinearMap","instAdd"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Eq"],["Semiring"]],"valueReferences":[["Semiring","toNonAssocSemiring"],["RingHom","id"],["LinearMap","add_apply"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","applyₗ","_proof_2"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_2}} {M₂ : Type.{u_3}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 : CommSemiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 : AddCommMonoid.{u_3} M₂] [inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 : Module.{u_1, u_2} R M 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inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (y : LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26), Eq.{succ u_3} M₂ (AddHom.toFun.{max u_3 u_2, u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (AddCommMagma.toAdd.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommSemigroup.toAddCommMagma.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddCommSemigroup.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))))))) (AddCommMagma.toAdd.{u_3} M₂ (AddCommSemigroup.toAddCommMagma.{u_3} M₂ (AddCommMonoid.toAddCommSemigroup.{u_3} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16))) (LinearMap.toAddHom.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (DFunLike.coe.{max (succ u_3) (succ u_2), succ u_2, max (succ u_3) (succ u_2)} (AddMonoidHom.{u_2, max u_3 u_2} M (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13))) (AddZeroClass.toAddZero.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R 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(LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_1, u_1, max u_2 u_3, u_3} R R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))))))) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoidHom.instFunLike.{u_2, max u_3 u_2} M (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13))) (AddZeroClass.toAddZero.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoid.toAddZeroClass.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_1, u_1, max u_2 u_3, u_3} R R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))))))) (LinearMap.applyₗ'.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) v)) (HAdd.hAdd.{max u_3 u_2, max u_3 u_2, max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (instHAdd.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMagma.toAdd.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommSemigroup.toAddCommMagma.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddCommSemigroup.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))))))) x y)) (HAdd.hAdd.{u_3, u_3, u_3} M₂ M₂ M₂ (instHAdd.{u_3} M₂ (AddCommMagma.toAdd.{u_3} M₂ (AddCommSemigroup.toAddCommMagma.{u_3} M₂ (AddCommMonoid.toAddCommSemigroup.{u_3} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16)))) (AddHom.toFun.{max u_3 u_2, u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (AddCommMagma.toAdd.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 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inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_1, u_1, max u_2 u_3, u_3} R R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))))))) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoidHom.instFunLike.{u_2, max u_3 u_2} M (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13))) (AddZeroClass.toAddZero.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoid.toAddZeroClass.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_1, u_1, max u_2 u_3, u_3} R R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))))))) (LinearMap.applyₗ'.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) v)) x) (AddHom.toFun.{max u_3 u_2, u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (AddCommMagma.toAdd.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommSemigroup.toAddCommMagma.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_1, u_1, max u_2 u_3, u_3} R R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))))))) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoidHom.instFunLike.{u_2, max u_3 u_2} M (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13))) (AddZeroClass.toAddZero.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoid.toAddZeroClass.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_1, u_1, max u_2 u_3, u_3} R R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))))))) (LinearMap.applyₗ'.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) v)) y))","typeFull":"∀ {R : Type u_1} {M : Type u_2} {M₂ : Type u_3} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₂] [inst_3 : Module R M] [inst_4 : Module R M₂] (v : M) (x y : M →ₗ[R] M₂),\n  ((LinearMap.applyₗ' R) v).toFun (x + y) = ((LinearMap.applyₗ' R) v).toFun x + ((LinearMap.applyₗ' R) v).toFun y","typeReadable":"∀ {R : Type u_1} {M : Type u_2} {M₂ : Type u_3} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₂] [inst_3 : Module R M] [inst_4 : Module R M₂] (v : M) (x y : M →ₗ[R] M₂),\n  ((LinearMap.applyₗ' R) v).toFun (x + y) = ((LinearMap.applyₗ' R) v).toFun x + ((LinearMap.applyₗ' R) v).toFun 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inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.23))) s y))","typeFull":"∀ {S : Type u_2} (M : Type u_1) [inst : AddCommMonoid M] [inst_1 : DistribSMul S M] (s : S) (x y : M),\n  s • (x + y) = s • x + s • y","typeReadable":"∀ {S : Type u_2} (M : Type u_1) [inst : AddCommMonoid M] [inst_1 : DistribSMul S M] (s : S) (x y : M),\n  s • (x + y) = s • x + s • y","typeReferences":[["instHAdd"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddZero","toAdd"],["AddZeroClass","toAddZero"],["DistribSMul"],["HAdd","hAdd"],["AddCommMonoid"],["HSMul","hSMul"],["instHSMul"],["Eq"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["DistribSMul","toSMulZeroClass"]],"valueReferences":[["DistribSMul","smul_add"],["AddCommMonoid","toAddMonoid"],["AddMonoid","toAddZeroClass"]]},{"isProp":false,"kind":"definition","name":["DistribMulAction","toLinearMap"],"typeFallback":"forall (R : Type.{u_1}) {S : Type.{u_3}} (M : Type.{u_4}) [inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13 : AddCommMonoid.{u_4} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.16 : Module.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.23 : DistribSMul.{u_3, u_4} S M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13))] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.27 : SMulCommClass.{u_3, u_1, u_4} S R M (SMulZeroClass.toSMul.{u_3, u_4} S M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M 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inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.16))))], S -> (LinearMap.{u_1, u_1, u_4, u_4} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.16)","typeFull":"(R : Type u_1) →\n  {S : Type u_3} →\n    (M : Type u_4) →\n      [inst : Semiring R] →\n        [inst_1 : AddCommMonoid M] →\n          [inst_2 : Module R M] → [inst_3 : DistribSMul S M] → [SMulCommClass S R M] → S → M →ₗ[R] M","typeReadable":"(R : Type u_1) →\n  {S : Type u_3} →\n    (M : Type u_4) →\n      [inst : Semiring R] →\n        [inst_1 : AddCommMonoid M] →\n          [inst_2 : Module R M] → [inst_3 : DistribSMul S M] → [SMulCommClass S R M] → S → M →ₗ[R] M","typeReferences":[["Module"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["LinearMap"],["AddZeroClass","toAddZero"],["DistribSMul"],["SMulCommClass"],["Module","toDistribMulAction"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["AddZero","toZero"],["Semiring"],["AddMonoid","toAddZeroClass"],["DistribSMul","toSMulZeroClass"]],"valueReferences":[["DistribSMul","toLinearMap"]]},{"isProp":false,"kind":"definition","name":["Module","End","instRing"],"typeFallback":"forall {R : Type.{u_1}} {N₁ : Type.{u_8}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16 : AddCommGroup.{u_8} N₁] [inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 : Module.{u_1, u_8} R N₁ 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N₁)","typeReferences":[["Module","End"],["Module"],["AddCommGroup","toAddCommMonoid"],["AddCommGroup"],["Ring"],["Semiring"]],"valueReferences":[["AddCommGroup","toAddGroup"],["Module","End","instRing","_proof_6"],["Module","End","instRing","_proof_1"],["Module","End","instRing","_proof_7"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["SubNegMonoid","toSub"],["Module","End","instRing","_proof_2"],["instHSMul"],["Module","End","instOne"],["AddGroup","toSubNegMonoid"],["Ring","mk"],["Module","End"],["Module","End","instSemiring"],["SubNegMonoid","zsmul"],["SubNegMonoid","toNeg"],["Module","End","instRing","_proof_4"],["LinearMap"],["OfNat","ofNat"],["Int"],["One","toOfNat1"],["Module","End","instRing","_proof_3"],["HSMul","hSMul"],["AddCommGroup","toAddCommMonoid"],["Module","End","instRing","_proof_5"],["LinearMap","addCommGroup"],["SubNegMonoid","toZSMul"],["IntCast","mk"]]},{"isProp":true,"kind":"theorem","name":["Module","End","smulLeft","_proof_2"],"typeFallback":"forall {R : Type.{u_2}} {M : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.10 : Semiring.{u_2} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.13 : AddCommMonoid.{u_1} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.19 : Module.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.13] (α : R) (b₁ : M) (b₂ : M), Eq.{succ u_1} M (HSMul.hSMul.{u_2, u_1, u_1} R M M (instHSMul.{u_2, u_1} R M (SMulZeroClass.toSMul.{u_2, u_1} R M (AddZero.toZero.{u_1} M (AddZeroClass.toAddZero.{u_1} M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_2, u_1} R M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_2, u_1} R M (MonoidWithZero.toMonoid.{u_2} R (Semiring.toMonoidWithZero.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.13) (Module.toDistribMulAction.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.19))))) α (HAdd.hAdd.{u_1, u_1, u_1} M M M (instHAdd.{u_1} M (AddZero.toAdd.{u_1} M (AddZeroClass.toAddZero.{u_1} M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.13))))) b₁ b₂)) (HAdd.hAdd.{u_1, u_1, u_1} M M M (instHAdd.{u_1} M (AddZero.toAdd.{u_1} M (AddZeroClass.toAddZero.{u_1} M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.19))))) α b₁) (HSMul.hSMul.{u_2, u_1, u_1} R M M (instHSMul.{u_2, u_1} R M (SMulZeroClass.toSMul.{u_2, u_1} R M (AddZero.toZero.{u_1} M (AddZeroClass.toAddZero.{u_1} M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_2, u_1} R M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_2, u_1} R M (MonoidWithZero.toMonoid.{u_2} R (Semiring.toMonoidWithZero.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.13) (Module.toDistribMulAction.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.19))))) α b₂))","typeFull":"∀ {R : Type u_2} {M : Type u_1} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (α : R)\n  (b₁ b₂ : M), α • (b₁ + b₂) = α • b₁ + α • b₂","typeReadable":"∀ {R : Type u_2} {M : Type u_1} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (α : R)\n  (b₁ b₂ : M), α • (b₁ + b₂) = α • b₁ + α • b₂","typeReferences":[["instHAdd"],["Module"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddZero","toAdd"],["AddZeroClass","toAddZero"],["HAdd","hAdd"],["Module","toDistribMulAction"],["AddCommMonoid"],["MonoidWithZero","toMonoid"],["HSMul","hSMul"],["instHSMul"],["Eq"],["AddZero","toZero"],["Semiring"],["AddMonoid","toAddZeroClass"],["DistribSMul","toSMulZeroClass"]],"valueReferences":[["Module","toDistribMulAction"],["MonoidWithZero","toMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["smul_add"],["AddCommMonoid","toAddMonoid"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","applyₗ_apply_apply"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_4}} {M₂ : Type.{u_6}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 : CommSemiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 : AddCommMonoid.{u_4} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 : AddCommMonoid.{u_6} M₂] [inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 : Module.{u_1, u_4} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 : Module.{u_1, u_6} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16] (v : M) (f : LinearMap.{u_1, u_1, u_4, u_6} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) 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inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) => M₂) (LinearMap.instFunLike.{u_1, u_1, max u_4 u_6, u_6} R R (LinearMap.{u_1, u_1, u_4, u_6} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_1, u_1, u_4, u_6} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) 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M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) (DFunLike.coe.{max (succ u_4) (succ (max u_6 u_4)), succ u_4, succ (max u_6 u_4)} (LinearMap.{u_1, u_1, u_4, max u_6 u_4} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M (LinearMap.{u_1, u_1, max u_6 u_4, u_6} R R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_4, u_6} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_4, u_6} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (smulCommClass_self.{u_1, u_6} R M₂ (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_6} R M₂ (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16) (Module.toDistribMulAction.{u_1, u_6} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_1, u_1, max u_4 u_6, u_6} R R (LinearMap.{u_1, u_1, u_4, u_6} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_1, u_1, u_4, u_6} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_4, u_6} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (smulCommClass_self.{u_1, u_6} R M₂ (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_6} R M₂ (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16) (Module.toDistribMulAction.{u_1, u_6} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 (LinearMap.module.{u_1, u_1, u_1, max u_4 u_6, u_6} R R R (LinearMap.{u_1, u_1, u_4, u_6} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_1, u_1, u_4, u_6} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_4, u_6} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (smulCommClass_self.{u_1, u_6} R M₂ (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_6} R M₂ (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16) (Module.toDistribMulAction.{u_1, u_6} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (smulCommClass_self.{u_1, u_6} R M₂ (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_6} R M₂ (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16) (Module.toDistribMulAction.{u_1, u_6} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26))))) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => LinearMap.{u_1, u_1, max u_6 u_4, u_6} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_4, u_6} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_4, u_6} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_4, u_6} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (smulCommClass_self.{u_1, u_6} R M₂ (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_6} R M₂ (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16) (Module.toDistribMulAction.{u_1, u_6} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.instFunLike.{u_1, u_1, u_4, max u_6 u_4} R R M (LinearMap.{u_1, u_1, max u_6 u_4, u_6} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_4, u_6} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_4, u_6} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_4, u_6} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (smulCommClass_self.{u_1, u_6} R M₂ (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_6} R M₂ (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16) (Module.toDistribMulAction.{u_1, u_6} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_1, u_1, max u_4 u_6, u_6} R R (LinearMap.{u_1, u_1, u_4, u_6} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_1, u_1, u_4, u_6} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_4, u_6} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (smulCommClass_self.{u_1, u_6} R M₂ (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_6} R M₂ (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16) (Module.toDistribMulAction.{u_1, u_6} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 (LinearMap.module.{u_1, u_1, u_1, max u_4 u_6, u_6} R R R (LinearMap.{u_1, u_1, u_4, u_6} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_1, u_1, u_4, u_6} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_4, u_6} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (smulCommClass_self.{u_1, u_6} R M₂ (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_6} R M₂ (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16) (Module.toDistribMulAction.{u_1, u_6} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (smulCommClass_self.{u_1, u_6} R M₂ (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_6} R M₂ (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16) (Module.toDistribMulAction.{u_1, u_6} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) (LinearMap.applyₗ.{u_1, u_4, u_6} R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) v) f) (DFunLike.coe.{max (succ u_4) (succ u_6), succ u_4, succ u_6} (LinearMap.{u_1, u_1, u_4, u_6} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M₂) (LinearMap.instFunLike.{u_1, u_1, u_4, u_6} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) f v)","typeFull":"∀ {R : Type u_1} {M : Type u_4} {M₂ : Type u_6} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₂] [inst_3 : Module R M] [inst_4 : Module R M₂] (v : M) (f : M →ₗ[R] M₂),\n  (LinearMap.applyₗ v) f = f v","typeReadable":"∀ {R : Type u_1} {M : Type u_4} {M₂ : Type u_6} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₂] [inst_3 : Module R M] [inst_4 : Module R M₂] (v : M) (f : M →ₗ[R] M₂),\n  (LinearMap.applyₗ v) f = f v","typeReferences":[["LinearMap","applyₗ","_proof_1"],["smulCommClass_self"],["CommMonoid","toMonoid"],["LinearMap","instFunLike"],["Module"],["CommSemiring"],["CommSemiring","toSemiring"],["LinearMap","module"],["AddCommMonoid","toAddMonoid"],["LinearMap"],["DFunLike","coe"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["DistribMulAction","toMulAction"],["Eq"],["LinearMap","apply��"]],"valueReferences":[["LinearMap","applyₗ","_proof_1"],["smulCommClass_self"],["CommMonoid","toMonoid"],["LinearMap","instFunLike"],["CommSemiring","toSemiring"],["LinearMap","module"],["AddCommMonoid","toAddMonoid"],["LinearMap"],["DFunLike","coe"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Eq","refl"],["DistribMulAction","toMulAction"],["LinearMap","applyₗ"]]},{"isProp":true,"kind":"theorem","name":["Module","End","instRing","_proof_2"],"typeFallback":"forall {R : Type.{u_1}} {N₁ : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16 : AddCommGroup.{u_2} N₁] [inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 : Module.{u_1, u_2} R N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16)] (a : LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23), Eq.{succ u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (SubNegMonoid.zsmul.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddGroup.toSubNegMonoid.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddCommGroup.toAddGroup.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (LinearMap.addCommGroup.{u_1, u_1, u_2, u_2} R R N₁ N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10))))) (OfNat.ofNat.{0} Int 0 (instOfNat 0)) a) (OfNat.ofNat.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) 0 (Zero.toOfNat0.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddMonoid.toZero.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (SubNegMonoid.toAddMonoid.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddGroup.toSubNegMonoid.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddCommGroup.toAddGroup.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (LinearMap.addCommGroup.{u_1, u_1, u_2, u_2} R R N₁ N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)))))))))","typeFull":"∀ {R : Type u_1} {N₁ : Type u_2} [inst : Semiring R] [inst_1 : AddCommGroup N₁] [inst_2 : Module R N₁]\n  (a : N₁ →ₗ[R] N₁), SubNegMonoid.zsmul 0 a = 0","typeReadable":"∀ {R : Type u_1} {N₁ : Type u_2} [inst : Semiring R] [inst_1 : AddCommGroup N₁] [inst_2 : Module R N₁]\n  (a : N₁ →ₗ[R] N₁), SubNegMonoid.zsmul 0 a = 0","typeReferences":[["AddMonoid","toZero"],["Module"],["SubNegMonoid","zsmul"],["AddCommGroup","toAddGroup"],["AddCommGroup"],["LinearMap"],["OfNat","ofNat"],["Int"],["Semiring","toNonAssocSemiring"],["SubNegMonoid","toAddMonoid"],["instOfNat"],["RingHom","id"],["AddCommGroup","toAddCommMonoid"],["Zero","toOfNat0"],["AddGroup","toSubNegMonoid"],["Eq"],["LinearMap","addCommGroup"],["Semiring"]],"valueReferences":[["Semiring","toNonAssocSemiring"],["RingHom","id"],["AddCommGroup","toAddGroup"],["AddCommGroup","toAddCommMonoid"],["AddGroup","toSubNegMonoid"],["LinearMap","addCommGroup"],["LinearMap"],["SubNegMonoid","zsmul_zero'"]]},{"isProp":true,"kind":"theorem","name":["Module","End","instRing","_proof_1"],"typeFallback":"forall {R : Type.{u_1}} {N₁ : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16 : AddCommGroup.{u_2} N₁] [inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 : Module.{u_1, u_2} R N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16)] (a : LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (b : LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23), Eq.{succ u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (HSub.hSub.{u_2, u_2, u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (instHSub.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (SubNegMonoid.toSub.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddGroup.toSubNegMonoid.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddCommGroup.toAddGroup.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (LinearMap.addCommGroup.{u_1, u_1, u_2, u_2} R R N₁ N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10))))))) a b) (HAdd.hAdd.{u_2, u_2, u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (instHAdd.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddSemigroup.toAdd.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddMonoid.toAddSemigroup.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (SubNegMonoid.toAddMonoid.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ 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inst._@.Mathlib.Algebra.Module.LinearMap.End.2552065102._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2552065102._hygCtx._hyg.19)))) (id.{succ u_4} M)","typeFull":"∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M], ⇑1 = id","typeReadable":"∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M], ⇑1 = id","typeReferences":[["Module","End"],["LinearMap","instFunLike"],["Module"],["DFunLike","coe"],["OfNat","ofNat"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["One","toOfNat1"],["RingHom","id"],["id"],["Module","End","instOne"],["Eq"],["Semiring"]],"valueReferences":[["rfl"],["Module","End"],["Semiring","toNonAssocSemiring"],["One","toOfNat1"],["LinearMap","instFunLike"],["RingHom","id"],["Module","End","instOne"],["DFunLike","coe"],["OfNat","ofNat"]]},{"isProp":true,"kind":"theorem","name":["RingEquiv","moduleEndSelfOp","_proof_2"],"typeFallback":"forall (R : Type.{u_1}) 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{R : Type.{u_1}} {M : Type.{u_4}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.13 : AddCommMonoid.{u_4} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.19 : Module.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.13] (α : R) (hα : Membership.mem.{u_1, u_1} R (Set.{u_1} R) (Set.instMembership.{u_1} R) (Set.center.{u_1} R (Distrib.toMul.{u_1} R (NonUnitalNonAssocSemiring.toDistrib.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.10))))) α) (x : M), Eq.{succ u_4} M (DFunLike.coe.{succ u_4, succ u_4, succ u_4} (LinearMap.{u_1, u_1, u_4, u_4} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.19) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (LinearMap.instFunLike.{u_1, u_1, u_4, u_4} R R M M inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.10))) (Module.End.smulLeft.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.19 α hα) x) (HSMul.hSMul.{u_1, u_4, u_4} R M M (instHSMul.{u_1, u_4} R M (SMulZeroClass.toSMul.{u_1, u_4} R M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_1, u_4} R M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_1, u_4} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1981914469._hygCtx._hyg.19))))) α x)","typeFull":"∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (α : R)\n  (hα : α ∈ Set.center R) (x : M), (Module.End.smulLeft α hα) x = α • x","typeReadable":"∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (α : R)\n  (hα : α ∈ Set.center R) (x : M), (Module.End.smulLeft α hα) x = α • x","typeReferences":[["LinearMap","instFunLike"],["Module"],["Membership","mem"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["instHSMul"],["Eq"],["DistribSMul","toSMulZeroClass"],["NonUnitalNonAssocSemiring","toDistrib"],["Set"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["Distrib","toMul"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["LinearMap"],["AddZeroClass","toAddZero"],["Set","instMembership"],["Module","toDistribMulAction"],["HSMul","hSMul"],["Module","End","smulLeft"],["AddZero","toZero"],["Set","center"],["Semiring"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["Semiring","toNonAssocSemiring"],["LinearMap","instFunLike"],["RingHom","id"],["Eq","refl"],["LinearMap"],["Module","End","smulLeft"],["DFunLike","coe"]]},{"isProp":true,"kind":"theorem","name":["Module","End","instRing","_proof_5"],"typeFallback":"forall {R : Type.{u_1}} {N₁ : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16 : AddCommGroup.{u_2} N₁] [inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 : Module.{u_1, u_2} R N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16)] (a : LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23), Eq.{succ u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (HAdd.hAdd.{u_2, u_2, u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (instHAdd.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddSemigroup.toAdd.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddMonoid.toAddSemigroup.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (SubNegMonoid.toAddMonoid.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddGroup.toSubNegMonoid.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddCommGroup.toAddGroup.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (LinearMap.addCommGroup.{u_1, u_1, u_2, u_2} R R N₁ N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10))))))))) (Neg.neg.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (SubNegMonoid.toNeg.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddGroup.toSubNegMonoid.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddCommGroup.toAddGroup.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (LinearMap.addCommGroup.{u_1, u_1, u_2, u_2} R R N₁ N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)))))) a) a) (OfNat.ofNat.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) 0 (Zero.toOfNat0.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddMonoid.toZero.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (SubNegMonoid.toAddMonoid.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddGroup.toSubNegMonoid.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddCommGroup.toAddGroup.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (LinearMap.addCommGroup.{u_1, u_1, u_2, u_2} R R N₁ N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)))))))))","typeFull":"∀ {R : Type u_1} {N₁ : Type u_2} [inst : Semiring R] [inst_1 : AddCommGroup N₁] [inst_2 : Module R N₁]\n  (a : N₁ →ₗ[R] N₁), -a + a = 0","typeReadable":"∀ {R : Type u_1} {N₁ : Type u_2} [inst : Semiring R] [inst_1 : AddCommGroup N₁] [inst_2 : Module R N₁]\n  (a : N₁ →ₗ[R] N₁), -a + a = 0","typeReferences":[["AddMonoid","toZero"],["Neg","neg"],["Module"],["instHAdd"],["AddCommGroup","toAddGroup"],["SubNegMonoid","toNeg"],["AddCommGroup"],["LinearMap"],["OfNat","ofNat"],["HAdd","hAdd"],["Semiring","toNonAssocSemiring"],["SubNegMonoid","toAddMonoid"],["RingHom","id"],["AddMonoid","toAddSemigroup"],["AddCommGroup","toAddCommMonoid"],["Zero","toOfNat0"],["AddGroup","toSubNegMonoid"],["LinearMap","addCommGroup"],["Eq"],["Semiring"],["AddSemigroup","toAdd"]],"valueReferences":[["Semiring","toNonAssocSemiring"],["RingHom","id"],["AddCommGroup","toAddGroup"],["AddCommGroup","toAddCommMonoid"],["LinearMap","addCommGroup"],["LinearMap"],["AddGroup","neg_add_cancel"]]},{"isProp":true,"kind":"theorem","name":["Module","End","instIsScalarTower"],"typeFallback":"forall {R : Type.{u_1}} {S : Type.{u_3}} {M : Type.{u_4}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13 : AddCommMonoid.{u_4} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.19 : Module.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.27 : Monoid.{u_3} S] [inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.30 : DistribMulAction.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.27 (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13)] [inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.34 : SMulCommClass.{u_1, u_3, u_4} R S M (SMulZeroClass.toSMul.{u_1, u_4} R M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_1, u_4} R M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_1, u_4} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.19)))) (SMulZeroClass.toSMul.{u_3, u_4} S M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_3, u_4} S M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.27 (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.30)))], IsScalarTower.{u_3, u_4, u_4} S (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.19) (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.19) (LinearMap.instSMul.{u_1, u_1, u_3, u_4, u_4} R R S M M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10)) (DistribMulAction.toDistribSMul.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.27 (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.30) inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.34) (SMulZeroClass.toSMul.{u_4, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.19) (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.19) (AddZero.toZero.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.19) (AddZeroClass.toAddZero.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.19) (AddMonoid.toAddZeroClass.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.19) (AddMonoidWithOne.toAddMonoid.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.19) (AddCommMonoidWithOne.toAddMonoidWithOne.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.19) (NonAssocSemiring.toAddCommMonoidWithOne.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.19) (Semiring.toNonAssocSemiring.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.19) (Module.End.instSemiring.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.19)))))))) (DistribSMul.toSMulZeroClass.{u_4, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.19) (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.19) (AddMonoid.toAddZeroClass.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.19) (AddMonoidWithOne.toAddMonoid.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.19) (AddCommMonoidWithOne.toAddMonoidWithOne.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.19) (NonAssocSemiring.toAddCommMonoidWithOne.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.19) (Semiring.toNonAssocSemiring.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.19) (Module.End.instSemiring.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.19)))))) (instDistribSMul.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.19) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.19) (Semiring.toNonAssocSemiring.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.19) (Module.End.instSemiring.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.19)))))) (LinearMap.instSMul.{u_1, u_1, u_3, u_4, u_4} R R S M M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.10)) (DistribMulAction.toDistribSMul.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.27 (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.30) inst._@.Mathlib.Algebra.Module.LinearMap.End.772748180._hygCtx._hyg.34)","typeFull":"∀ {R : Type u_1} {S : Type u_3} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  [inst_3 : Monoid S] [inst_4 : DistribMulAction S M] [inst_5 : SMulCommClass R S M],\n  IsScalarTower S (Module.End R M) (Module.End R M)","typeReadable":"∀ {R : Type u_1} {S : Type u_3} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  [inst_3 : Monoid S] [inst_4 : DistribMulAction S M] [inst_5 : SMulCommClass R S M],\n  IsScalarTower S (Module.End R M) (Module.End R M)","typeReferences":[["Module"],["IsScalarTower"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["instDistribSMul"],["AddMonoidWithOne","toAddMonoid"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["NonAssocSemiring","toAddCommMonoidWithOne"],["DistribMulAction"],["DistribSMul","toSMulZeroClass"],["Module","End"],["Module","End","instSemiring"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["SMulCommClass"],["Module","toDistribMulAction"],["Monoid"],["LinearMap","instSMul"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["Module","End"],["Module","End","instSemiring"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["DistribMulAction","toDistribSMul"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["instDistribSMul"],["AddZeroClass","toAddZero"],["AddMonoidWithOne","toAddMonoid"],["IsScalarTower","mk"],["LinearMap","smul_comp"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Module","End","instMul","_proof_1"],["LinearMap","instSMul"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["NonAssocSemiring","toAddCommMonoidWithOne"],["AddZero","toZero"],["DistribSMul","toSMulZeroClass"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","smulRight_apply_eq_zero_iff","_simp_1"],"typeFallback":"forall {R : Type.{u_1}} {S : Type.{u_3}} {M : Type.{u_4}} {M₁ : Type.{u_5}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.13 : AddCommMonoid.{u_4} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.16 : AddCommMonoid.{u_5} M₁] [inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.19 : Module.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.23 : Module.{u_1, u_5} R M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.27 : Semiring.{u_3} S] [inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.30 : Module.{u_1, u_3} R S inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.10 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.27)))] [inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.34 : Module.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.38 : IsScalarTower.{u_1, u_3, u_4} R S M (SMulZeroClass.toSMul.{u_1, u_3} R S (AddZero.toZero.{u_3} S (AddZeroClass.toAddZero.{u_3} S (AddMonoid.toAddZeroClass.{u_3} S (AddMonoidWithOne.toAddMonoid.{u_3} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_3} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.27))) inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.30)))) (SMulZeroClass.toSMul.{u_3, u_4} S M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_3, u_4} S M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_3, u_4} S M (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.27)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.34)))) (SMulZeroClass.toSMul.{u_1, u_4} R M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_1, u_4} R M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_1, u_4} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.19))))] [inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.43 : IsDomain.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.27] {f : LinearMap.{u_1, u_1, u_5, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.10)) M₁ S inst._@.Mathlib.Algebra.Module.LinearMap.End.987621749._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} S 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 [inst_7 : Module S M] [inst_8 : IsScalarTower R S M] [IsDomain S] {f : M₁ →ₗ[R] S} {x : M} [Module.IsTorsionFree S M],\n  (f.smulRight x = 0) = (f = 0 ∨ x = 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R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1804534584._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1804534584._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1804534584._hygCtx._hyg.19) (HMul.hMul.{u_4, u_4, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1804534584._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1804534584._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1804534584._hygCtx._hyg.19) (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1804534584._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1804534584._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1804534584._hygCtx._hyg.19) (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1804534584._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1804534584._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1804534584._hygCtx._hyg.19) (instHMul.{u_4} 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1804534584._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.1804534584._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.1804534584._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1804534584._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1804534584._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1804534584._hygCtx._hyg.10)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.1804534584._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1804534584._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1804534584._hygCtx._hyg.10))) f g)","typeFull":"∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  (f g : Module.End R M), f * g = f ∘ₗ g","typeReadable":"∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  (f g : Module.End R M), f * g = f ∘ₗ g","typeReferences":[["Module","End"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHomCompTriple","ids"],["RingHom","id"],["Module"],["LinearMap","comp"],["instHMul"],["HMul","hMul"],["Eq"],["Module","End","instMul"],["Semiring"]],"valueReferences":[["rfl"],["Module","End"],["instHMul"],["HMul","hMul"],["Module","End","instMul"]]},{"isProp":true,"kind":"theorem","name":["Module","toModuleEnd","_proof_1"],"typeFallback":"forall (R : Type.{u_2}) {S : Type.{u_3}} (M : Type.{u_1}) [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 : Semiring.{u_2} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 : AddCommMonoid.{u_1} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16 : Module.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20 : Semiring.{u_3} S] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.23 : Module.{u_3, u_1} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.27 : SMulCommClass.{u_3, u_2, u_1} S R M (SMulZeroClass.toSMul.{u_3, u_1} S M (AddZero.toZero.{u_1} M (AddZeroClass.toAddZero.{u_1} M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_3, u_1} S M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M 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inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16)))))) (MonoidHom.toOneHom.{u_3, u_1} S (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (MulOneClass.toMulOne.{u_3} S (Monoid.toMulOneClass.{u_3} S (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20)))) (MulOneClass.toMulOne.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (MulZeroOneClass.toMulOneClass.{u_1} (Module.End.{u_2, u_1} R M 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inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16))))) (DistribMulAction.toModuleEnd.{u_2, u_3, u_1} R S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16 (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20)) (Module.toDistribMulAction.{u_3, u_1} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.23) inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.27)) (OfNat.ofNat.{u_3} S 1 (One.toOfNat1.{u_3} S (MulOne.toOne.{u_3} S (MulOneClass.toMulOne.{u_3} S (Monoid.toMulOneClass.{u_3} S (MonoidWithZero.toMonoid.{u_3} S 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inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) (x._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.59 : M), Eq.{succ u_2} M (HSMul.hSMul.{u_2, u_2, u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) M M (instHSMul.{u_2, u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) M (SMul.mk.{u_2, u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 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inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) (instHMul.{u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) (Semigroup.toMul.{u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) (Monoid.toSemigroup.{u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) (MonoidWithZero.toMonoid.{u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) (Semiring.toMonoidWithZero.{u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) (Module.End.instSemiring.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19)))))) x._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.55 x._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.57) x._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.59) (HSMul.hSMul.{u_2, u_2, u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) M M (instHSMul.{u_2, u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) M (SMul.mk.{u_2, u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) M (fun (x1._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.43 : Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) (x2._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.43 : M) => DFunLike.coe.{succ u_2, succ u_2, succ u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (LinearMap.instFunLike.{u_1, u_1, u_2, u_2} R R M M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10))) x1._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.43 x2._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.43))) (HMul.hMul.{u_2, u_2, u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) (instHMul.{u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) (Semigroup.toMul.{u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 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m'","typeReferences":[["LinearMap","smulRight"],["IsScalarTower","left"],["instHAdd"],["Module"],["CommSemiring"],["CommSemiring","toSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["Semiring","toMonoidWithZero"],["AddCommMonoid","toAddMonoid"],["LinearMap"],["LinearMap","addCommMonoid"],["HAdd","hAdd"],["Module","toDistribMulAction"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["AddCommMonoid","toAddCommSemigroup"],["RingHom","id"],["MonoidWithZero","toMonoid"],["DistribMulAction","toMulAction"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Semiring","toModule"],["Eq"]],"valueReferences":[["LinearMap","instFunLike"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["LinearMap","ext"],["MonoidWithZero","toMonoid"],["DistribMulAction","toMulAction"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Semiring","toModule"],["LinearMap","smulRight"],["IsScalarTower","left"],["instHAdd"],["CommSemiring","toSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["LinearMap"],["HAdd","hAdd"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["AddCommMonoid","toAddCommSemigroup"],["smul_add"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["RingEquiv","moduleEndSelfOp","_proof_6"],"typeFallback":"forall 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(Semiring.toNonAssocSemiring.{u_1} (Module.End.{u_1, u_1} (MulOpposite.{u_1} R) R (MulOpposite.instSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10))) (Semiring.toOppositeModule.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10)) (Module.End.instSemiring.{u_1, u_1} (MulOpposite.{u_1} R) R (MulOpposite.instSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10))) (Semiring.toOppositeModule.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10)))))))))) (OneHom.toFun.{u_1, u_1} R (Module.End.{u_1, u_1} (MulOpposite.{u_1} R) R (MulOpposite.instSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10))) (Semiring.toOppositeModule.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10)) (MulOne.toOne.{u_1} R (MulOneClass.toMulOne.{u_1} R (MulZeroOneClass.toMulOneClass.{u_1} R (NonAssocSemiring.toMulZeroOneClass.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10))))) (MulOne.toOne.{u_1} (Module.End.{u_1, u_1} (MulOpposite.{u_1} R) R (MulOpposite.instSemiring.{u_1} R 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(Module.End.{u_1, u_1} (MulOpposite.{u_1} R) R (MulOpposite.instSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10))) (Semiring.toOppositeModule.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10)) (Module.End.instSemiring.{u_1, u_1} (MulOpposite.{u_1} R) R (MulOpposite.instSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10))) (Semiring.toOppositeModule.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10))))))) (MonoidHom.toOneHom.{u_1, u_1} R (Module.End.{u_1, u_1} (MulOpposite.{u_1} R) R (MulOpposite.instSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10))) (Semiring.toOppositeModule.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10)) (MulOneClass.toMulOne.{u_1} R (MulZeroOneClass.toMulOneClass.{u_1} R (NonAssocSemiring.toMulZeroOneClass.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10)))) (MulOneClass.toMulOne.{u_1} (Module.End.{u_1, u_1} (MulOpposite.{u_1} R) R (MulOpposite.instSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10))) (Semiring.toOppositeModule.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10)) (MulZeroOneClass.toMulOneClass.{u_1} (Module.End.{u_1, u_1} (MulOpposite.{u_1} R) R (MulOpposite.instSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10))) (Semiring.toOppositeModule.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10)) (NonAssocSemiring.toMulZeroOneClass.{u_1} (Module.End.{u_1, u_1} (MulOpposite.{u_1} R) R (MulOpposite.instSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10))) (Semiring.toOppositeModule.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10)) (Semiring.toNonAssocSemiring.{u_1} (Module.End.{u_1, u_1} (MulOpposite.{u_1} R) R (MulOpposite.instSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10))) (Semiring.toOppositeModule.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10)) (Module.End.instSemiring.{u_1, u_1} (MulOpposite.{u_1} R) R (MulOpposite.instSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10) (Semiring.toNonAssocSemiring.{u_1} (Module.End.{u_1, u_1} (MulOpposite.{u_1} R) R (MulOpposite.instSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10))) (Semiring.toOppositeModule.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10)) (Module.End.instSemiring.{u_1, u_1} (MulOpposite.{u_1} R) R (MulOpposite.instSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10))) (Semiring.toOppositeModule.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10))) (Module.toModuleEnd.{u_1, u_1, u_1} (MulOpposite.{u_1} R) R R (MulOpposite.instSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10))) (Semiring.toOppositeModule.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10 (Semiring.toModule.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10) (RingEquiv.moduleEndSelfOp._proof_1.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10)))) x) (OneHom.toFun.{u_1, u_1} R (Module.End.{u_1, u_1} (MulOpposite.{u_1} R) R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10))) (Semiring.toOppositeModule.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10)) (Module.End.instSemiring.{u_1, u_1} (MulOpposite.{u_1} R) R (MulOpposite.instSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10))) (Semiring.toOppositeModule.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10))))))) (MonoidHom.toOneHom.{u_1, u_1} R (Module.End.{u_1, u_1} (MulOpposite.{u_1} R) R (MulOpposite.instSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10))) (Semiring.toOppositeModule.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10)) (MulOneClass.toMulOne.{u_1} R (MulZeroOneClass.toMulOneClass.{u_1} R (NonAssocSemiring.toMulZeroOneClass.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10)))) (MulOneClass.toMulOne.{u_1} (Module.End.{u_1, u_1} (MulOpposite.{u_1} R) R (MulOpposite.instSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10))) (Semiring.toOppositeModule.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10)) (MulZeroOneClass.toMulOneClass.{u_1} (Module.End.{u_1, u_1} (MulOpposite.{u_1} R) R (MulOpposite.instSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10))) (Semiring.toOppositeModule.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10)) (NonAssocSemiring.toMulZeroOneClass.{u_1} (Module.End.{u_1, u_1} (MulOpposite.{u_1} R) R (MulOpposite.instSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10))) (Semiring.toOppositeModule.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10)) (Semiring.toNonAssocSemiring.{u_1} (Module.End.{u_1, u_1} (MulOpposite.{u_1} R) R (MulOpposite.instSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10))) (Semiring.toOppositeModule.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10)) (Module.End.instSemiring.{u_1, u_1} (MulOpposite.{u_1} R) R (MulOpposite.instSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10))) (Semiring.toOppositeModule.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10)))))) (RingHom.toMonoidHom.{u_1, u_1} R (Module.End.{u_1, u_1} (MulOpposite.{u_1} R) R (MulOpposite.instSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10))) (Semiring.toOppositeModule.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10)) (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10) (Semiring.toNonAssocSemiring.{u_1} (Module.End.{u_1, u_1} (MulOpposite.{u_1} R) R (MulOpposite.instSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10))) (Semiring.toOppositeModule.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10)) (Module.End.instSemiring.{u_1, u_1} (MulOpposite.{u_1} R) R (MulOpposite.instSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10))) (Semiring.toOppositeModule.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10))) (Module.toModuleEnd.{u_1, u_1, u_1} (MulOpposite.{u_1} R) R R (MulOpposite.instSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10))) (Semiring.toOppositeModule.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10 (Semiring.toModule.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10) (RingEquiv.moduleEndSelfOp._proof_1.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10)))) y))","typeFull":"∀ (R : Type u_1) [inst : Semiring R] (x y : R),\n  (↑↑(Module.toModuleEnd Rᵐᵒᵖ R)).toFun (x + y) =\n    (↑↑(Module.toModuleEnd Rᵐᵒᵖ R)).toFun x + (↑↑(Module.toModuleEnd Rᵐᵒᵖ R)).toFun y","typeReadable":"∀ (R : Type u_1) [inst : Semiring R] (x y : R),\n  (↑↑(Module.toModuleEnd Rᵐᵒᵖ R)).toFun (x + y) =\n    (↑↑(Module.toModuleEnd Rᵐᵒᵖ R)).toFun x + (↑↑(Module.toModuleEnd Rᵐᵒᵖ R)).toFun y","typeReferences":[["MulOneClass","toMulOne"],["RingEquiv","moduleEndSelfOp","_proof_1"],["MulZeroOneClass","toMulOneClass"],["AddMonoidWithOne","toAddMonoid"],["OneHom","toFun"],["RingHom","toMonoidHom"],["MulOpposite"],["Semiring","toNonAssocSemiring"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Eq"],["Semiring","toModule"],["NonAssocSemiring","toAddCommMonoidWithOne"],["MulOpposite","instSemiring"],["NonAssocSemiring","toMulZeroOneClass"],["Module","toModuleEnd"],["Module","End"],["Module","End","instSemiring"],["MulOne","toOne"],["instHAdd"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["AddZero","toAdd"],["AddZeroClass","toAddZero"],["HAdd","hAdd"],["Semiring","toOppositeModule"],["MonoidHom","toOneHom"],["Semiring"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["Module","toModuleEnd"],["MulOpposite"],["Module","End"],["RingEquiv","moduleEndSelfOp","_proof_1"],["Module","End","instSemiring"],["Semiring","toNonAssocSemiring"],["Semiring","toOppositeModule"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["RingHom","map_add'"],["Semiring","toModule"],["MulOpposite","instSemiring"]]},{"isProp":false,"kind":"definition","name":["LinearMap","compRight"],"typeFallback":"forall {R : Type.{u_1}} (S : Type.{u_3}) {M : Type.{u_4}} {M₁ : Type.{u_5}} {M₂ : Type.{u_6}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13 : Semiring.{u_3} S] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 : AddCommMonoid.{u_4} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 : AddCommMonoid.{u_5} M₁] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 : AddCommMonoid.{u_6} M₂] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 : Module.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29 : Module.{u_1, u_5} R M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.33 : Module.{u_1, u_6} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.37 : Module.{u_3, u_5} S M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.41 : Module.{u_3, u_6} S M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.45 : SMulCommClass.{u_1, u_3, u_5} R S M₁ (SMulZeroClass.toSMul.{u_1, u_5} R M₁ (AddZero.toZero.{u_5} M₁ (AddZeroClass.toAddZero.{u_5} M₁ (AddMonoid.toAddZeroClass.{u_5} M₁ (AddCommMonoid.toAddMonoid.{u_5} M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19)))) (DistribSMul.toSMulZeroClass.{u_1, u_5} R M₁ (AddMonoid.toAddZeroClass.{u_5} M₁ (AddCommMonoid.toAddMonoid.{u_5} M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19)) (DistribMulAction.toDistribSMul.{u_1, u_5} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_5} M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19) (Module.toDistribMulAction.{u_1, u_5} R M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29)))) (SMulZeroClass.toSMul.{u_3, u_5} S M₁ (AddZero.toZero.{u_5} M₁ (AddZeroClass.toAddZero.{u_5} M₁ (AddMonoid.toAddZeroClass.{u_5} M₁ (AddCommMonoid.toAddMonoid.{u_5} M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19)))) (DistribSMul.toSMulZeroClass.{u_3, u_5} S M₁ (AddMonoid.toAddZeroClass.{u_5} M₁ (AddCommMonoid.toAddMonoid.{u_5} M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19)) (DistribMulAction.toDistribSMul.{u_3, u_5} S M₁ (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13)) (AddCommMonoid.toAddMonoid.{u_5} M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19) (Module.toDistribMulAction.{u_3, u_5} S M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.37))))] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.50 : SMulCommClass.{u_1, u_3, u_6} R S M₂ (SMulZeroClass.toSMul.{u_1, u_6} R M₂ (AddZero.toZero.{u_6} M₂ (AddZeroClass.toAddZero.{u_6} M₂ (AddMonoid.toAddZeroClass.{u_6} M₂ (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22)))) (DistribSMul.toSMulZeroClass.{u_1, u_6} R M₂ (AddMonoid.toAddZeroClass.{u_6} M₂ (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22)) (DistribMulAction.toDistribSMul.{u_1, u_6} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22) (Module.toDistribMulAction.{u_1, u_6} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.33)))) (SMulZeroClass.toSMul.{u_3, u_6} S M₂ (AddZero.toZero.{u_6} M₂ (AddZeroClass.toAddZero.{u_6} M₂ (AddMonoid.toAddZeroClass.{u_6} M₂ (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22)))) (DistribSMul.toSMulZeroClass.{u_3, u_6} S M₂ (AddMonoid.toAddZeroClass.{u_6} M₂ (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22)) (DistribMulAction.toDistribSMul.{u_3, u_6} S M₂ (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13)) (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22) (Module.toDistribMulAction.{u_3, u_6} S M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.41))))] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.55 : LinearMap.CompatibleSMul.{u_5, u_6, u_3, u_1} M₁ M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 S R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (SMulZeroClass.toSMul.{u_3, u_5} S M₁ (AddZero.toZero.{u_5} M₁ (AddZeroClass.toAddZero.{u_5} M₁ (AddMonoid.toAddZeroClass.{u_5} M₁ (AddCommMonoid.toAddMonoid.{u_5} M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19)))) (DistribSMul.toSMulZeroClass.{u_3, u_5} S M₁ (AddMonoid.toAddZeroClass.{u_5} M₁ (AddCommMonoid.toAddMonoid.{u_5} M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19)) (DistribMulAction.toDistribSMul.{u_3, u_5} S M₁ (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13)) (AddCommMonoid.toAddMonoid.{u_5} M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19) (Module.toDistribMulAction.{u_3, u_5} S M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.37)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29 (SMulZeroClass.toSMul.{u_3, u_6} S M₂ (AddZero.toZero.{u_6} M₂ (AddZeroClass.toAddZero.{u_6} M₂ (AddMonoid.toAddZeroClass.{u_6} M₂ (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22)))) (DistribSMul.toSMulZeroClass.{u_3, u_6} S M₂ (AddMonoid.toAddZeroClass.{u_6} M₂ (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22)) (DistribMulAction.toDistribSMul.{u_3, u_6} S M₂ (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13)) (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22) (Module.toDistribMulAction.{u_3, u_6} S M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.41)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.33], (LinearMap.{u_1, u_1, u_5, u_6} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M₁ M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.33) -> (LinearMap.{u_3, u_3, max u_5 u_4, max u_6 u_4} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13)) (LinearMap.{u_1, u_1, u_4, u_5} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29) (LinearMap.{u_1, u_1, u_4, u_6} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.33) (LinearMap.addCommMonoid.{u_1, u_1, u_4, u_5} R R M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10))) (LinearMap.addCommMonoid.{u_1, u_1, u_4, u_6} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10))) (LinearMap.module.{u_1, u_1, u_3, u_4, u_5} R R S M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.37 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.45) (LinearMap.module.{u_1, u_1, u_3, u_4, u_6} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.50))","typeFull":"{R : Type u_1} →\n  (S : Type u_3) →\n    {M : Type u_4} →\n      {M₁ : Type u_5} →\n        {M₂ : Type u_6} →\n          [inst : Semiring R] →\n            [inst_1 : Semiring S] →\n              [inst_2 : AddCommMonoid M] →\n                [inst_3 : AddCommMonoid M₁] →\n                  [inst_4 : AddCommMonoid M₂] →\n                    [inst_5 : Module R M] →\n                      [inst_6 : Module R M₁] →\n                        [inst_7 : Module R M₂] →\n                          [inst_8 : Module S M₁] →\n                            [inst_9 : Module S M₂] →\n                              [inst_10 : SMulCommClass R S M₁] →\n                                [inst_11 : SMulCommClass R S M₂] →\n                                  [LinearMap.CompatibleSMul M₁ M₂ S R] → (M₁ →ₗ[R] M₂) → (M →ₗ[R] M₁) →ₗ[S] M →ₗ[R] M₂","typeReadable":"{R : Type u_1} →\n  (S : Type u_3) →\n    {M : Type u_4} →\n      {M₁ : Type u_5} →\n        {M₂ : Type u_6} →\n          [inst : Semiring R] →\n            [inst_1 : Semiring S] →\n              [inst_2 : AddCommMonoid M] →\n                [inst_3 : AddCommMonoid M₁] →\n                  [inst_4 : AddCommMonoid M₂] →\n                    [inst_5 : Module R M] →\n                      [inst_6 : Module R M₁] →\n                        [inst_7 : Module R M₂] →\n                          [inst_8 : Module S M₁] →\n                            [inst_9 : Module S M₂] →\n                              [inst_10 : SMulCommClass R S M₁] →\n                                [inst_11 : SMulCommClass R S M₂] →\n                                  [LinearMap.CompatibleSMul M₁ M₂ S R] → (M₁ →ₗ[R] M₂) → (M →ₗ[R] M₁) →ₗ[S] M →ₗ[R] M₂","typeReferences":[["LinearMap","CompatibleSMul"],["Module"],["LinearMap","module"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["LinearMap"],["AddZeroClass","toAddZero"],["LinearMap","addCommMonoid"],["SMulCommClass"],["Module","toDistribMulAction"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["AddZero","toZero"],["Semiring"],["AddMonoid","toAddZeroClass"],["DistribSMul","toSMulZeroClass"]],"valueReferences":[["LinearMap","compRight","_proof_1"],["LinearMap","mk"],["LinearMap","module"],["AddHom","mk"],["LinearMap","comp"],["LinearMap","compRight","_proof_2"],["LinearMap"],["LinearMap","addCommMonoid"],["Semiring","toNonAssocSemiring"],["AddCommMonoid","toAddCommSemigroup"],["RingHom","id"],["Module","End","instMul","_proof_1"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","applyₗ","_proof_5"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_2}} {M₂ : Type.{u_3}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 : CommSemiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 : AddCommMonoid.{u_3} M₂] [inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 : Module.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 : Module.{u_1, u_3} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16] (x._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.109 : R) (x._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.111 : M) (x : LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (y : LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26), Eq.{succ u_3} M₂ (AddHom.toFun.{max u_3 u_2, u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (AddCommMagma.toAdd.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommSemigroup.toAddCommMagma.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddCommSemigroup.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))))))) (AddCommMagma.toAdd.{u_3} M₂ (AddCommSemigroup.toAddCommMagma.{u_3} M₂ (AddCommMonoid.toAddCommSemigroup.{u_3} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16))) (LinearMap.toAddHom.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) 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inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13))) (AddZeroClass.toAddZero.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_1, u_1, max u_2 u_3, u_3} R R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))))))) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoidHom.instFunLike.{u_2, max u_3 u_2} M (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13))) (AddZeroClass.toAddZero.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoid.toAddZeroClass.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_1, u_1, max u_2 u_3, u_3} R R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))))))) (LinearMap.applyₗ'.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) (HSMul.hSMul.{u_1, u_2, u_2} R M M (instHSMul.{u_1, u_2} R M (SMulZeroClass.toSMul.{u_1, u_2} R M (AddZero.toZero.{u_2} M (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_1, u_2} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22))))) x._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.109 x._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.111))) (HAdd.hAdd.{max u_3 u_2, max u_3 u_2, max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (instHAdd.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMagma.toAdd.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommSemigroup.toAddCommMagma.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddCommSemigroup.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoid.toAddZeroClass.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_1, u_1, max u_2 u_3, u_3} R R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))))))) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoidHom.instFunLike.{u_2, max u_3 u_2} M (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13))) (AddZeroClass.toAddZero.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoid.toAddZeroClass.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_1, u_1, max u_2 u_3, u_3} R R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R 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(AddZeroClass.toAddZero.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoid.toAddZeroClass.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_1, u_1, max u_2 u_3, u_3} R R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))))))) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoidHom.instFunLike.{u_2, max u_3 u_2} M (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13))) (AddZeroClass.toAddZero.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoid.toAddZeroClass.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_1, u_1, max u_2 u_3, u_3} R R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))))))) (LinearMap.applyₗ'.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) (HSMul.hSMul.{u_1, u_2, u_2} R M M (instHSMul.{u_1, u_2} R M (SMulZeroClass.toSMul.{u_1, u_2} R M (AddZero.toZero.{u_2} M (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M 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(One.toOfNat1.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3515149178._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3515149178._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3515149178._hygCtx._hyg.19) (Module.End.instOne.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3515149178._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3515149178._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3515149178._hygCtx._hyg.19))) (LinearMap.id.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3515149178._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3515149178._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3515149178._hygCtx._hyg.19)","typeFull":"∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M], 1 = LinearMap.id","typeReadable":"∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 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inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddZero.toZero.{u_2} M (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13)))) (AddZero.toZero.{max u_1 u_2} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddZeroClass.toAddZero.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoid.toAddZeroClass.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddMonoid.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_3, u_3, max u_2 u_1, u_1} R R (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))))))) (AddMonoidHom.toZeroHom.{u_2, max u_1 u_2} M (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13))) (AddZeroClass.toAddZero.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoid.toAddZeroClass.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddMonoid.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_3, u_3, max u_2 u_1, u_1} R R (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))))))) (LinearMap.applyₗ'.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26))) (HAdd.hAdd.{u_2, u_2, u_2} M M M (instHAdd.{u_2} M (AddZero.toAdd.{u_2} M (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13))))) x y)) (HAdd.hAdd.{max u_1 u_2, max u_1 u_2, max u_1 u_2} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (instHAdd.{max u_1 u_2} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddZero.toAdd.{max u_1 u_2} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddZeroClass.toAddZero.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoid.toAddZeroClass.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddMonoid.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_3, u_3, max u_2 u_1, u_1} R R (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))))))))) (ZeroHom.toFun.{u_2, max u_1 u_2} M (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddZero.toZero.{u_2} M (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13)))) (AddZero.toZero.{max u_1 u_2} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddZeroClass.toAddZero.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoid.toAddZeroClass.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddMonoid.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_3, u_3, max u_2 u_1, u_1} R R (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))))))) (AddMonoidHom.toZeroHom.{u_2, max u_1 u_2} M (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13))) (AddZeroClass.toAddZero.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoid.toAddZeroClass.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddMonoid.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_3, u_3, max u_2 u_1, u_1} R R (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))))))) (LinearMap.applyₗ'.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26))) x) (ZeroHom.toFun.{u_2, max u_1 u_2} M (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddZero.toZero.{u_2} M (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13)))) (AddZero.toZero.{max u_1 u_2} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddZeroClass.toAddZero.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoid.toAddZeroClass.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddMonoid.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_3, u_3, max u_2 u_1, u_1} R R (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))))))) (AddMonoidHom.toZeroHom.{u_2, max u_1 u_2} M (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13))) (AddZeroClass.toAddZero.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoid.toAddZeroClass.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddMonoid.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_3, u_3, max u_2 u_1, u_1} R R (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))))))) (LinearMap.applyₗ'.{u_3, u_3, u_2, u_1} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26))) y))","typeFull":"∀ {R : Type u_3} {M : Type u_2} {M₂ : Type u_1} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₂] [inst_3 : Module R M] [inst_4 : Module R M₂] (x y : M),\n  (↑(LinearMap.applyₗ' R)).toFun (x + y) = (↑(LinearMap.applyₗ' R)).toFun x + (↑(LinearMap.applyₗ' R)).toFun y","typeReadable":"∀ {R : Type u_3} {M : Type u_2} {M₂ : Type u_1} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₂] [inst_3 : Module R M] [inst_4 : Module R M₂] (x y : M),\n  (↑(LinearMap.applyₗ' R)).toFun (x + y) = (↑(LinearMap.applyₗ' R)).toFun x + (↑(LinearMap.applyₗ' R)).toFun y","typeReferences":[["LinearMap","applyₗ","_proof_1"],["LinearMap","applyₗ'"],["instHAdd"],["Module"],["AddMonoidHom","toZeroHom"],["CommSemiring"],["CommSemiring","toSemiring"],["LinearMap","module"],["ZeroHom","toFun"],["AddCommMonoid","toAddMonoid"],["AddZero","toAdd"],["AddZeroClass","toAddZero"],["LinearMap"],["HAdd","hAdd"],["LinearMap","addCommMonoid"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Eq"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["LinearMap","applyₗ","_proof_1"],["AddMonoidHom","map_add'"],["smulCommClass_self"],["LinearMap","applyₗ'"],["CommMonoid","toMonoid"],["CommSemiring","toSemiring"],["LinearMap","module"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["LinearMap"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["DistribMulAction","toMulAction"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","smulRight","_proof_2"],"typeFallback":"forall {R : Type.{u_4}} {S : Type.{u_2}} {M : Type.{u_1}} {M₁ : Type.{u_3}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10 : Semiring.{u_4} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.13 : AddCommMonoid.{u_1} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.16 : AddCommMonoid.{u_3} M₁] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.19 : Module.{u_4, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.23 : Module.{u_4, u_3} R M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.27 : Semiring.{u_2} S] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.30 : Module.{u_4, u_2} R S inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.27)))] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.34 : Module.{u_2, u_1} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.38 : IsScalarTower.{u_4, u_2, u_1} R S M (SMulZeroClass.toSMul.{u_4, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} 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(RingHom.id R) b • f y • x","typeReadable":"∀ {R : Type u_4} {S : Type u_2} {M : Type u_1} {M₁ : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₁] [inst_3 : Module R M] [inst_4 : Module R M₁] [inst_5 : Semiring S] [inst_6 : Module R S]\n  [inst_7 : Module S M] [IsScalarTower R S M] (f : M₁ →ₗ[R] S) (x : M) (b : R) (y : M₁),\n  f (b • y) • x = (RingHom.id R) b • f y • x","typeReferences":[["RingHom"],["LinearMap","instFunLike"],["IsScalarTower"],["Module"],["RingHom","instFunLike"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddMonoidWithOne","toAddMonoid"],["DFunLike","coe"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["instHSMul"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Eq"],["NonAssocSemiring","toAddCommMonoidWithOne"],["DistribSMul","toSMulZeroClass"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["LinearMap"],["Module","toDistribMulAction"],["HSMul","hSMul"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["RingHom"],["LinearMap","instFunLike"],["RingHom","id_apply"],["RingHom","instFunLike"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddMonoidWithOne","toAddMonoid"],["map_smul"],["DFunLike","coe"],["congrArg"],["LinearMap","semilinearMapClass"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["instHSMul"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Eq"],["NonAssocSemiring","toAddCommMonoidWithOne"],["DistribSMul","toSMulZeroClass"],["SemilinearMapClass","toMulActionSemiHomClass"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["LinearMap"],["Module","toDistribMulAction"],["Eq","refl"],["HSMul","hSMul"],["id"],["smul_assoc"],["Eq","mpr"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["Module","End","apply_smulCommClass"],"typeFallback":"forall {R : Type.{u_1}} {S : Type.{u_3}} {M : Type.{u_4}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.13 : AddCommMonoid.{u_4} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.19 : Module.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.27 : SMul.{u_3, u_1} S R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.31 : SMul.{u_3, u_4} S M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.35 : IsScalarTower.{u_3, u_1, u_4} S R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.27 (SMulZeroClass.toSMul.{u_1, u_4} R M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_1, u_4} R M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_1, u_4} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.19)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.31], SMulCommClass.{u_3, u_4, u_4} S (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.19) M inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.31 (SMulZeroClass.toSMul.{u_4, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.19) M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_4, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.19) M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_4, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.19) M (Module.End.instMonoid.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.19) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.13) (Module.toDistribMulAction.{u_4, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.19) M (Module.End.instSemiring.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.19) inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.13 (Module.End.applyModule.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3489826275._hygCtx._hyg.19)))))","typeFull":"∀ {R : Type u_1} {S : Type u_3} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  [inst_3 : SMul S R] [inst_4 : SMul S M] [IsScalarTower S R M], SMulCommClass S (Module.End R M) M","typeReadable":"∀ {R : Type u_1} {S : Type u_3} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  [inst_3 : SMul S R] [inst_4 : SMul S M] [IsScalarTower S R M], SMulCommClass S (Module.End R M) M","typeReferences":[["Module","End"],["Module","End","instSemiring"],["Module"],["IsScalarTower"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["SMulCommClass"],["Module","End","applyModule"],["Module","toDistribMulAction"],["AddCommMonoid"],["SMul"],["MonoidWithZero","toMonoid"],["Module","End","instMonoid"],["AddZero","toZero"],["Semiring"],["AddMonoid","toAddZeroClass"],["DistribSMul","toSMulZeroClass"]],"valueReferences":[["Module","End"],["Module","End","instSemiring"],["LinearMap","instFunLike"],["SMulCommClass","mk"],["DistribMulAction","toDistribSMul"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["LinearMap"],["AddZeroClass","toAddZero"],["DFunLike","coe"],["Module","toDistribMulAction"],["Module","End","applyModule"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["LinearMap","IsScalarTower","compatibleSMul"],["HSMul","hSMul"],["Eq","symm"],["instHSMul"],["LinearMap","map_smul_of_tower"],["Module","End","instMonoid"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["DistribSMul","toSMulZeroClass"]]},{"isProp":true,"kind":"theorem","name":["DistribSMul","toLinearMap","_proof_2"],"typeFallback":"forall (R : Type.{u_3}) {S : Type.{u_2}} (M : Type.{u_1}) [inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.10 : Semiring.{u_3} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13 : AddCommMonoid.{u_1} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.16 : Module.{u_3, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.23 : DistribSMul.{u_2, u_1} S M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13))] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.27 : SMulCommClass.{u_2, u_3, u_1} S R M (SMulZeroClass.toSMul.{u_2, u_1} S M (AddZero.toZero.{u_1} M (AddZeroClass.toAddZero.{u_1} M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} 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inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.16))))] (s : S) (x._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.55 : R) (x._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.57 : M), Eq.{succ u_1} M (HSMul.hSMul.{u_2, u_1, u_1} S M M (instHSMul.{u_2, u_1} S M (SMulZeroClass.toSMul.{u_2, u_1} S M (AddZero.toZero.{u_1} M (AddZeroClass.toAddZero.{u_1} M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_2, u_1} S M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13)) 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inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.16))))) x._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.55 x._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.57)) (HSMul.hSMul.{u_3, u_1, u_1} R M M (instHSMul.{u_3, u_1} R M (SMulZeroClass.toSMul.{u_3, u_1} R M (AddZero.toZero.{u_1} M (AddZeroClass.toAddZero.{u_1} M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_3, u_1} R M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_3, u_1} R M (MonoidWithZero.toMonoid.{u_3} R (Semiring.toMonoidWithZero.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M 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x._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.57))","typeFull":"∀ (R : Type u_3) {S : Type u_2} (M : Type u_1) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  [inst_3 : DistribSMul S M] [SMulCommClass S R M] (s : S) (x : R) (x_1 : M), s • x • x_1 = x • s • x_1","typeReadable":"∀ (R : Type u_3) {S : Type u_2} (M : Type u_1) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  [inst_3 : DistribSMul S M] [SMulCommClass S R M] (s : S) (x : R) (x_1 : M), s • x • x_1 = x • s • x_1","typeReferences":[["Module"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["DistribSMul"],["SMulCommClass"],["Module","toDistribMulAction"],["AddCommMonoid"],["HSMul","hSMul"],["MonoidWithZero","toMonoid"],["instHSMul"],["Eq"],["AddZero","toZero"],["Semiring"],["AddMonoid","toAddZeroClass"],["DistribSMul","toSMulZeroClass"]],"valueReferences":[["Module","toDistribMulAction"],["MonoidWithZero","toMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["AddZero","toZero"],["SMulCommClass","smul_comm"],["DistribSMul","toSMulZeroClass"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["RingEquiv","moduleEndSelfOp_symm_apply"],"typeFallback":"forall (R : Type.{u_1}) [inst._@.Mathlib.Algebra.Module.LinearMap.End.1691597331._hygCtx._hyg.10 : 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{R : Type.{u_1}} (S : Type.{u_4}) {M : Type.{u_2}} {M₂ : Type.{u_3}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 : Semiring.{u_4} S] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 : AddCommMonoid.{u_3} M₂] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 : Module.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 : Module.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 : Module.{u_4, u_3} S M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50 : SMulCommClass.{u_1, u_4, u_3} R S M₂ (SMulZeroClass.toSMul.{u_1, u_3} R M₂ (AddZero.toZero.{u_3} M₂ (AddZeroClass.toAddZero.{u_3} M₂ (AddMonoid.toAddZeroClass.{u_3} M₂ (AddCommMonoid.toAddMonoid.{u_3} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22)))) (DistribSMul.toSMulZeroClass.{u_1, u_3} R M₂ (AddMonoid.toAddZeroClass.{u_3} M₂ (AddCommMonoid.toAddMonoid.{u_3} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22)) (DistribMulAction.toDistribSMul.{u_1, u_3} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_3} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22) (Module.toDistribMulAction.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33)))) (SMulZeroClass.toSMul.{u_4, u_3} S M₂ (AddZero.toZero.{u_3} M₂ (AddZeroClass.toAddZero.{u_3} M₂ (AddMonoid.toAddZeroClass.{u_3} M₂ (AddCommMonoid.toAddMonoid.{u_3} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22)))) (DistribSMul.toSMulZeroClass.{u_4, u_3} S M₂ (AddMonoid.toAddZeroClass.{u_3} M₂ (AddCommMonoid.toAddMonoid.{u_3} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22)) (DistribMulAction.toDistribSMul.{u_4, u_3} S M₂ (MonoidWithZero.toMonoid.{u_4} S (Semiring.toMonoidWithZero.{u_4} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (AddCommMonoid.toAddMonoid.{u_3} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22) 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inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M₂) (LinearMap.instFunLike.{u_1, u_1, u_2, u_3} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 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inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (AddCommMonoid.toAddMonoid.{u_3} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22) (Module.toDistribMulAction.{u_4, u_3} S M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50)) x f) v) (HSMul.hSMul.{u_4, u_3, u_3} S M₂ M₂ (instHSMul.{u_4, u_3} S M₂ (SMulZeroClass.toSMul.{u_4, u_3} S M₂ (AddZero.toZero.{u_3} M₂ (AddZeroClass.toAddZero.{u_3} M₂ (AddMonoid.toAddZeroClass.{u_3} M₂ (AddCommMonoid.toAddMonoid.{u_3} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22)))) (DistribSMul.toSMulZeroClass.{u_4, u_3} S M₂ (AddMonoid.toAddZeroClass.{u_3} M₂ (AddCommMonoid.toAddMonoid.{u_3} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22)) (DistribMulAction.toDistribSMul.{u_4, u_3} S M₂ (MonoidWithZero.toMonoid.{u_4} S (Semiring.toMonoidWithZero.{u_4} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (AddCommMonoid.toAddMonoid.{u_3} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22) (Module.toDistribMulAction.{u_4, u_3} S M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41))))) x (DFunLike.coe.{max (succ u_3) (succ u_2), succ u_2, succ u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M₂) (LinearMap.instFunLike.{u_1, u_1, u_2, u_3} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) f v))","typeFull":"∀ {R : Type u_1} (S : Type u_4) {M : Type u_2} {M₂ : Type u_3} [inst : Semiring R] [inst_1 : Semiring S]\n  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R M₂]\n  [inst_6 : Module S M₂] [inst_7 : SMulCommClass R S M₂] (v : M) (x : S) (f : M →ₗ[R] M₂), (x • f) v = x • f v","typeReadable":"∀ {R : Type u_1} (S : Type u_4) {M : Type u_2} {M₂ : Type u_3} [inst : Semiring R] [inst_1 : Semiring S]\n  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R M₂]\n  [inst_6 : Module S M₂] [inst_7 : SMulCommClass R S M₂] (v : M) (x : S) (f : M →ₗ[R] M₂), (x • f) v = x • f 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[inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 : Semiring.{u_2} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 : AddCommMonoid.{u_1} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 : Module.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13], Eq.{succ u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 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inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) (instHSMul.{0, u_1} Nat (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) (SMulZeroClass.toSMul.{0, u_1} Nat (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) (LinearMap.instZero.{u_2, u_2, u_1, u_1} R R M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10))) (SMulWithZero.toSMulZeroClass.{0, u_1} Nat (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) (MulZeroClass.toZero.{0} Nat Nat.instMulZeroClass) (LinearMap.instZero.{u_2, u_2, u_1, u_1} R R M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10))) (instSMulWithZeroNat.{u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 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inst._@.Mathlib.Algebra.Module.LinearMap.End.2880213917._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2880213917._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2880213917._hygCtx._hyg.19) Nat (Monoid.toPow.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.2880213917._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2880213917._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2880213917._hygCtx._hyg.19) (Module.End.instMonoid.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.2880213917._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2880213917._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2880213917._hygCtx._hyg.19))) f l) m) (OfNat.ofNat.{u_4} M 0 (Zero.toOfNat0.{u_4} M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2880213917._hygCtx._hyg.13)))))))","typeFull":"∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  {f : Module.End R M} {m : M} {k l : ℕ}, k ≤ l → (f ^ k) m = 0 → (f ^ l) m = 0","typeReadable":"∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  {f : Module.End R M} {m : M} {k l : ℕ}, k ≤ l → (f ^ k) m = 0 → (f ^ l) m = 0","typeReferences":[["instHPow"],["Module","End"],["LinearMap","instFunLike"],["Module"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["HPow","hPow"],["DFunLike","coe"],["OfNat","ofNat"],["AddCommMonoid"],["Nat"],["Semiring","toNonAssocSemiring"],["Monoid","toPow"],["RingHom","id"],["LE","le"],["Zero","toOfNat0"],["Module","End","instMonoid"],["Eq"],["AddZero","toZero"],["instLENat"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["MulOneClass","toMulOne"],["instAddNat"],["RingHom"],["LinearMap","instFunLike"],["RingHom","instFunLike"],["HMul","hMul"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["congrArg"],["LinearMap","semilinearMapClass"],["DistribMulActionSemiHomClass","toAddMonoidHomClass"],["MulOne","toMul"],["Semiring","toNonAssocSemiring"],["Monoid","toPow"],["Nat","sub_add_cancel"],["RingHom","id"],["MonoidWithZero","toMonoid"],["Monoid","toMulOneClass"],["Eq","symm"],["HSub","hSub"],["Zero","toOfNat0"],["map_zero"],["Eq"],["instHPow"],["Module","End"],["pow_add"],["instHAdd"],["AddMonoidHomClass","toZeroHomClass"],["Semiring","toMonoidWithZero"],["HPow","hPow"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["Module","End","instMul"],["HAdd","hAdd"],["Module","toDistribMulAction"],["Nat"],["instSubNat"],["Eq","refl"],["id"],["instHMul"],["Module","End","instMonoid"],["Eq","mpr"],["Module","End","mul_apply"],["instHSub"],["AddZero","toZero"],["SemilinearMapClass","distribMulActionSemiHomClass"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["Module","End","instSemiring","_proof_7"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 : Module.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13] (a : Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19), Eq.{succ u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) (HMul.hMul.{u_2, u_2, u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) (instHMul.{u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) 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inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) 1 (One.toOfNat1.{u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) (Monoid.toOne.{u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) (Module.End.instMonoid.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19)))) a) a","typeFull":"∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  (a : Module.End R M), 1 * a = a","typeReadable":"∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  (a : Module.End R M), 1 * a = a","typeReferences":[["Module","End"],["Module"],["Monoid","toOne"],["HMul","hMul"],["OfNat","ofNat"],["Semigroup","toMul"],["AddCommMonoid"],["One","toOfNat1"],["instHMul"],["Module","End","instMonoid"],["Monoid","toSemigroup"],["Eq"],["Semiring"]],"valueReferences":[["Module","End"],["Monoid","one_mul"],["Module","End","instMonoid"]]},{"isProp":true,"kind":"theorem","name":["Module","End","instRing","_proof_7"],"typeFallback":"forall {R : Type.{u_2}} {N₁ : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 : Semiring.{u_2} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16 : AddCommGroup.{u_1} N₁] [inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 : Module.{u_2, u_1} R N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 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inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddCommGroup.toAddGroup.{u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (LinearMap.addCommGroup.{u_2, u_2, u_1, u_1} R R N₁ N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10))))))) (Int.negSucc n) (OfNat.ofNat.{u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) 1 (One.toOfNat1.{u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (Module.End.instOne.{u_2, u_1} R N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23)))) (Neg.neg.{u_1} (Module.End.{u_2, u_1} R N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (SubNegMonoid.toNeg.{u_1} (Module.End.{u_2, u_1} R N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddGroup.toSubNegMonoid.{u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddCommGroup.toAddGroup.{u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (LinearMap.addCommGroup.{u_2, u_2, u_1, u_1} R R N₁ N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)))))) (HSMul.hSMul.{0, u_1, u_1} Nat (Module.End.{u_2, u_1} R N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (Module.End.{u_2, u_1} R N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (instHSMul.{0, u_1} Nat (Module.End.{u_2, u_1} R N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddMonoid.toNSMul.{u_1} (Module.End.{u_2, u_1} R N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (SubNegMonoid.toAddMonoid.{u_1} (Module.End.{u_2, u_1} R N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddGroup.toSubNegMonoid.{u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddCommGroup.toAddGroup.{u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (LinearMap.addCommGroup.{u_2, u_2, u_1, u_1} R R N₁ N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)))))))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) 1 (One.toOfNat1.{u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (Module.End.instOne.{u_2, u_1} R N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23)))))","typeFull":"∀ {R : Type u_2} {N₁ : Type u_1} [inst : Semiring R] [inst_1 : AddCommGroup N₁] [inst_2 : Module R N₁] (n : ℕ),\n  Int.negSucc n • 1 = -((n + 1) • 1)","typeReadable":"∀ {R : Type u_2} {N₁ : Type u_1} [inst : Semiring R] [inst_1 : AddCommGroup N₁] [inst_2 : Module R N₁] (n : ℕ),\n  Int.negSucc n • 1 = -((n + 1) • 1)","typeReferences":[["instAddNat"],["Module"],["AddCommGroup","toAddGroup"],["Semiring","toNonAssocSemiring"],["instOfNatNat"],["RingHom","id"],["instHSMul"],["Module","End","instOne"],["AddGroup","toSubNegMonoid"],["Eq"],["Module","End"],["instHAdd"],["Neg","neg"],["SubNegMonoid","toNeg"],["Int","negSucc"],["AddCommGroup"],["LinearMap"],["OfNat","ofNat"],["Int"],["HAdd","hAdd"],["Nat"],["One","toOfNat1"],["AddMonoid","toNSMul"],["SubNegMonoid","toAddMonoid"],["HSMul","hSMul"],["AddCommGroup","toAddCommMonoid"],["SubNegMonoid","toZSMul"],["LinearMap","addCommGroup"],["Semiring"]],"valueReferences":[["negSucc_zsmul"],["Module","End"],["Semiring","toNonAssocSemiring"],["One","toOfNat1"],["RingHom","id"],["AddCommGroup","toAddGroup"],["AddCommGroup","toAddCommMonoid"],["Module","End","instOne"],["AddGroup","toSubNegMonoid"],["LinearMap","addCommGroup"],["LinearMap"],["OfNat","ofNat"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","compRight","_proof_2"],"typeFallback":"forall {R : Type.{u_1}} (S : Type.{u_5}) {M : Type.{u_2}} {M₁ : Type.{u_3}} {M₂ : Type.{u_4}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13 : Semiring.{u_5} S] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 : AddCommMonoid.{u_3} M₁] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 : AddCommMonoid.{u_4} M₂] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 : Module.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29 : Module.{u_1, u_3} R M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.33 : Module.{u_1, u_4} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.37 : Module.{u_5, u_3} S M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.41 : Module.{u_5, u_4} S M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.45 : SMulCommClass.{u_1, u_5, u_3} R S M₁ (SMulZeroClass.toSMul.{u_1, u_3} R M₁ (AddZero.toZero.{u_3} M₁ (AddZeroClass.toAddZero.{u_3} M₁ (AddMonoid.toAddZeroClass.{u_3} M₁ (AddCommMonoid.toAddMonoid.{u_3} M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19)))) (DistribSMul.toSMulZeroClass.{u_1, u_3} R M₁ (AddMonoid.toAddZeroClass.{u_3} M₁ (AddCommMonoid.toAddMonoid.{u_3} M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19)) (DistribMulAction.toDistribSMul.{u_1, u_3} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_3} M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19) (Module.toDistribMulAction.{u_1, u_3} R M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29)))) (SMulZeroClass.toSMul.{u_5, u_3} S M₁ (AddZero.toZero.{u_3} M₁ (AddZeroClass.toAddZero.{u_3} M₁ (AddMonoid.toAddZeroClass.{u_3} M₁ (AddCommMonoid.toAddMonoid.{u_3} M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19)))) (DistribSMul.toSMulZeroClass.{u_5, u_3} S M₁ (AddMonoid.toAddZeroClass.{u_3} M₁ (AddCommMonoid.toAddMonoid.{u_3} M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19)) (DistribMulAction.toDistribSMul.{u_5, u_3} S M₁ (MonoidWithZero.toMonoid.{u_5} S (Semiring.toMonoidWithZero.{u_5} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13)) (AddCommMonoid.toAddMonoid.{u_3} M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19) (Module.toDistribMulAction.{u_5, u_3} S M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.37))))] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.50 : SMulCommClass.{u_1, u_5, u_4} R S M₂ (SMulZeroClass.toSMul.{u_1, u_4} R M₂ (AddZero.toZero.{u_4} M₂ (AddZeroClass.toAddZero.{u_4} M₂ (AddMonoid.toAddZeroClass.{u_4} M₂ (AddCommMonoid.toAddMonoid.{u_4} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22)))) (DistribSMul.toSMulZeroClass.{u_1, u_4} R M₂ (AddMonoid.toAddZeroClass.{u_4} M₂ (AddCommMonoid.toAddMonoid.{u_4} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22)) (DistribMulAction.toDistribSMul.{u_1, u_4} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_4} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22) (Module.toDistribMulAction.{u_1, u_4} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.33)))) (SMulZeroClass.toSMul.{u_5, u_4} S M₂ (AddZero.toZero.{u_4} M₂ (AddZeroClass.toAddZero.{u_4} M₂ (AddMonoid.toAddZeroClass.{u_4} M₂ (AddCommMonoid.toAddMonoid.{u_4} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22)))) (DistribSMul.toSMulZeroClass.{u_5, u_4} S M₂ (AddMonoid.toAddZeroClass.{u_4} M₂ (AddCommMonoid.toAddMonoid.{u_4} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22)) (DistribMulAction.toDistribSMul.{u_5, u_4} S M₂ (MonoidWithZero.toMonoid.{u_5} S (Semiring.toMonoidWithZero.{u_5} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13)) (AddCommMonoid.toAddMonoid.{u_4} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22) (Module.toDistribMulAction.{u_5, u_4} S M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.41))))] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.55 : LinearMap.CompatibleSMul.{u_3, u_4, u_5, u_1} M₁ M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 S R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (SMulZeroClass.toSMul.{u_5, u_3} S M₁ (AddZero.toZero.{u_3} M₁ (AddZeroClass.toAddZero.{u_3} M₁ (AddMonoid.toAddZeroClass.{u_3} M₁ (AddCommMonoid.toAddMonoid.{u_3} M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19)))) (DistribSMul.toSMulZeroClass.{u_5, u_3} S M₁ (AddMonoid.toAddZeroClass.{u_3} M₁ (AddCommMonoid.toAddMonoid.{u_3} M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19)) (DistribMulAction.toDistribSMul.{u_5, u_3} S M₁ (MonoidWithZero.toMonoid.{u_5} S (Semiring.toMonoidWithZero.{u_5} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13)) (AddCommMonoid.toAddMonoid.{u_3} M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19) (Module.toDistribMulAction.{u_5, u_3} S M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.37)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29 (SMulZeroClass.toSMul.{u_5, u_4} S M₂ (AddZero.toZero.{u_4} M₂ (AddZeroClass.toAddZero.{u_4} M₂ (AddMonoid.toAddZeroClass.{u_4} M₂ (AddCommMonoid.toAddMonoid.{u_4} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22)))) (DistribSMul.toSMulZeroClass.{u_5, u_4} S M₂ (AddMonoid.toAddZeroClass.{u_4} M₂ (AddCommMonoid.toAddMonoid.{u_4} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22)) (DistribMulAction.toDistribSMul.{u_5, u_4} S M₂ (MonoidWithZero.toMonoid.{u_5} S (Semiring.toMonoidWithZero.{u_5} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13)) (AddCommMonoid.toAddMonoid.{u_4} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22) (Module.toDistribMulAction.{u_5, u_4} S M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.41)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.33] (f : LinearMap.{u_1, u_1, u_3, u_4} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M₁ M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.33) (x._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.126 : S) (x._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.128 : LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 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inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) (Module.End.instMul._proof_1.{u_1} R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29) (instHSMul.{u_5, max u_2 u_3} S (LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29) (SMulZeroClass.toSMul.{u_5, max u_2 u_3} S (LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29) (AddZero.toZero.{max u_2 u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29) (AddZeroClass.toAddZero.{max u_2 u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29) (AddMonoid.toAddZeroClass.{max u_2 u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10))))))) (DistribSMul.toSMulZeroClass.{u_5, max u_2 u_3} S (LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29) (AddMonoid.toAddZeroClass.{max u_2 u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10))))) (DistribMulAction.toDistribSMul.{u_5, max u_2 u_3} S (LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29) (MonoidWithZero.toMonoid.{u_5} S (Semiring.toMonoidWithZero.{u_5} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13)) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)))) (Module.toDistribMulAction.{u_5, max u_2 u_3} S (LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29) inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 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inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.45)))))) x._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.126 x._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.128)) (HSMul.hSMul.{u_5, max u_2 u_4, max u_2 u_4} S (LinearMap.{u_1, u_1, u_2, u_4} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.33) (LinearMap.{u_1, u_1, u_2, u_4} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.33) (instHSMul.{u_5, max u_2 u_4} S (LinearMap.{u_1, u_1, u_2, u_4} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 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(RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10))))))) (DistribSMul.toSMulZeroClass.{u_5, max u_2 u_4} S (LinearMap.{u_1, u_1, u_2, u_4} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.33) (AddMonoid.toAddZeroClass.{max u_2 u_4} (LinearMap.{u_1, u_1, u_2, u_4} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.33) (AddCommMonoid.toAddMonoid.{max u_2 u_4} (LinearMap.{u_1, u_1, u_2, u_4} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 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(RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.33) (MonoidWithZero.toMonoid.{u_5} S (Semiring.toMonoidWithZero.{u_5} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13)) (AddCommMonoid.toAddMonoid.{max u_2 u_4} (LinearMap.{u_1, u_1, u_2, u_4} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.33) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_4} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)))) (Module.toDistribMulAction.{u_5, max u_2 u_4} S (LinearMap.{u_1, u_1, u_2, u_4} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.33) inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_4} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10))) (LinearMap.module.{u_1, u_1, u_5, u_2, u_4} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.50)))))) (DFunLike.coe.{succ u_5, succ u_5, succ u_5} (RingHom.{u_5, u_5} S S (Semiring.toNonAssocSemiring.{u_5} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13) (Semiring.toNonAssocSemiring.{u_5} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13)) S (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : S) => S) (RingHom.instFunLike.{u_5, u_5} S S (Semiring.toNonAssocSemiring.{u_5} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13) (Semiring.toNonAssocSemiring.{u_5} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13)) (RingHom.id.{u_5} S (Semiring.toNonAssocSemiring.{u_5} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.13)) x._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.126) (LinearMap.comp.{u_1, u_1, u_1, u_2, u_3, u_4} R R R M M₁ M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.29 inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10)) (Module.End.instMul._proof_1.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.10) f x._@.Mathlib.Algebra.Module.LinearMap.End.3759090398._hygCtx._hyg.128))","typeFull":"∀ {R : Type u_1} (S : Type u_5) {M : Type u_2} {M₁ : Type u_3} {M₂ : Type u_4} [inst : Semiring R] [inst_1 : Semiring S]\n  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₁] [inst_4 : AddCommMonoid M₂] [inst_5 : Module R M]\n  [inst_6 : Module R M₁] [inst_7 : Module R M₂] [inst_8 : Module S M₁] [inst_9 : Module S M₂]\n  [inst_10 : SMulCommClass R S M₁] [inst_11 : SMulCommClass R S M₂] [LinearMap.CompatibleSMul M₁ M₂ S R]\n  (f : M₁ →ₗ[R] M₂) (x : S) (x_1 : M →ₗ[R] M₁), f ∘ₗ (x • x_1) = (RingHom.id S) x • f ∘ₗ x_1","typeReadable":"∀ {R : Type u_1} (S : Type u_5) {M : Type u_2} {M₁ : Type u_3} {M₂ : Type u_4} [inst : Semiring R] [inst_1 : Semiring S]\n  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₁] [inst_4 : AddCommMonoid M₂] [inst_5 : Module R M]\n  [inst_6 : Module R M₁] [inst_7 : Module R M₂] [inst_8 : Module S M₁] [inst_9 : Module S M₂]\n  [inst_10 : SMulCommClass R S M₁] [inst_11 : SMulCommClass R S M₂] [LinearMap.CompatibleSMul M₁ M₂ S R]\n  (f : M₁ →ₗ[R] M₂) (x : S) (x_1 : M →ₗ[R] M₁), f ∘ₗ (x • x_1) = (RingHom.id S) x • f ∘ₗ x_1","typeReferences":[["RingHom"],["LinearMap","CompatibleSMul"],["Module"],["RingHom","instFunLike"],["LinearMap","comp"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["instHSMul"],["Eq"],["DistribSMul","toSMulZeroClass"],["LinearMap","module"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["LinearMap"],["LinearMap","addCommMonoid"],["SMulCommClass"],["Module","toDistribMulAction"],["Module","End","instMul","_proof_1"],["HSMul","hSMul"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["RingHom"],["LinearMap","instFunLike"],["RingHomCompTriple","ids"],["LinearMap","comp"],["RingHom","instFunLike"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["LinearMap","ext"],["MonoidWithZero","toMonoid"],["instHSMul"],["DistribSMul","toSMulZeroClass"],["LinearMap","module"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["LinearMap"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["HSMul","hSMul"],["LinearMap","map_smul_of_tower"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["Module","End","iterate_succ'"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_4}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.13 : AddCommMonoid.{u_4} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.19 : Module.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.13] {f' : Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.19} (n : Nat), Eq.{succ u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.19) (HPow.hPow.{u_4, 0, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.19) Nat (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.19) (instHPow.{u_4, 0} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.19) Nat (Monoid.toPow.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.19) (Module.End.instMonoid.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.19))) f' (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (LinearMap.comp.{u_1, u_1, u_1, u_4, u_4, u_4} R R R M M M inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.10)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.10))) f' (HPow.hPow.{u_4, 0, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.19) Nat (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.19) (instHPow.{u_4, 0} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.19) Nat (Monoid.toPow.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.19) (Module.End.instMonoid.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3923468267._hygCtx._hyg.19))) f' n))","typeFull":"∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  {f' : Module.End R M} (n : ℕ), f' ^ (n + 1) = f' ∘ₗ f' ^ n","typeReadable":"∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  {f' : Module.End R M} (n : ℕ), f' ^ (n + 1) = f' ∘ₗ f' ^ n","typeReferences":[["instHPow"],["instAddNat"],["Module","End"],["RingHomCompTriple","ids"],["Module"],["instHAdd"],["LinearMap","comp"],["HPow","hPow"],["OfNat","ofNat"],["HAdd","hAdd"],["AddCommMonoid"],["Nat"],["Semiring","toNonAssocSemiring"],["Monoid","toPow"],["RingHom","id"],["instOfNatNat"],["Module","End","instMonoid"],["Eq"],["Semiring"]],"valueReferences":[["instAddNat"],["MulOneClass","toMulOne"],["pow_succ'"],["RingHomCompTriple","ids"],["LinearMap","comp"],["HMul","hMul"],["congrArg"],["MulOne","toMul"],["Semiring","toNonAssocSemiring"],["Monoid","toPow"],["instOfNatNat"],["RingHom","id"],["Monoid","toMulOneClass"],["Eq"],["instHPow"],["Module","End"],["instHAdd"],["HPow","hPow"],["OfNat","ofNat"],["Module","End","instMul"],["HAdd","hAdd"],["Nat"],["Eq","refl"],["id"],["instHMul"],["Module","End","mul_eq_comp"],["Module","End","instMonoid"],["Eq","mpr"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","smulRight_apply"],"typeFallback":"forall {R : Type.{u_1}} {S : Type.{u_3}} {M : Type.{u_4}} {M₁ : Type.{u_5}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.13 : AddCommMonoid.{u_4} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.16 : AddCommMonoid.{u_5} M₁] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.19 : Module.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.23 : Module.{u_1, u_5} R M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.27 : Semiring.{u_3} S] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.30 : Module.{u_1, u_3} R S inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.10 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.27)))] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.34 : Module.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.38 : IsScalarTower.{u_1, u_3, u_4} R S M (SMulZeroClass.toSMul.{u_1, u_3} R S (AddZero.toZero.{u_3} S (AddZeroClass.toAddZero.{u_3} S (AddMonoid.toAddZeroClass.{u_3} S (AddMonoidWithOne.toAddMonoid.{u_3} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_3} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.27))))))) (DistribSMul.toSMulZeroClass.{u_1, u_3} R S (AddMonoid.toAddZeroClass.{u_3} S (AddMonoidWithOne.toAddMonoid.{u_3} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_3} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.27))))) (DistribMulAction.toDistribSMul.{u_1, u_3} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.10)) (AddMonoidWithOne.toAddMonoid.{u_3} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_3} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.27)))) (Module.toDistribMulAction.{u_1, u_3} R S inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.10 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.27))) inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.30)))) (SMulZeroClass.toSMul.{u_3, u_4} S M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_3, u_4} S M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_3, u_4} S M (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.27)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.34)))) (SMulZeroClass.toSMul.{u_1, u_4} R M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_1, u_4} R M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_1, u_4} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.19))))] (f : LinearMap.{u_1, u_1, u_5, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.10)) M₁ S inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.27))) inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.30) (x : M) (c : M₁), Eq.{succ u_4} M (DFunLike.coe.{max (succ u_4) (succ u_5), succ u_5, succ u_4} (LinearMap.{u_1, u_1, u_5, u_4} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.10)) M₁ M inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.3708130724._hygCtx._hyg.19) M₁ (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M₁) => M) (LinearMap.instFunLike.{u_1, u_1, u_5, u_4} R R M₁ M 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inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_2} R R M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10))))))) b a)","typeFull":"∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (a b : M →ₗ[R] M),\n  a + b = b + a","typeReadable":"∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (a b : M →ₗ[R] M),\n  a + b = b + a","typeReferences":[["Module"],["instHAdd"],["AddCommMonoid","toAddMonoid"],["LinearMap"],["HAdd","hAdd"],["LinearMap","addCommMonoid"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["AddMonoid","toAddSemigroup"],["Eq"],["Semiring"],["AddSemigroup","toAdd"]],"valueReferences":[["LinearMap","addCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["AddCommMonoid","add_comm"],["LinearMap"]]},{"isProp":true,"kind":"theorem","name":["Module","End","commute_id_left"],"typeFallback":"forall {R : Type.{u_9}} {M : Type.{u_10}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.2173483174._hygCtx._hyg.12 : Ring.{u_9} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2173483174._hygCtx._hyg.15 : AddCommGroup.{u_10} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2173483174._hygCtx._hyg.18 : Module.{u_9, u_10} R M (Ring.toSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2173483174._hygCtx._hyg.12) (AddCommGroup.toAddCommMonoid.{u_10} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2173483174._hygCtx._hyg.15)] (f : Module.End.{u_9, u_10} R M (Ring.toSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2173483174._hygCtx._hyg.12) (AddCommGroup.toAddCommMonoid.{u_10} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2173483174._hygCtx._hyg.15) inst._@.Mathlib.Algebra.Module.LinearMap.End.2173483174._hygCtx._hyg.18), Commute.{u_10} (LinearMap.{u_9, u_9, u_10, u_10} R R (Ring.toSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2173483174._hygCtx._hyg.12) (Ring.toSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2173483174._hygCtx._hyg.12) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R (Ring.toSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2173483174._hygCtx._hyg.12))) M M (AddCommGroup.toAddCommMonoid.{u_10} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2173483174._hygCtx._hyg.15) (AddCommGroup.toAddCommMonoid.{u_10} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2173483174._hygCtx._hyg.15) inst._@.Mathlib.Algebra.Module.LinearMap.End.2173483174._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.LinearMap.End.2173483174._hygCtx._hyg.18) (Module.End.instMul.{u_9, u_10} R M (Ring.toSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2173483174._hygCtx._hyg.12) (AddCommGroup.toAddCommMonoid.{u_10} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2173483174._hygCtx._hyg.15) inst._@.Mathlib.Algebra.Module.LinearMap.End.2173483174._hygCtx._hyg.18) (LinearMap.id.{u_9, u_10} R M (Ring.toSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2173483174._hygCtx._hyg.12) (AddCommGroup.toAddCommMonoid.{u_10} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2173483174._hygCtx._hyg.15) inst._@.Mathlib.Algebra.Module.LinearMap.End.2173483174._hygCtx._hyg.18) f","typeFull":"∀ {R : Type u_9} {M : Type u_10} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (f : Module.End R M),\n  Commute LinearMap.id f","typeReadable":"∀ {R : Type u_9} {M : Type u_10} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (f : Module.End R M),\n  Commute LinearMap.id f","typeReferences":[["Module","End"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Commute"],["Module"],["AddCommGroup","toAddCommMonoid"],["AddCommGroup"],["LinearMap"],["LinearMap","id"],["Module","End","instMul"],["Ring","toSemiring"],["Ring"]],"valueReferences":[["Module","End"],["LinearMap","instFunLike"],["HMul","hMul"],["LinearMap"],["LinearMap","id"],["DFunLike","coe"],["Ring","toSemiring"],["Module","End","instMul"],["eq_self"],["Semiring","toNonAssocSemiring"],["of_eq_true"],["RingHom","id"],["LinearMap","ext"],["AddCommGroup","toAddCommMonoid"],["instHMul"],["Eq"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","applyₗ'","_proof_7"],"typeFallback":"forall {R : Type.{u_1}} (S : Type.{u_4}) {M : Type.{u_2}} {M₂ : Type.{u_3}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 : Semiring.{u_4} S] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 : AddCommMonoid.{u_3} M₂] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 : Module.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 : Module.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 : Module.{u_4, u_3} S M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50 : SMulCommClass.{u_1, u_4, u_3} R S M₂ (SMulZeroClass.toSMul.{u_1, u_3} R M₂ (AddZero.toZero.{u_3} M₂ (AddZeroClass.toAddZero.{u_3} M₂ (AddMonoid.toAddZeroClass.{u_3} M₂ (AddCommMonoid.toAddMonoid.{u_3} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22)))) (DistribSMul.toSMulZeroClass.{u_1, u_3} R M₂ (AddMonoid.toAddZeroClass.{u_3} M₂ (AddCommMonoid.toAddMonoid.{u_3} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22)) (DistribMulAction.toDistribSMul.{u_1, u_3} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_3} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22) (Module.toDistribMulAction.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33)))) (SMulZeroClass.toSMul.{u_4, u_3} S M₂ (AddZero.toZero.{u_3} M₂ (AddZeroClass.toAddZero.{u_3} M₂ (AddMonoid.toAddZeroClass.{u_3} M₂ (AddCommMonoid.toAddMonoid.{u_3} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22)))) (DistribSMul.toSMulZeroClass.{u_4, u_3} S M₂ (AddMonoid.toAddZeroClass.{u_3} M₂ (AddCommMonoid.toAddMonoid.{u_3} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22)) (DistribMulAction.toDistribSMul.{u_4, u_3} S M₂ (MonoidWithZero.toMonoid.{u_4} S (Semiring.toMonoidWithZero.{u_4} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (AddCommMonoid.toAddMonoid.{u_3} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22) (Module.toDistribMulAction.{u_4, u_3} S M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41))))] 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inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M₂) (LinearMap.instFunLike.{u_1, u_1, u_2, u_3} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) (HSMul.hSMul.{u_4, max u_3 u_2, max u_3 u_2} S (LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) (LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 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inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22) (Module.toDistribMulAction.{u_4, u_3} S M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50)) x f) (HAdd.hAdd.{u_2, u_2, u_2} M M M (instHAdd.{u_2} M (AddZero.toAdd.{u_2} M (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16))))) x._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.119 x._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.121)) (HSMul.hSMul.{u_4, u_3, u_3} S M₂ M₂ (instHSMul.{u_4, u_3} S M₂ (SMulZeroClass.toSMul.{u_4, u_3} S M₂ (AddZero.toZero.{u_3} M₂ (AddZeroClass.toAddZero.{u_3} M₂ (AddMonoid.toAddZeroClass.{u_3} M₂ 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inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M₂) (LinearMap.instFunLike.{u_1, u_1, u_2, u_3} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 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inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.45 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.10)) σ₁₂ σ₁₂ (RingHomCompTriple.ids.{u_1, u_2} R R₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.39 σ₁₂) f g)) -> (forall (k : Nat), Eq.{max (succ u_4) (succ u_6)} (LinearMap.{u_1, u_2, u_4, u_6} R R₂ 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inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.45 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.45 σ₁₂ (RingHom.id.{u_2} R₂ (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.39)) σ₁₂ (RingHomCompTriple.right_ids.{u_1, u_2} R R₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.39 σ₁₂) (HPow.hPow.{u_6, 0, u_6} (Module.End.{u_2, u_6} R₂ M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.45) Nat (Module.End.{u_2, u_6} R₂ M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.45) (instHPow.{u_6, 0} (Module.End.{u_2, u_6} R₂ M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.45) Nat (Monoid.toPow.{u_6} (Module.End.{u_2, u_6} R₂ M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.45) (Module.End.instMonoid.{u_2, u_6} R₂ M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.45))) g₂ k) f) (LinearMap.comp.{u_1, u_1, u_2, u_4, u_4, u_6} R R R₂ M M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.45 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.10)) σ₁₂ σ₁₂ (RingHomCompTriple.ids.{u_1, u_2} R R₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.39 σ₁₂) f (HPow.hPow.{u_4, 0, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.19) Nat (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.19) (instHPow.{u_4, 0} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.19) Nat (Monoid.toPow.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.19) (Module.End.instMonoid.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2359263374._hygCtx._hyg.19))) g k)))","typeFull":"∀ {R : Type u_1} {R₂ : Type u_2} {M : Type u_4} {M₂ : Type u_6} [inst : Semiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : Module R M] [inst_3 : Semiring R₂] [inst_4 : AddCommMonoid M₂] [inst_5 : Module R₂ M₂] {σ₁₂ : R →+* R₂}\n  {f : M →ₛₗ[σ₁₂] M₂} {g : Module.End R M} {g₂ : Module.End R₂ M₂},\n  g₂ ∘ₛₗ f = f ∘ₛₗ g → ∀ (k : ℕ), (g₂ ^ k) ∘ₛₗ f = f ∘ₛₗ (g ^ k)","typeReadable":"∀ {R : Type u_1} {R₂ : Type u_2} {M : Type u_4} {M₂ : Type u_6} [inst : Semiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : Module R M] [inst_3 : Semiring R₂] [inst_4 : AddCommMonoid M₂] [inst_5 : Module R₂ M₂] {σ₁₂ : R →+* R₂}\n  {f : M →ₛₗ[σ₁₂] M₂} {g : Module.End R M} {g₂ : Module.End R₂ M₂},\n  g₂ ∘ₛₗ f = f ∘ₛₗ g → ∀ (k : ℕ), (g₂ ^ k) ∘ₛₗ f = f ∘ₛₗ (g ^ k)","typeReferences":[["instHPow"],["RingHom"],["Module","End"],["RingHomCompTriple","right_ids"],["Module"],["RingHomCompTriple","ids"],["LinearMap","comp"],["HPow","hPow"],["LinearMap"],["AddCommMonoid"],["Nat"],["Semiring","toNonAssocSemiring"],["Monoid","toPow"],["RingHom","id"],["Module","End","instMonoid"],["Eq"],["Semiring"]],"valueReferences":[["MulOneClass","toMulOne"],["instAddNat"],["pow_succ'"],["RingHomCompTriple","right_ids"],["Eq","trans"],["RingHomCompTriple","ids"],["LinearMap","comp_assoc"],["HMul","hMul"],["LinearMap","comp"],["LinearMap","id"],["congrArg"],["MulOne","toMul"],["Semiring","toNonAssocSemiring"],["Monoid","toPow"],["LinearMap","comp","congr_simp"],["RingHom","id"],["instOfNatNat"],["congr"],["Monoid","toMulOneClass"],["Eq","symm"],["Eq"],["instHPow"],["Module","End"],["True"],["instHAdd"],["Nat","recAux"],["HPow","hPow"],["LinearMap"],["OfNat","ofNat"],["Module","End","instMul"],["HAdd","hAdd"],["eq_self"],["Nat"],["of_eq_true"],["Eq","refl"],["id"],["instHMul"],["Module","End","mul_eq_comp"],["Eq","mpr"],["Module","End","instMonoid"],["pow_zero"]]},{"isProp":true,"kind":"theorem","name":["Module","End","instMonoid","_proof_2"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19 : Module.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13] (n : Nat) (x : Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19), Eq.{succ u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (npowRecAuto.{u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Semigroup.mk.{u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Mul.mk.{u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Mul.mul.{u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.instMul.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19))) (fun (x._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.42 : Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (x._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.44 : Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (x._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.46 : Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) => LinearMap.ext.{u_1, u_1, u_2, u_2} R R M M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10)) (HMul.hMul.{u_2, u_2, u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (instHMul.{u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.instMul.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19)) (HMul.hMul.{u_2, u_2, u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (instHMul.{u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.instMul.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19)) x._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.42 x._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.44) x._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.46) (HMul.hMul.{u_2, u_2, u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (instHMul.{u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.instMul.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19)) x._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.42 (HMul.hMul.{u_2, u_2, u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (instHMul.{u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.instMul.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19)) x._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.44 x._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.46)) (fun (x._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.51 : M) => rfl.{succ u_2} M (DFunLike.coe.{succ u_2, succ u_2, succ u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (LinearMap.instFunLike.{u_1, u_1, u_2, u_2} R R M M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10))) (HMul.hMul.{u_2, 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inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.instMul.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19))) (fun (x._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.42 : Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (x._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.44 : Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (x._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.46 : Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) => LinearMap.ext.{u_1, u_1, u_2, u_2} R R M M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (instHMul.{u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.instMul.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19)) x._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.42 x._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.44) x._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.46) (HMul.hMul.{u_2, u_2, u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (instHMul.{u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.instMul.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19)) x._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.42 (HMul.hMul.{u_2, u_2, u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (instHMul.{u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19) (Module.End.instMul.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19)) x._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.44 x._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.46)) (fun (x._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.51 : M) => rfl.{succ u_2} M (DFunLike.coe.{succ u_2, succ u_2, succ u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 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u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13] (x._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.64 : M), Eq.{succ u_1} M (HSMul.hSMul.{u_1, u_1, u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) M M (instHSMul.{u_1, u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) M (SMul.mk.{u_1, u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 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inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10))) x1._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.43 x2._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.43))) (OfNat.ofNat.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) 1 (One.toOfNat1.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) (MulOne.toOne.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) (MulOneClass.toMulOne.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) (Monoid.toMulOneClass.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) (MonoidWithZero.toMonoid.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) (Semiring.toMonoidWithZero.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) (Module.End.instSemiring.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19)))))))) x._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.64) (HSMul.hSMul.{u_1, u_1, u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) M M (instHSMul.{u_1, u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) M (SMul.mk.{u_1, u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) M (fun (x1._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.43 : Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) (x2._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.43 : M) => DFunLike.coe.{succ u_1, succ u_1, succ u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (LinearMap.instFunLike.{u_2, u_2, u_1, u_1} R R M M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10))) x1._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.43 x2._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.43))) (OfNat.ofNat.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) 1 (One.toOfNat1.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) (MulOne.toOne.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) (MulOneClass.toMulOne.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) (Monoid.toMulOneClass.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) (MonoidWithZero.toMonoid.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) (Semiring.toMonoidWithZero.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) (Module.End.instSemiring.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19)))))))) x._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.64)","typeFull":"∀ {R : Type u_2} {M : Type u_1} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (x : M),\n  1 • x = 1 • x","typeReadable":"∀ {R : Type u_2} {M : Type u_1} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (x : M),\n  1 • x = 1 • x","typeReferences":[["MulOneClass","toMulOne"],["SMul","mk"],["Module","End"],["Module","End","instSemiring"],["MulOne","toOne"],["LinearMap","instFunLike"],["Module"],["Semiring","toMonoidWithZero"],["DFunLike","coe"],["OfNat","ofNat"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["One","toOfNat1"],["RingHom","id"],["MonoidWithZero","toMonoid"],["Monoid","toMulOneClass"],["HSMul","hSMul"],["instHSMul"],["Eq"],["Semiring"]],"valueReferences":[["rfl"],["MulOneClass","toMulOne"],["SMul","mk"],["Module","End"],["Module","End","instSemiring"],["LinearMap","instFunLike"],["MulOne","toOne"],["Semiring","toMonoidWithZero"],["DFunLike","coe"],["OfNat","ofNat"],["Semiring","toNonAssocSemiring"],["One","toOfNat1"],["RingHom","id"],["MonoidWithZero","toMonoid"],["Monoid","toMulOneClass"],["HSMul","hSMul"],["instHSMul"]]},{"isProp":true,"kind":"theorem","name":["DistribMulAction","toModuleEnd_apply"],"typeFallback":"forall (R : Type.{u_1}) {S : Type.{u_3}} (M : Type.{u_4}) [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 : AddCommMonoid.{u_4} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16 : Module.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.20 : Monoid.{u_3} S] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.23 : DistribMulAction.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.20 (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13)] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.27 : SMulCommClass.{u_3, u_1, u_4} S R M (SMulZeroClass.toSMul.{u_3, u_4} S M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_3, u_4} S M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.20 (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.23))) (SMulZeroClass.toSMul.{u_1, u_4} R M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_1, u_4} R M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_1, u_4} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16))))] (s : S), Eq.{succ u_4} (LinearMap.{u_1, u_1, u_4, u_4} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16) (DFunLike.coe.{max (succ u_3) (succ u_4), succ u_3, succ u_4} (MonoidHom.{u_3, u_4} S (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16) (MulOneClass.toMulOne.{u_3} S (Monoid.toMulOneClass.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.20)) (MulOneClass.toMulOne.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 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(Module.End.instSemiring.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16)))))) S (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : S) => Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16) (MonoidHom.instFunLike.{u_3, u_4} S (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16) (MulOneClass.toMulOne.{u_3} S (Monoid.toMulOneClass.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.20)) (MulOneClass.toMulOne.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16) (MulZeroOneClass.toMulOneClass.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16) (NonAssocSemiring.toMulZeroOneClass.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16) (Semiring.toNonAssocSemiring.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16) (Module.End.instSemiring.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16)))))) (DistribMulAction.toModuleEnd.{u_1, u_3, u_4} R S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.27) s) (DistribSMul.toLinearMap.{u_1, u_3, u_4} R S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16 (DistribMulAction.toDistribSMul.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.20 (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.23) inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.27 s)","typeFull":"∀ (R : Type u_1) {S : Type u_3} (M : Type u_4) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  [inst_3 : Monoid S] [inst_4 : DistribMulAction S M] [inst_5 : SMulCommClass S R M] (s : S),\n  (DistribMulAction.toModuleEnd R M) s = DistribSMul.toLinearMap R M s","typeReadable":"∀ (R : Type u_1) {S : Type u_3} (M : Type u_4) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  [inst_3 : Monoid S] [inst_4 : DistribMulAction S M] [inst_5 : SMulCommClass S R M] (s : S),\n  (DistribMulAction.toModuleEnd R M) s = DistribSMul.toLinearMap R M s","typeReferences":[["MulOneClass","toMulOne"],["Module"],["MonoidHom"],["MonoidHom","instFunLike"],["MulZeroOneClass","toMulOneClass"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["DistribSMul","toLinearMap"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["Monoid","toMulOneClass"],["Eq"],["NonAssocSemiring","toMulZeroOneClass"],["DistribMulAction"],["DistribSMul","toSMulZeroClass"],["Module","End"],["Module","End","instSemiring"],["DistribMulAction","toModuleEnd"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["LinearMap"],["SMulCommClass"],["Module","toDistribMulAction"],["Monoid"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["MulOneClass","toMulOne"],["Module","End"],["Module","End","instSemiring"],["DistribMulAction","toModuleEnd"],["MonoidHom"],["MonoidHom","instFunLike"],["MulZeroOneClass","toMulOneClass"],["LinearMap"],["DFunLike","coe"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Eq","refl"],["Monoid","toMulOneClass"],["NonAssocSemiring","toMulZeroOneClass"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","applyₗ","_proof_3"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_2}} {M₂ : Type.{u_3}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 : CommSemiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 : AddCommMonoid.{u_3} M₂] [inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 : Module.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 : Module.{u_1, u_3} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16] (v : M) (m : R) (x : LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26), Eq.{succ u_3} M₂ (AddHom.toFun.{max u_3 u_2, u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (AddCommMagma.toAdd.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommSemigroup.toAddCommMagma.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddCommSemigroup.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))))))) (AddCommMagma.toAdd.{u_3} M₂ (AddCommSemigroup.toAddCommMagma.{u_3} M₂ (AddCommMonoid.toAddCommSemigroup.{u_3} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16))) (LinearMap.toAddHom.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) 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inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 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inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13))) (AddZeroClass.toAddZero.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoid.toAddZeroClass.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_1, u_1, max u_2 u_3, u_3} R R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))))))) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoidHom.instFunLike.{u_2, max u_3 u_2} M (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13))) (AddZeroClass.toAddZero.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoid.toAddZeroClass.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_1, u_1, max u_2 u_3, u_3} R R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))))))) (LinearMap.applyₗ'.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) v)) (HSMul.hSMul.{u_1, max u_3 u_2, max u_3 u_2} R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (instHSMul.{u_1, max u_3 u_2} R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (SMulZeroClass.toSMul.{u_1, max u_3 u_2} R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddZero.toZero.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddZeroClass.toAddZero.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoid.toAddZeroClass.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddMonoid.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))))))) (DistribSMul.toSMulZeroClass.{u_1, max u_3 u_2} R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoid.toAddZeroClass.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddMonoid.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))))) (DistribMulAction.toDistribSMul.{u_1, max u_3 u_2} R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) 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inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))))) (Module.toDistribMulAction.{u_1, max u_3 u_2} R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26))))))) m x)) (HSMul.hSMul.{u_1, u_3, u_3} R M₂ M₂ (instHSMul.{u_1, u_3} R M₂ (SMulZeroClass.toSMul.{u_1, u_3} R M₂ (AddZero.toZero.{u_3} M₂ (AddZeroClass.toAddZero.{u_3} M₂ (AddMonoid.toAddZeroClass.{u_3} M₂ (AddCommMonoid.toAddMonoid.{u_3} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16)))) (DistribSMul.toSMulZeroClass.{u_1, u_3} R M₂ (AddMonoid.toAddZeroClass.{u_3} M₂ (AddCommMonoid.toAddMonoid.{u_3} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16)) (DistribMulAction.toDistribSMul.{u_1, u_3} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{u_3} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16) (Module.toDistribMulAction.{u_1, u_3} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26))))) (DFunLike.coe.{succ u_1, succ u_1, succ u_1} (RingHom.{u_1, u_1} R R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)) (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) R (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : R) => R) (RingHom.instFunLike.{u_1, u_1} R R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)) (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (RingHom.id.{u_1} R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommSemigroup.toAddCommMagma.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))))))) (AddCommMagma.toAdd.{u_3} M₂ (AddCommSemigroup.toAddCommMagma.{u_3} 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inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoid.toAddZeroClass.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))))))) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoidHom.instFunLike.{u_2, max u_3 u_2} M (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13))) (AddZeroClass.toAddZero.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddMonoid.toAddZeroClass.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (LinearMap.{u_1, u_1, max u_3 u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) (LinearMap.addCommMonoid.{u_1, u_1, max u_2 u_3, u_3} R R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))))))) (LinearMap.applyₗ'.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (LinearMap.applyₗ._proof_1.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26)) v)) x))","typeFull":"∀ {R : Type u_1} {M : Type u_2} {M₂ : Type u_3} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₂] [inst_3 : Module R M] [inst_4 : Module R M₂] (v : M) (m : R) (x : M →ₗ[R] M₂),\n  ((LinearMap.applyₗ' R) v).toFun (m • x) = (RingHom.id R) m • ((LinearMap.applyₗ' R) v).toFun x","typeReadable":"∀ {R : Type u_1} {M : Type u_2} {M₂ : Type u_3} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₂] [inst_3 : Module R M] [inst_4 : Module R M₂] (v : M) (m : R) (x : M →ₗ[R] M₂),\n  ((LinearMap.applyₗ' R) v).toFun (m • x) = (RingHom.id R) m • ((LinearMap.applyₗ' R) v).toFun x","typeReferences":[["RingHom"],["Module"],["CommSemiring"],["RingHom","instFunLike"],["LinearMap","toAddHom"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["AddMonoidHom"],["MonoidWithZero","toMonoid"],["AddMonoidHom","instFunLike"],["instHSMul"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["AddHom","toFun"],["Eq"],["DistribSMul","toSMulZeroClass"],["LinearMap","applyₗ","_proof_1"],["LinearMap","applyₗ'"],["CommSemiring","toSemiring"],["LinearMap","module"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["LinearMap"],["AddZeroClass","toAddZero"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["AddCommMonoid","toAddCommSemigroup"],["HSMul","hSMul"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["LinearMap","applyₗ","_proof_1"],["smulCommClass_self"],["LinearMap","applyₗ'"],["CommMonoid","toMonoid"],["CommSemiring","toSemiring"],["LinearMap","module"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["LinearMap"],["DFunLike","coe"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["AddMonoidHom"],["DistribMulAction","toMulAction"],["AddMonoidHom","instFunLike"],["LinearMap","map_smul'"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["Module","End","ofNat_apply"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_4}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.13 : AddCommMonoid.{u_4} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.19 : Module.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.13] (n : Nat) [inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.30 : Nat.AtLeastTwo n] (m : M), Eq.{succ u_4} M (DFunLike.coe.{succ u_4, succ u_4, succ u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.19) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (LinearMap.instFunLike.{u_1, u_1, u_4, u_4} R R M M inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.10))) ([mdata noindex:1 OfNat.ofNat.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.19) n (instOfNatAtLeastTwo.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.19) n (AddMonoidWithOne.toNatCast.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.19) (AddCommMonoidWithOne.toAddMonoidWithOne.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.19) (NonAssocSemiring.toAddCommMonoidWithOne.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.19) (Semiring.toNonAssocSemiring.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.19) (Module.End.instSemiring.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.19))))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.30)]) m) (HSMul.hSMul.{0, u_4, u_4} Nat M M (instHSMul.{0, u_4} Nat M (AddMonoid.toNSMul.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1254881606._hygCtx._hyg.13))) ([mdata noindex:1 OfNat.ofNat.{0} Nat n (instOfNatNat n)]) m)","typeFull":"∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (n : ℕ)\n  [inst_3 : n.AtLeastTwo] (m : M), (OfNat.ofNat n) m = OfNat.ofNat n • m","typeReadable":"∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (n : ℕ)\n  [inst_3 : n.AtLeastTwo] (m : M), (OfNat.ofNat n) m = OfNat.ofNat n • m","typeReferences":[["Module","End"],["Module","End","instSemiring"],["LinearMap","instFunLike"],["Module"],["instOfNatAtLeastTwo"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["OfNat","ofNat"],["AddCommMonoid"],["Nat"],["AddMonoidWithOne","toNatCast"],["Semiring","toNonAssocSemiring"],["AddMonoid","toNSMul"],["instOfNatNat"],["Nat","AtLeastTwo"],["RingHom","id"],["HSMul","hSMul"],["instHSMul"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Eq"],["NonAssocSemiring","toAddCommMonoidWithOne"],["Semiring"]],"valueReferences":[["rfl"],["Module","End"],["Module","End","instSemiring"],["AddMonoidWithOne","toNatCast"],["Semiring","toNonAssocSemiring"],["LinearMap","instFunLike"],["RingHom","id"],["instOfNatAtLeastTwo"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["NonAssocSemiring","toAddCommMonoidWithOne"],["DFunLike","coe"],["OfNat","ofNat"]]},{"isProp":false,"kind":"definition","name":["DistribSMul","toLinearMap"],"typeFallback":"forall (R : Type.{u_1}) {S : Type.{u_3}} (M : Type.{u_4}) [inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13 : AddCommMonoid.{u_4} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.16 : Module.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.23 : DistribSMul.{u_3, u_4} S M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13))] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.27 : SMulCommClass.{u_3, u_1, u_4} S R M (SMulZeroClass.toSMul.{u_3, u_4} S M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_3, u_4} S M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13)) inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.23)) (SMulZeroClass.toSMul.{u_1, u_4} R M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_1, u_4} R M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_1, u_4} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.16))))], S -> (LinearMap.{u_1, u_1, u_4, u_4} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3803786946._hygCtx._hyg.16)","typeFull":"(R : Type u_1) →\n  {S : Type u_3} →\n    (M : Type u_4) →\n      [inst : Semiring R] →\n        [inst_1 : AddCommMonoid M] →\n          [inst_2 : Module R M] → [inst_3 : DistribSMul S M] → [SMulCommClass S R M] → S → M →ₗ[R] M","typeReadable":"(R : Type u_1) →\n  {S : Type u_3} →\n    (M : Type u_4) →\n      [inst : Semiring R] →\n        [inst_1 : AddCommMonoid M] →\n          [inst_2 : Module R M] → [inst_3 : DistribSMul S M] → [SMulCommClass S R M] → S → M →ₗ[R] M","typeReferences":[["Module"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["LinearMap"],["AddZeroClass","toAddZero"],["DistribSMul"],["SMulCommClass"],["Module","toDistribMulAction"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["AddZero","toZero"],["Semiring"],["AddMonoid","toAddZeroClass"],["DistribSMul","toSMulZeroClass"]],"valueReferences":[["LinearMap","mk"],["AddHom","mk"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["DistribSMul","toLinearMap","_proof_2"],["Semiring","toNonAssocSemiring"],["AddCommMonoid","toAddCommSemigroup"],["RingHom","id"],["HSMul","hSMul"],["DistribSMul","toLinearMap","_proof_1"],["instHSMul"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["AddZero","toZero"],["DistribSMul","toSMulZeroClass"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["Module","End","instSemiring","_proof_10"],"typeFallback":"forall 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inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)))) (Module.End.instOne.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) 1 (One.toOfNat1.{u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) (Module.End.instOne.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19)))) (HAdd.hAdd.{u_1, u_1, u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 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(LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) (AddMonoid.toAddSemigroup.{u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) (AddMonoidWithOne.toAddMonoid.{u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) (AddMonoidWithOne.unary.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) (AddCommMonoid.toAddMonoid.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) (LinearMap.addCommMonoid.{u_2, u_2, u_1, u_1} R R M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 (RingHom.id.{u_2} R 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(AddMonoidWithOne.toAddMonoid.{u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) (AddMonoidWithOne.unary.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) (AddCommMonoid.toAddMonoid.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) (LinearMap.addCommMonoid.{u_2, u_2, u_1, u_1} R R M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)))) (Module.End.instOne.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19))) n (OfNat.ofNat.{u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) 1 (One.toOfNat1.{u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) (Module.End.instOne.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19)))) (OfNat.ofNat.{u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) 1 (One.toOfNat1.{u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) (Module.End.instOne.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19))))","typeFull":"∀ {R : Type u_2} {M : Type u_1} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (n : ℕ),\n  AddMonoid.nsmul (n + 1) 1 = AddMonoid.nsmul n 1 + 1","typeReadable":"∀ {R : Type u_2} {M : Type u_1} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (n : ℕ),\n  AddMonoid.nsmul (n + 1) 1 = AddMonoid.nsmul n 1 + 1","typeReferences":[["instAddNat"],["Module","End"],["instHAdd"],["Module"],["AddCommMonoid","toAddMonoid"],["LinearMap"],["AddMonoid","nsmul"],["AddMonoidWithOne","toAddMonoid"],["OfNat","ofNat"],["HAdd","hAdd"],["LinearMap","addCommMonoid"],["AddCommMonoid"],["Nat"],["AddMonoidWithOne","unary"],["Semiring","toNonAssocSemiring"],["One","toOfNat1"],["instOfNatNat"],["RingHom","id"],["AddMonoid","toAddSemigroup"],["Module","End","instOne"],["Eq"],["AddSemigroup","toAdd"],["Semiring"]],"valueReferences":[["LinearMap","addCommMonoid"],["Module","End"],["AddMonoidWithOne","unary"],["Semiring","toNonAssocSemiring"],["One","toOfNat1"],["RingHom","id"],["Module","End","instOne"],["AddMonoid","nsmul_succ"],["AddCommMonoid","toAddMonoid"],["AddMonoidWithOne","toAddMonoid"],["LinearMap"],["OfNat","ofNat"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","smulRight","congr_simp"],"typeFallback":"forall {R : Type.{u_1}} {S : Type.{u_3}} {M : Type.{u_4}} {M₁ : Type.{u_5}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.13 : AddCommMonoid.{u_4} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.16 : AddCommMonoid.{u_5} M₁] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.19 : Module.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.23 : Module.{u_1, u_5} R M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.27 : Semiring.{u_3} S] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.30 : Module.{u_1, u_3} R S inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.27)))] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.34 : Module.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.38 : IsScalarTower.{u_1, u_3, u_4} R S M (SMulZeroClass.toSMul.{u_1, u_3} R S (AddZero.toZero.{u_3} S (AddZeroClass.toAddZero.{u_3} S (AddMonoid.toAddZeroClass.{u_3} S (AddMonoidWithOne.toAddMonoid.{u_3} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_3} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.27))))))) (DistribSMul.toSMulZeroClass.{u_1, u_3} R S (AddMonoid.toAddZeroClass.{u_3} S (AddMonoidWithOne.toAddMonoid.{u_3} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_3} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.27))))) (DistribMulAction.toDistribSMul.{u_1, u_3} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10)) (AddMonoidWithOne.toAddMonoid.{u_3} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_3} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.27)))) (Module.toDistribMulAction.{u_1, u_3} R S inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.27))) inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.30)))) (SMulZeroClass.toSMul.{u_3, u_4} S M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_3, u_4} S M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_3, u_4} S M (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.27)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.34)))) (SMulZeroClass.toSMul.{u_1, u_4} R M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_1, u_4} R M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_1, u_4} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.19))))] (f : LinearMap.{u_1, u_1, u_5, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10)) M₁ S inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.27))) inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.30) (f_1 : LinearMap.{u_1, u_1, u_5, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10)) M₁ S inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.27))) inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.30), (Eq.{max (succ u_5) (succ u_3)} (LinearMap.{u_1, u_1, u_5, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10)) M₁ S inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.27))) inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.30) f f_1) -> (forall (x : M) (x_1 : M), (Eq.{succ u_4} M x x_1) -> (Eq.{max (succ u_5) (succ u_4)} (LinearMap.{u_1, u_1, u_5, u_4} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10)) M₁ M inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.19) (LinearMap.smulRight.{u_1, u_3, u_4, u_5} R S M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.34 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.38 f x) (LinearMap.smulRight.{u_1, u_3, u_4, u_5} R S M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.34 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.38 f_1 x_1)))","typeFull":"∀ {R : Type u_1} {S : Type u_3} {M : Type u_4} {M₁ : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₁] [inst_3 : Module R M] [inst_4 : Module R M₁] [inst_5 : Semiring S] [inst_6 : Module R S]\n  [inst_7 : Module S M] [inst_8 : IsScalarTower R S M] (f f_1 : M₁ →ₗ[R] S),\n  f = f_1 → ∀ (x x_1 : M), x = x_1 → f.smulRight x = f_1.smulRight x_1","typeReadable":"∀ {R : Type u_1} {S : Type u_3} {M : Type u_4} {M₁ : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₁] [inst_3 : Module R M] [inst_4 : Module R M₁] [inst_5 : Semiring S] [inst_6 : Module R S]\n  [inst_7 : Module S M] [inst_8 : IsScalarTower R S M] (f f_1 : M₁ →ₗ[R] S),\n  f = f_1 → ∀ (x x_1 : M), x = x_1 → f.smulRight x = f_1.smulRight x_1","typeReferences":[["LinearMap","smulRight"],["Module"],["IsScalarTower"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["LinearMap"],["AddZeroClass","toAddZero"],["AddMonoidWithOne","toAddMonoid"],["Module","toDistribMulAction"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Eq"],["NonAssocSemiring","toAddCommMonoidWithOne"],["AddZero","toZero"],["DistribSMul","toSMulZeroClass"],["Semiring"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["LinearMap","smulRight"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Eq","refl"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["Eq"],["LinearMap"],["Eq","rec"]]},{"isProp":true,"kind":"theorem","name":["Module","End","apply_faithfulSMul"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_4}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.711589862._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.711589862._hygCtx._hyg.13 : AddCommMonoid.{u_4} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.711589862._hygCtx._hyg.19 : Module.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.711589862._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.711589862._hygCtx._hyg.13], FaithfulSMul.{u_4, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.711589862._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.711589862._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.711589862._hygCtx._hyg.19) M (SMulZeroClass.toSMul.{u_4, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.711589862._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.711589862._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.711589862._hygCtx._hyg.19) M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.711589862._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_4, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.711589862._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.711589862._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.711589862._hygCtx._hyg.19) M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.711589862._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_4, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.711589862._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.711589862._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.711589862._hygCtx._hyg.19) M (Module.End.instMonoid.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.711589862._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.711589862._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.711589862._hygCtx._hyg.19) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.711589862._hygCtx._hyg.13) (Module.toDistribMulAction.{u_4, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.711589862._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.711589862._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.711589862._hygCtx._hyg.19) M (Module.End.instSemiring.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.711589862._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.711589862._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.711589862._hygCtx._hyg.19) inst._@.Mathlib.Algebra.Module.LinearMap.End.711589862._hygCtx._hyg.13 (Module.End.applyModule.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.711589862._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.711589862._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.711589862._hygCtx._hyg.19)))))","typeFull":"∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],\n  FaithfulSMul (Module.End R M) M","typeReadable":"∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],\n  FaithfulSMul (Module.End R M) M","typeReferences":[["Module","End"],["Module","End","instSemiring"],["Module"],["DistribMulAction","toDistribSMul"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["FaithfulSMul"],["AddZeroClass","toAddZero"],["Module","End","applyModule"],["Module","toDistribMulAction"],["AddCommMonoid"],["Module","End","instMonoid"],["AddZero","toZero"],["Semiring"],["AddMonoid","toAddZeroClass"],["DistribSMul","toSMulZeroClass"]],"valueReferences":[["Module","End"],["Module","End","instSemiring"],["DistribMulAction","toDistribSMul"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["Module","toDistribMulAction"],["Module","End","applyModule"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["LinearMap","ext"],["Module","End","instMonoid"],["FaithfulSMul","mk"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["DistribSMul","toSMulZeroClass"]]},{"isProp":true,"kind":"theorem","name":["Module","End","apply_isScalarTower"],"typeFallback":"forall {R : Type.{u_1}} {S : Type.{u_3}} {M : Type.{u_4}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.13 : AddCommMonoid.{u_4} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.19 : Module.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.27 : Monoid.{u_3} S] [inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.30 : DistribMulAction.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.27 (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.13)] [inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.34 : SMulCommClass.{u_1, u_3, u_4} R S M (SMulZeroClass.toSMul.{u_1, u_4} R M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_1, u_4} R M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_1, u_4} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.19)))) (SMulZeroClass.toSMul.{u_3, u_4} S M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_3, u_4} S M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.27 (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.30)))], IsScalarTower.{u_3, u_4, u_4} S (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.19) M (LinearMap.instSMul.{u_1, u_1, u_3, u_4, u_4} R R S M M inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.10)) (DistribMulAction.toDistribSMul.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.27 (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.30) inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.34) (SMulZeroClass.toSMul.{u_4, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.19) M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_4, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.19) M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_4, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.19) M (Module.End.instMonoid.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.19) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.13) (Module.toDistribMulAction.{u_4, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.19) M (Module.End.instSemiring.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.19) inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.13 (Module.End.applyModule.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.19))))) (SMulZeroClass.toSMul.{u_3, u_4} S M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_3, u_4} S M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.27 (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.LinearMap.End.1611029379._hygCtx._hyg.30)))","typeFull":"∀ {R : Type u_1} {S : Type u_3} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  [inst_3 : Monoid S] [inst_4 : DistribMulAction S M] [inst_5 : SMulCommClass R S M], IsScalarTower S (Module.End R M) M","typeReadable":"∀ {R : Type u_1} {S : Type u_3} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  [inst_3 : Monoid S] [inst_4 : DistribMulAction S M] [inst_5 : SMulCommClass R S M], IsScalarTower S (Module.End R M) M","typeReferences":[["Module","End"],["Module","End","instSemiring"],["IsScalarTower"],["Module"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["SMulCommClass"],["Module","End","applyModule"],["Module","toDistribMulAction"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["Monoid"],["LinearMap","instSMul"],["Module","End","instMonoid"],["AddZero","toZero"],["DistribMulAction"],["Semiring"],["AddMonoid","toAddZeroClass"],["DistribSMul","toSMulZeroClass"]],"valueReferences":[["rfl"],["Module","End"],["Module","End","instSemiring"],["DistribMulAction","toDistribSMul"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["IsScalarTower","mk"],["Module","End","applyModule"],["Module","toDistribMulAction"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["HSMul","hSMul"],["instHSMul"],["LinearMap","instSMul"],["Module","End","instMonoid"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["DistribSMul","toSMulZeroClass"]]},{"isProp":false,"kind":"definition","name":["Module","End","applyModule"],"typeFallback":"forall 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inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13","typeFull":"{R : Type u_1} →\n  {M : Type u_4} → [inst : Semiring R] → [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → Module (Module.End R M) M","typeReadable":"{R : Type u_1} →\n  {M : Type u_4} → [inst : Semiring R] → [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → Module (Module.End R M) M","typeReferences":[["Module","End"],["AddCommMonoid"],["Module","End","instSemiring"],["Module"],["Semiring"]],"valueReferences":[["SMul","mk"],["Module","End","applyModule","_proof_2"],["Module","End"],["Module","End","instSemiring"],["LinearMap","instFunLike"],["SemigroupAction","mk"],["Module","End","applyModule","_proof_5"],["DistribMulAction","mk"],["Semiring","toMonoidWithZero"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["Module","End","applyModule","_proof_3"],["Module","mk"],["Semiring","toNonAssocSemiring"],["Module","End","applyModule","_proof_4"],["RingHom","id"],["MonoidWithZero","toMonoid"],["Module","End","applyModule","_proof_6"],["Monoid","toSemigroup"],["Module","End","applyModule","_proof_1"],["MulAction","mk"]]},{"isProp":true,"kind":"theorem","name":["Module","End","instMonoid","_proof_4"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19 : Module.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13] (f : LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.3319175497._hygCtx._hyg.19), Eq.{succ u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10))))) f) (OfNat.ofNat.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 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inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)))))","typeFull":"∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (f : M →ₗ[R] M),\n  0 ∘ₗ f = 0","typeReadable":"∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (f : M →ₗ[R] M),\n  0 ∘ₗ f = 0","typeReferences":[["LinearMap","instZero"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Module"],["Module","End","instMul","_proof_1"],["LinearMap","comp"],["Zero","toOfNat0"],["Eq"],["LinearMap"],["OfNat","ofNat"],["Semiring"]],"valueReferences":[["Semiring","toNonAssocSemiring"],["RingHom","id"],["Module","End","instMul","_proof_1"],["LinearMap","zero_comp"]]},{"isProp":true,"kind":"theorem","name":["_private","Mathlib","Algebra","Module","LinearMap","End",0,"LinearMap","smulRight_apply_eq_zero_iff","_simp_1_2"],"typeFallback":"forall {α : Sort.{u_1}} {q : Prop} {p : α -> Prop}, Eq.{1} Prop (forall (x : α), Or (p x) q) (Or (forall (x : α), p x) q)","typeFull":"∀ {α : Sort u_1} {q : Prop} {p : α → Prop}, (∀ (x : α), p x ∨ q) = ((∀ (x : α), p x) ∨ q)","typeReadable":"∀ {α : Sort u_1} {q : Prop} {p : α → Prop}, (∀ (x : α), p x ∨ q) = ((∀ (x : α), p x) ∨ q)","typeReferences":[["Or"],["Eq"]],"valueReferences":[["forall_or_right"],["Or"],["propext"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","applyₗ'","_proof_5"],"typeFallback":"forall {R : Type.{u_4}} (S : Type.{u_3}) {M : Type.{u_2}} {M₂ : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 : Semiring.{u_4} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 : Semiring.{u_3} S] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 : AddCommMonoid.{u_1} M₂] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 : Module.{u_4, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 : Module.{u_4, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 : Module.{u_3, u_1} S M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50 : SMulCommClass.{u_4, u_3, u_1} R S M₂ (SMulZeroClass.toSMul.{u_4, u_1} R M₂ (AddZero.toZero.{u_1} M₂ (AddZeroClass.toAddZero.{u_1} M₂ (AddMonoid.toAddZeroClass.{u_1} M₂ (AddCommMonoid.toAddMonoid.{u_1} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22)))) (DistribSMul.toSMulZeroClass.{u_4, u_1} R M₂ (AddMonoid.toAddZeroClass.{u_1} M₂ (AddCommMonoid.toAddMonoid.{u_1} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22)) (DistribMulAction.toDistribSMul.{u_4, u_1} R M₂ (MonoidWithZero.toMonoid.{u_4} R (Semiring.toMonoidWithZero.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22) (Module.toDistribMulAction.{u_4, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33)))) (SMulZeroClass.toSMul.{u_3, u_1} S M₂ (AddZero.toZero.{u_1} M₂ (AddZeroClass.toAddZero.{u_1} M₂ (AddMonoid.toAddZeroClass.{u_1} M₂ (AddCommMonoid.toAddMonoid.{u_1} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22)))) (DistribSMul.toSMulZeroClass.{u_3, u_1} S M₂ (AddMonoid.toAddZeroClass.{u_1} M₂ (AddCommMonoid.toAddMonoid.{u_1} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22)) (DistribMulAction.toDistribSMul.{u_3, u_1} S M₂ (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (AddCommMonoid.toAddMonoid.{u_1} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22) (Module.toDistribMulAction.{u_3, u_1} S M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41))))], Eq.{max (succ u_1) (succ (max u_2 u_1))} (LinearMap.{u_3, u_3, max u_2 u_1, u_1} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (LinearMap.addCommMonoid.{u_4, u_4, u_2, u_1} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_4, u_4, u_3, u_2, u_1} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41) (LinearMap.mk.{u_3, u_3, max u_2 u_1, u_1} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (LinearMap.addCommMonoid.{u_4, u_4, u_2, u_1} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_4, u_4, u_3, u_2, u_1} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 (AddHom.mk.{max u_2 u_1, u_1} (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (AddCommMagma.toAdd.{max u_2 u_1} (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) (AddCommSemigroup.toAddCommMagma.{max u_2 u_1} (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) (AddCommMonoid.toAddCommSemigroup.{max u_2 u_1} (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) (LinearMap.addCommMonoid.{u_4, u_4, u_2, u_1} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)))))) (AddCommMagma.toAdd.{u_1} M₂ (AddCommSemigroup.toAddCommMagma.{u_1} M₂ (AddCommMonoid.toAddCommSemigroup.{u_1} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22))) (fun (f : LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) => DFunLike.coe.{max (succ u_2) (succ u_1), succ u_2, succ u_1} (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M₂) (LinearMap.instFunLike.{u_4, u_4, u_2, u_1} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) f (OfNat.ofNat.{u_2} M 0 (Zero.toOfNat0.{u_2} M (AddZero.toZero.{u_2} M (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16))))))) (LinearMap.applyₗ'._proof_3.{u_4, u_2, u_1} R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33)) (LinearMap.applyₗ'._proof_4.{u_4, u_2, u_1, u_3} R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50)) (OfNat.ofNat.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (LinearMap.addCommMonoid.{u_4, u_4, u_2, u_1} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_4, u_4, u_3, u_2, u_1} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41) 0 (Zero.toOfNat0.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (LinearMap.addCommMonoid.{u_4, u_4, u_2, u_1} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_4, u_4, u_3, u_2, u_1} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41) (AddZero.toZero.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (LinearMap.addCommMonoid.{u_4, u_4, u_2, u_1} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_4, u_4, u_3, u_2, u_1} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41) (AddZeroClass.toAddZero.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (LinearMap.addCommMonoid.{u_4, u_4, u_2, u_1} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_4, u_4, u_3, u_2, u_1} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41) (AddMonoid.toAddZeroClass.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (LinearMap.addCommMonoid.{u_4, u_4, u_2, u_1} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_4, u_4, u_3, u_2, u_1} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41) (AddCommMonoid.toAddMonoid.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (LinearMap.addCommMonoid.{u_4, u_4, u_2, u_1} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_4, u_4, u_3, u_2, u_1} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41) (LinearMap.addCommMonoid.{u_3, u_3, max u_2 u_1, u_1} S S (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_4, u_4, u_2, u_1} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 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inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)))))))))","typeFull":"∀ {R : Type u_4} (S : Type u_3) {M : Type u_2} {M₂ : Type u_1} [inst : Semiring R] [inst_1 : Semiring S]\n  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R M₂]\n  [inst_6 : Module S M₂] [inst_7 : SMulCommClass R S M₂], { toFun := fun f => f 0, map_add' := ⋯, map_smul' := ⋯ } = 0","typeReadable":"∀ {R : Type u_4} (S : Type u_3) {M : Type u_2} {M₂ : Type u_1} [inst : Semiring R] [inst_1 : Semiring S]\n  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R M₂]\n  [inst_6 : Module S M₂] [inst_7 : SMulCommClass R S M₂], { toFun := fun f => f 0, map_add' := ⋯, map_smul' := ⋯ } = 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(R : Type.{u_1}) {S : Type.{u_3}} (M : Type.{u_4}) [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 : AddCommMonoid.{u_4} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16 : Module.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.20 : Monoid.{u_3} S] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.23 : DistribMulAction.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.20 (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13)] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.27 : SMulCommClass.{u_3, u_1, u_4} S R M 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M] →\n            [inst_3 : Monoid S] → [inst_4 : DistribMulAction S M] → [SMulCommClass S R M] → S →* Module.End R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.2494121438._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2494121438._hygCtx._hyg.19) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (LinearMap.instFunLike.{u_1, u_1, u_4, u_4} R R M M inst._@.Mathlib.Algebra.Module.LinearMap.End.2494121438._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2494121438._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2494121438._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2494121438._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2494121438._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.2494121438._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2494121438._hygCtx._hyg.10))) (HPow.hPow.{u_4, 0, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.2494121438._hygCtx._hyg.10 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inst._@.Mathlib.Algebra.Module.LinearMap.End.2494121438._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2494121438._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2494121438._hygCtx._hyg.19))) f' n))) -> (Function.Surjective.{succ u_4, succ u_4} M M (DFunLike.coe.{succ u_4, succ u_4, succ u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.2494121438._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2494121438._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2494121438._hygCtx._hyg.19) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (LinearMap.instFunLike.{u_1, u_1, u_4, u_4} R R M M inst._@.Mathlib.Algebra.Module.LinearMap.End.2494121438._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2494121438._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2494121438._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2494121438._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2494121438._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.2494121438._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2494121438._hygCtx._hyg.10))) f'))","typeFull":"∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  {f' : Module.End R M} {n : ℕ}, n ≠ 0 → Function.Surjective ⇑(f' ^ n) → Function.Surjective ⇑f'","typeReadable":"∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  {f' : Module.End R M} {n : ℕ}, n ≠ 0 → Function.Surjective ⇑(f' ^ n) → Function.Surjective 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{R : Type.{u_1}} {S : Type.{u_3}} {M : Type.{u_4}} {M₁ : Type.{u_5}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.2009836238._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2009836238._hygCtx._hyg.13 : AddCommMonoid.{u_4} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2009836238._hygCtx._hyg.16 : AddCommMonoid.{u_5} M₁] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2009836238._hygCtx._hyg.19 : Module.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.2009836238._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2009836238._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2009836238._hygCtx._hyg.23 : Module.{u_1, u_5} R M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.2009836238._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2009836238._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2009836238._hygCtx._hyg.27 : Semiring.{u_3} S] 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inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddGroup.toSubNegMonoid.{u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddCommGroup.toAddGroup.{u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (LinearMap.addCommGroup.{u_2, u_2, u_1, u_1} R R N₁ N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10))))))) (Nat.cast.{0} Int instNatCastInt n) (OfNat.ofNat.{u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) 1 (One.toOfNat1.{u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (Module.End.instOne.{u_2, u_1} R N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23)))) (HSMul.hSMul.{0, u_1, u_1} Nat (Module.End.{u_2, u_1} R N₁ 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(AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (SubNegMonoid.toAddMonoid.{u_1} (Module.End.{u_2, u_1} R N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddGroup.toSubNegMonoid.{u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddCommGroup.toAddGroup.{u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (LinearMap.addCommGroup.{u_2, u_2, u_1, u_1} R R N₁ N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)))))))) n (OfNat.ofNat.{u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) 1 (One.toOfNat1.{u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (Module.End.instOne.{u_2, u_1} R N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_1} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23))))","typeFull":"∀ {R : Type u_2} {N₁ : Type u_1} [inst : Semiring R] [inst_1 : AddCommGroup N₁] [inst_2 : Module R N₁] (n : ℕ),\n  ↑n • 1 = n • 1","typeReadable":"∀ {R : Type u_2} {N₁ : Type u_1} [inst : Semiring R] [inst_1 : AddCommGroup N₁] [inst_2 : Module R N₁] (n : ℕ),\n  ↑n • 1 = n • 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[inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19 : Module.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13] (f : LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19 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inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (LinearMap.instFunLike.{u_1, u_1, u_2, u_2} R R M M inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10))) f x) (DFunLike.coe.{succ u_2, succ u_2, succ u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.4080895308._hygCtx._hyg.10))) g x))","typeFull":"∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (f g : M →ₗ[R] M)\n  (x : M), (f + g) x = f x + g x","typeReadable":"∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (f g : M →ₗ[R] M)\n  (x : M), (f + g) x = f x + g x","typeReferences":[["LinearMap","instFunLike"],["Module"],["instHAdd"],["LinearMap"],["DFunLike","coe"],["HAdd","hAdd"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["AddCommMonoid","toAddCommSemigroup"],["RingHom","id"],["LinearMap","instAdd"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Eq"],["Semiring"]],"valueReferences":[["Semiring","toNonAssocSemiring"],["RingHom","id"],["LinearMap","add_apply"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","smulRightₗ","_proof_7"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10 : CommSemiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 : Module.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13], IsScalarTower.{u_1, u_1, u_2} R R M (SemigroupAction.toSMul.{u_1, u_1} R R (Monoid.toSemigroup.{u_1} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) (MulAction.toSemigroupAction.{u_1, u_1} R R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (Monoid.toMulAction.{u_1} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))))) (SemigroupAction.toSMul.{u_1, u_2} R M (Monoid.toSemigroup.{u_1} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22))))","typeFull":"∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],\n  IsScalarTower R R M","typeReadable":"∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],\n  IsScalarTower R R M","typeReferences":[["Module"],["IsScalarTower"],["CommSemiring"],["CommSemiring","toSemiring"],["SemigroupAction","toSMul"],["Semiring","toMonoidWithZero"],["AddCommMonoid","toAddMonoid"],["Monoid","toMulAction"],["Module","toDistribMulAction"],["AddCommMonoid"],["MonoidWithZero","toMonoid"],["DistribMulAction","toMulAction"],["Monoid","toSemigroup"],["MulAction","toSemigroupAction"]],"valueReferences":[["Module","toDistribMulAction"],["IsScalarTower","left"],["CommSemiring","toSemiring"],["MonoidWithZero","toMonoid"],["DistribMulAction","toMulAction"],["Semiring","toMonoidWithZero"],["AddCommMonoid","toAddMonoid"]]},{"isProp":true,"kind":"theorem","name":["_private","Mathlib","Algebra","Module","LinearMap","End",0,"LinearMap","smulRight_apply_eq_zero_iff","_simp_1_1"],"typeFallback":"forall {F : Sort.{u_1}} {α : Sort.{u_2}} {β : α -> Sort.{u_3}} [i : DFunLike.{u_1, u_2, u_3} F α β] {f : F} {g : F}, Eq.{1} Prop (Eq.{u_1} F f g) (forall (x : α), Eq.{u_3} (β x) (DFunLike.coe.{u_1, u_2, u_3} F α β i f x) (DFunLike.coe.{u_1, u_2, u_3} F α β i g x))","typeFull":"∀ {F : Sort u_1} {α : Sort u_2} {β : α → Sort u_3} [i : DFunLike F α β] {f g : F}, (f = g) = ∀ (x : α), f x = g x","typeReadable":"∀ {F : Sort u_1} {α : Sort u_2} {β : α → Sort u_3} [i : DFunLike F α β] {f g : F}, (f = g) = ∀ (x : α), f x = g x","typeReferences":[["DFunLike"],["Eq"],["DFunLike","coe"]],"valueReferences":[["DFunLike","ext_iff"],["Eq"],["DFunLike","coe"],["propext"]]},{"isProp":true,"kind":"theorem","name":["Module","toModuleEnd","_proof_4"],"typeFallback":"forall (R : Type.{u_2}) {S : Type.{u_3}} (M : Type.{u_1}) [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 : Semiring.{u_2} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 : AddCommMonoid.{u_1} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16 : Module.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20 : Semiring.{u_3} S] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.23 : Module.{u_3, u_1} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.27 : SMulCommClass.{u_3, u_2, u_1} S R M (SMulZeroClass.toSMul.{u_3, u_1} S M (AddZero.toZero.{u_1} M (AddZeroClass.toAddZero.{u_1} M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_3, u_1} S M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_3, u_1} S M 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(MonoidWithZero.toMonoid.{u_2} R (Semiring.toMonoidWithZero.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13) (Module.toDistribMulAction.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16))))] (x._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.63 : S) (x._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.65 : S), Eq.{succ u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (DistribSMul.toLinearMap.{u_2, u_3, u_1} R S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16 (DistribMulAction.toDistribSMul.{u_3, u_1} S M (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20 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(AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (Semiring.toNonAssocSemiring.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (Module.End.instSemiring.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16))))))))) (DistribSMul.toLinearMap.{u_2, u_3, u_1} R S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16 (DistribMulAction.toDistribSMul.{u_3, u_1} S M (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.23)) 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inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.27 x._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.65))","typeFull":"∀ (R : Type u_2) {S : Type u_3} (M : Type u_1) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  [inst_3 : Semiring S] [inst_4 : Module S M] [inst_5 : SMulCommClass S R M] (x x_1 : S),\n  DistribSMul.toLinearMap R M (x + x_1) = DistribSMul.toLinearMap R M x + DistribSMul.toLinearMap R M x_1","typeReadable":"∀ (R : Type u_2) {S : Type u_3} (M : Type u_1) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  [inst_3 : Semiring S] [inst_4 : Module S M] [inst_5 : SMulCommClass S R M] (x x_1 : S),\n  DistribSMul.toLinearMap R M (x + x_1) = DistribSMul.toLinearMap R M x + DistribSMul.toLinearMap R M x_1","typeReferences":[["Module"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddMonoidWithOne","toAddMonoid"],["DistribSMul","toLinearMap"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Eq"],["NonAssocSemiring","toAddCommMonoidWithOne"],["DistribSMul","toSMulZeroClass"],["Module","End"],["Module","End","instSemiring"],["instHAdd"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["LinearMap"],["AddZero","toAdd"],["HAdd","hAdd"],["SMulCommClass"],["Module","toDistribMulAction"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["Module","End"],["Module","End","instSemiring"],["instHAdd"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddCommMonoid","toAddMonoid"],["AddMonoidWithOne","toAddMonoid"],["AddZero","toAdd"],["AddZeroClass","toAddZero"],["DistribSMul","toLinearMap"],["HAdd","hAdd"],["Module","toDistribMulAction"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["LinearMap","ext"],["MonoidWithZero","toMonoid"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["NonAssocSemiring","toAddCommMonoidWithOne"],["add_smul"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["Module","End","instSemiring","_proof_11"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 : Module.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13] (x : Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19), Eq.{succ u_2} (Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) (Monoid.npow.{u_2} (Module.End.{u_1, 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inst._@.Mathlib.Algebra.Module.LinearMap.End.262892056._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.262892056._hygCtx._hyg.19) (n : Nat) (m : M), Eq.{succ u_4} M (DFunLike.coe.{succ u_4, succ u_4, succ u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.262892056._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.262892056._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.262892056._hygCtx._hyg.19) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (LinearMap.instFunLike.{u_1, u_1, u_4, u_4} R R M M inst._@.Mathlib.Algebra.Module.LinearMap.End.262892056._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.262892056._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.262892056._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.262892056._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.262892056._hygCtx._hyg.19 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inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13] (g : LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19), Eq.{succ u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) 0 (Zero.toOfNat0.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) (LinearMap.instZero.{u_1, u_1, u_2, u_2} R R M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 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inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) 0 (Zero.toOfNat0.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) (LinearMap.instZero.{u_1, u_1, u_2, u_2} R R M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 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inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23), Eq.{succ u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (SubNegMonoid.zsmul.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddGroup.toSubNegMonoid.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddCommGroup.toAddGroup.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (LinearMap.addCommGroup.{u_1, u_1, u_2, u_2} R R N₁ N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10))))) (Nat.cast.{0} Int instNatCastInt (Nat.succ n)) a) (HAdd.hAdd.{u_2, u_2, u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (instHAdd.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddSemigroup.toAdd.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddMonoid.toAddSemigroup.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (SubNegMonoid.toAddMonoid.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddGroup.toSubNegMonoid.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddCommGroup.toAddGroup.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (LinearMap.addCommGroup.{u_1, u_1, u_2, u_2} R R N₁ N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10))))))))) (SubNegMonoid.zsmul.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddGroup.toSubNegMonoid.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (AddCommGroup.toAddGroup.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10)) N₁ N₁ (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23) (LinearMap.addCommGroup.{u_1, u_1, u_2, u_2} R R N₁ N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_2} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.23 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.401737074._hygCtx._hyg.10))))) (Nat.cast.{0} Int instNatCastInt n) a) a)","typeFull":"∀ {R : Type u_1} {N₁ : Type u_2} [inst : Semiring R] [inst_1 : AddCommGroup N₁] [inst_2 : Module R N₁] (n : ℕ)\n  (a : N₁ →ₗ[R] N₁), SubNegMonoid.zsmul (↑n.succ) a = SubNegMonoid.zsmul (↑n) a + a","typeReadable":"∀ {R : Type u_1} {N₁ : Type u_2} [inst : Semiring R] [inst_1 : AddCommGroup N₁] [inst_2 : Module R N₁] (n : ℕ)\n  (a : N₁ →ₗ[R] N₁), SubNegMonoid.zsmul (↑n.succ) a = SubNegMonoid.zsmul (↑n) a + a","typeReferences":[["Nat","cast"],["instHAdd"],["Module"],["SubNegMonoid","zsmul"],["AddCommGroup","toAddGroup"],["AddCommGroup"],["LinearMap"],["Int"],["HAdd","hAdd"],["Nat"],["Semiring","toNonAssocSemiring"],["SubNegMonoid","toAddMonoid"],["Nat","succ"],["RingHom","id"],["AddMonoid","toAddSemigroup"],["AddCommGroup","toAddCommMonoid"],["AddGroup","toSubNegMonoid"],["Eq"],["LinearMap","addCommGroup"],["AddSemigroup","toAdd"],["instNatCastInt"],["Semiring"]],"valueReferences":[["Semiring","toNonAssocSemiring"],["RingHom","id"],["AddCommGroup","toAddGroup"],["SubNegMonoid","zsmul_succ'"],["AddCommGroup","toAddCommMonoid"],["AddGroup","toSubNegMonoid"],["LinearMap","addCommGroup"],["LinearMap"]]},{"isProp":true,"kind":"theorem","name":["Module","End","smul_def"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_4}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.13 : AddCommMonoid.{u_4} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.19 : Module.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.13] (f : Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.19) (a : M), Eq.{succ u_4} M (HSMul.hSMul.{u_4, u_4, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.19) M M (instHSMul.{u_4, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.19) M (SMulZeroClass.toSMul.{u_4, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.19) M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_4, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.19) M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_4, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.19) M (Module.End.instMonoid.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.19) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.13) (Module.toDistribMulAction.{u_4, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.19) M (Module.End.instSemiring.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.19) inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.13 (Module.End.applyModule.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.19)))))) f a) (DFunLike.coe.{succ u_4, succ u_4, succ u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.19) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (LinearMap.instFunLike.{u_1, u_1, u_4, u_4} R R M M inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1925582909._hygCtx._hyg.10))) f a)","typeFull":"∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  (f : Module.End R M) (a : M), f • a = f a","typeReadable":"∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  (f : Module.End R M) (a : M), f • a = f a","typeReferences":[["Module","End"],["Module","End","instSemiring"],["LinearMap","instFunLike"],["Module"],["DistribMulAction","toDistribSMul"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["DFunLike","coe"],["Module","End","applyModule"],["Module","toDistribMulAction"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["HSMul","hSMul"],["instHSMul"],["Module","End","instMonoid"],["Eq"],["AddZero","toZero"],["Semiring"],["AddMonoid","toAddZeroClass"],["DistribSMul","toSMulZeroClass"]],"valueReferences":[["rfl"],["Module","End"],["Module","End","instSemiring"],["DistribMulAction","toDistribSMul"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["Module","End","applyModule"],["Module","toDistribMulAction"],["HSMul","hSMul"],["instHSMul"],["Module","End","instMonoid"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["DistribSMul","toSMulZeroClass"]]},{"isProp":true,"kind":"theorem","name":["DistribMulAction","toModuleEnd","_proof_2"],"typeFallback":"forall (R : Type.{u_2}) {S : Type.{u_3}} (M : Type.{u_1}) [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 : Semiring.{u_2} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 : AddCommMonoid.{u_1} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16 : Module.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.20 : Monoid.{u_3} S] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.23 : DistribMulAction.{u_3, u_1} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.20 (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13)] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.27 : SMulCommClass.{u_3, u_2, u_1} S R M (SMulZeroClass.toSMul.{u_3, u_1} S M (AddZero.toZero.{u_1} M (AddZeroClass.toAddZero.{u_1} M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_3, u_1} S M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_3, u_1} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.20 (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.23))) (SMulZeroClass.toSMul.{u_2, u_1} R M (AddZero.toZero.{u_1} M (AddZeroClass.toAddZero.{u_1} M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_2, u_1} R M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_2, u_1} R M (MonoidWithZero.toMonoid.{u_2} R (Semiring.toMonoidWithZero.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13) (Module.toDistribMulAction.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16))))] (x._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.56 : S) (x._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.58 : S), Eq.{succ u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16) (DistribSMul.toLinearMap.{u_2, u_3, u_1} R S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16 (DistribMulAction.toDistribSMul.{u_3, u_1} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.20 (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.23) inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.27 (HMul.hMul.{u_3, u_3, u_3} S S S (instHMul.{u_3} S (MulOne.toMul.{u_3} S (MulOneClass.toMulOne.{u_3} S (Monoid.toMulOneClass.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.20)))) x._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.56 x._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.58)) (HMul.hMul.{u_1, u_1, u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16) (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16) (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16) (instHMul.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16) (MulOne.toMul.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16) (MulOneClass.toMulOne.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16) (MulZeroOneClass.toMulOneClass.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16) (NonAssocSemiring.toMulZeroOneClass.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16) (Semiring.toNonAssocSemiring.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16) (Module.End.instSemiring.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16))))))) (DistribSMul.toLinearMap.{u_2, u_3, u_1} R S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16 (DistribMulAction.toDistribSMul.{u_3, u_1} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.20 (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.23) inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.27 x._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.56) (DistribSMul.toLinearMap.{u_2, 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DistribSMul.toLinearMap R M x_1","typeReadable":"∀ (R : Type u_2) {S : Type u_3} (M : Type u_1) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  [inst_3 : Monoid S] [inst_4 : DistribMulAction S M] [inst_5 : SMulCommClass S R M] (x x_1 : S),\n  DistribSMul.toLinearMap R M (x * x_1) = DistribSMul.toLinearMap R M x * DistribSMul.toLinearMap R M 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{R : Type.{u_1}} {S : Type.{u_3}} {M : Type.{u_4}} {M₁ : Type.{u_5}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.13 : AddCommMonoid.{u_4} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.16 : AddCommMonoid.{u_5} M₁] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.19 : Module.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.23 : Module.{u_1, u_5} R M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.27 : Semiring.{u_3} S] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.30 : Module.{u_1, u_3} R S inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.27)))] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.34 : Module.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.38 : IsScalarTower.{u_1, u_3, u_4} R S M (SMulZeroClass.toSMul.{u_1, u_3} R S (AddZero.toZero.{u_3} S (AddZeroClass.toAddZero.{u_3} S (AddMonoid.toAddZeroClass.{u_3} S (AddMonoidWithOne.toAddMonoid.{u_3} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_3} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_3} 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.27))) inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.30)))) (SMulZeroClass.toSMul.{u_3, u_4} S M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_3, u_4} S M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_3, u_4} S M (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.27)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.34)))) (SMulZeroClass.toSMul.{u_1, u_4} R M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_1, u_4} R M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_1, u_4} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.19))))], (LinearMap.{u_1, u_1, u_5, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10)) M₁ S inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.27))) inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.30) -> M -> (LinearMap.{u_1, u_1, u_5, u_4} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10)) M₁ M inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.19)","typeFull":"{R : Type u_1} →\n  {S : Type u_3} →\n    {M : Type u_4} →\n      {M₁ : Type u_5} →\n        [inst : Semiring R] →\n          [inst_1 : AddCommMonoid M] →\n            [inst_2 : AddCommMonoid M₁] →\n              [inst_3 : Module R M] →\n                [inst_4 : Module R M₁] →\n                  [inst_5 : Semiring S] →\n                    [inst_6 : Module R S] →\n                      [inst_7 : Module S M] → [IsScalarTower R S M] → (M₁ →ₗ[R] S) → M → M₁ →ₗ[R] M","typeReadable":"{R : Type u_1} →\n  {S : Type u_3} →\n    {M : Type u_4} →\n      {M₁ : Type u_5} →\n        [inst : Semiring R] →\n          [inst_1 : AddCommMonoid M] →\n            [inst_2 : AddCommMonoid M₁] →\n              [inst_3 : Module R M] →\n                [inst_4 : Module R M₁] →\n                  [inst_5 : Semiring S] →\n                    [inst_6 : Module R S] →\n                      [inst_7 : Module S M] → [IsScalarTower R S M] → (M₁ →ₗ[R] S) → M → M₁ →ₗ[R] M","typeReferences":[["Module"],["IsScalarTower"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["LinearMap"],["AddZeroClass","toAddZero"],["AddMonoidWithOne","toAddMonoid"],["Module","toDistribMulAction"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["NonAssocSemiring","toAddCommMonoidWithOne"],["AddZero","toZero"],["DistribSMul","toSMulZeroClass"],["Semiring"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["LinearMap","instFunLike"],["LinearMap","smulRight","_proof_2"],["LinearMap","mk"],["AddHom","mk"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["instHSMul"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["DistribSMul","toSMulZeroClass"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["LinearMap"],["Module","toDistribMulAction"],["AddCommMonoid","toAddCommSemigroup"],["HSMul","hSMul"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["LinearMap","smulRight","_proof_1"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","applyₗ'_apply_apply"],"typeFallback":"forall {R : Type.{u_1}} (S : Type.{u_3}) {M : Type.{u_4}} {M₂ : Type.{u_6}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 : Semiring.{u_3} S] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 : AddCommMonoid.{u_4} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 : AddCommMonoid.{u_6} M₂] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 : Module.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 : Module.{u_1, u_6} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 : Module.{u_3, u_6} S M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50 : SMulCommClass.{u_1, u_3, u_6} R S M₂ (SMulZeroClass.toSMul.{u_1, u_6} R M₂ (AddZero.toZero.{u_6} M₂ (AddZeroClass.toAddZero.{u_6} M₂ (AddMonoid.toAddZeroClass.{u_6} M₂ (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22)))) (DistribSMul.toSMulZeroClass.{u_1, u_6} R M₂ (AddMonoid.toAddZeroClass.{u_6} M₂ (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22)) (DistribMulAction.toDistribSMul.{u_1, u_6} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22) (Module.toDistribMulAction.{u_1, u_6} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33)))) (SMulZeroClass.toSMul.{u_3, u_6} S M₂ (AddZero.toZero.{u_6} M₂ (AddZeroClass.toAddZero.{u_6} M₂ (AddMonoid.toAddZeroClass.{u_6} M₂ (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22)))) (DistribSMul.toSMulZeroClass.{u_3, u_6} S M₂ (AddMonoid.toAddZeroClass.{u_6} M₂ (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22)) (DistribMulAction.toDistribSMul.{u_3, u_6} S M₂ (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22) (Module.toDistribMulAction.{u_3, u_6} S M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41))))] (v : M) (f : LinearMap.{u_1, u_1, u_4, u_6} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33), Eq.{succ u_6} M₂ (DFunLike.coe.{max (succ (max u_4 u_6)) (succ u_6), succ (max u_4 u_6), succ u_6} (LinearMap.{u_3, u_3, max u_4 u_6, u_6} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (LinearMap.{u_1, u_1, u_4, u_6} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_4, u_6} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_1, u_1, u_3, u_4, u_6} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41) (LinearMap.{u_1, u_1, u_4, u_6} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : LinearMap.{u_1, u_1, u_4, u_6} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) => M₂) (LinearMap.instFunLike.{u_3, u_3, max u_4 u_6, u_6} S S (LinearMap.{u_1, u_1, u_4, u_6} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_1, u_1, u_4, u_6} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_1, u_1, u_3, u_4, u_6} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13))) (DFunLike.coe.{max (succ u_4) (succ (max u_6 u_4)), succ u_4, succ (max u_6 u_4)} (AddMonoidHom.{u_4, max u_6 u_4} M (LinearMap.{u_3, u_3, max u_6 u_4, u_6} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (LinearMap.{u_1, u_1, u_4, u_6} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_1} R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41) (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16))) (AddZeroClass.toAddZero.{max u_4 u_6} (LinearMap.{u_3, u_3, max u_6 u_4, u_6} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (LinearMap.{u_1, u_1, u_4, u_6} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 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inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41) (AddMonoid.toAddZeroClass.{max u_4 u_6} (LinearMap.{u_3, u_3, max u_6 u_4, u_6} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 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(Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41) (AddCommMonoid.toAddMonoid.{max u_4 u_6} (LinearMap.{u_3, u_3, max u_6 u_4, u_6} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (LinearMap.{u_1, u_1, u_4, u_6} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R 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u_6, u_6} S S (LinearMap.{u_1, u_1, u_4, u_6} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_1, u_1, u_4, u_6} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_1, u_1, u_3, u_4, u_6} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13))))))) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => LinearMap.{u_3, u_3, max u_6 u_4, u_6} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (LinearMap.{u_1, u_1, u_4, u_6} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_4, u_6} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_1, u_1, u_3, u_4, u_6} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41) (AddMonoidHom.instFunLike.{u_4, max u_6 u_4} M (LinearMap.{u_3, u_3, max u_6 u_4, u_6} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (LinearMap.{u_1, u_1, u_4, u_6} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_4, u_6} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_1, u_1, u_3, u_4, u_6} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41) (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16))) (AddZeroClass.toAddZero.{max u_4 u_6} (LinearMap.{u_3, u_3, max u_6 u_4, u_6} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (LinearMap.{u_1, u_1, u_4, u_6} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_4, u_6} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_1, u_1, u_3, u_4, u_6} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41) (AddMonoid.toAddZeroClass.{max u_4 u_6} (LinearMap.{u_3, u_3, max u_6 u_4, u_6} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (LinearMap.{u_1, u_1, u_4, u_6} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_4, u_6} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_1, u_1, u_3, u_4, u_6} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41) (AddCommMonoid.toAddMonoid.{max u_4 u_6} (LinearMap.{u_3, u_3, max u_6 u_4, u_6} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (LinearMap.{u_1, u_1, u_4, u_6} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_4, u_6} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_1, u_1, u_3, u_4, u_6} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41) (LinearMap.addCommMonoid.{u_3, u_3, max u_4 u_6, u_6} S S (LinearMap.{u_1, u_1, u_4, u_6} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_1, u_1, u_4, u_6} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_1, u_1, u_3, u_4, u_6} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13))))))) (LinearMap.applyₗ'.{u_1, u_3, u_4, u_6} R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) v) f) (DFunLike.coe.{max (succ u_4) (succ u_6), succ u_4, succ u_6} (LinearMap.{u_1, u_1, u_4, u_6} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M₂) (LinearMap.instFunLike.{u_1, u_1, u_4, u_6} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) f v)","typeFull":"∀ {R : Type u_1} (S : Type u_3) {M : Type u_4} {M₂ : Type u_6} [inst : Semiring R] [inst_1 : Semiring S]\n  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R M₂]\n  [inst_6 : Module S M₂] [inst_7 : SMulCommClass R S M₂] (v : M) (f : M →ₗ[R] M₂), ((LinearMap.applyₗ' S) v) f = f v","typeReadable":"∀ {R : Type u_1} (S : Type u_3) {M : Type u_4} {M₂ : Type u_6} [inst : Semiring R] [inst_1 : Semiring S]\n  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R M₂]\n  [inst_6 : Module S M₂] [inst_7 : SMulCommClass R S M₂] (v : M) (f : M →ₗ[R] M₂), ((LinearMap.applyₗ' S) v) f = f v","typeReferences":[["LinearMap","instFunLike"],["Module"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["AddMonoidHom"],["MonoidWithZero","toMonoid"],["AddMonoidHom","instFunLike"],["Eq"],["DistribSMul","toSMulZeroClass"],["LinearMap","applyₗ'"],["LinearMap","module"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["LinearMap"],["LinearMap","addCommMonoid"],["SMulCommClass"],["Module","toDistribMulAction"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["LinearMap","applyₗ'"],["LinearMap","instFunLike"],["LinearMap","module"],["AddCommMonoid","toAddMonoid"],["LinearMap"],["AddZeroClass","toAddZero"],["DFunLike","coe"],["LinearMap","addCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Eq","refl"],["AddMonoidHom"],["AddMonoidHom","instFunLike"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["Module","End","instSMulCommClass"],"typeFallback":"forall {R : Type.{u_1}} {S : Type.{u_3}} {M : Type.{u_4}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13 : AddCommMonoid.{u_4} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.19 : Module.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.27 : Monoid.{u_3} S] [inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.30 : DistribMulAction.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.27 (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13)] [inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.34 : SMulCommClass.{u_1, u_3, u_4} R S M (SMulZeroClass.toSMul.{u_1, u_4} R M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_1, u_4} R M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_1, u_4} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.19)))) (SMulZeroClass.toSMul.{u_3, u_4} S M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_3, u_4} S M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.27 (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.30)))] [inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.39 : SMul.{u_3, u_1} S R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.43 : IsScalarTower.{u_3, u_1, u_4} S R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.39 (SMulZeroClass.toSMul.{u_1, u_4} R M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_1, u_4} R M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_1, u_4} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.19)))) (SMulZeroClass.toSMul.{u_3, u_4} S M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_3, u_4} S M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.27 (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.30)))], SMulCommClass.{u_3, u_4, u_4} S (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.19) (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.19) (LinearMap.instSMul.{u_1, u_1, u_3, u_4, u_4} R R S M M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.10)) (DistribMulAction.toDistribSMul.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.27 (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.30) inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.34) (SMulZeroClass.toSMul.{u_4, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.19) (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.19) (AddZero.toZero.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.19) (AddZeroClass.toAddZero.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.19) (AddMonoid.toAddZeroClass.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.19) (AddMonoidWithOne.toAddMonoid.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.19) (AddCommMonoidWithOne.toAddMonoidWithOne.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.19) (NonAssocSemiring.toAddCommMonoidWithOne.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.19) (Semiring.toNonAssocSemiring.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.19) (Module.End.instSemiring.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.19)))))))) (DistribSMul.toSMulZeroClass.{u_4, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.19) (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.19) (AddMonoid.toAddZeroClass.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.19) (AddMonoidWithOne.toAddMonoid.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.19) (AddCommMonoidWithOne.toAddMonoidWithOne.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.19) (NonAssocSemiring.toAddCommMonoidWithOne.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.19) (Semiring.toNonAssocSemiring.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.19) (Module.End.instSemiring.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.19)))))) (instDistribSMul.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.19) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1193137464._hygCtx._hyg.13 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[inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 : AddCommMonoid.{u_1} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16 : Module.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20 : Semiring.{u_3} S] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.23 : Module.{u_3, u_1} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.27 : SMulCommClass.{u_3, u_2, u_1} S R M (SMulZeroClass.toSMul.{u_3, u_1} S M (AddZero.toZero.{u_1} M (AddZeroClass.toAddZero.{u_1} M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_3, u_1} S M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_3, u_1} S M (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.23)))) (SMulZeroClass.toSMul.{u_2, u_1} R M (AddZero.toZero.{u_1} M (AddZeroClass.toAddZero.{u_1} M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_2, u_1} R M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_2, u_1} R M (MonoidWithZero.toMonoid.{u_2} R (Semiring.toMonoidWithZero.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13) (Module.toDistribMulAction.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16))))], Eq.{succ u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (DistribSMul.toLinearMap.{u_2, u_3, u_1} R S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16 (DistribMulAction.toDistribSMul.{u_3, u_1} S M (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.20)) (AddCommMonoid.toAddMonoid.{u_1} M 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inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) 0 (Zero.toOfNat0.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (AddZero.toZero.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (AddZeroClass.toAddZero.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395354._hygCtx._hyg.16) (AddMonoid.toAddZeroClass.{u_1} (Module.End.{u_2, u_1} R M 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(Module.toDistribMulAction.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33)))) (SMulZeroClass.toSMul.{u_4, u_3} S M₂ (AddZero.toZero.{u_3} M₂ (AddZeroClass.toAddZero.{u_3} M₂ (AddMonoid.toAddZeroClass.{u_3} M₂ (AddCommMonoid.toAddMonoid.{u_3} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22)))) (DistribSMul.toSMulZeroClass.{u_4, u_3} S M₂ (AddMonoid.toAddZeroClass.{u_3} M₂ (AddCommMonoid.toAddMonoid.{u_3} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22)) (DistribMulAction.toDistribSMul.{u_4, u_3} S M₂ (MonoidWithZero.toMonoid.{u_4} S (Semiring.toMonoidWithZero.{u_4} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (AddCommMonoid.toAddMonoid.{u_3} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22) 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inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22)))) (DistribSMul.toSMulZeroClass.{u_4, u_3} S M₂ (AddMonoid.toAddZeroClass.{u_3} M₂ (AddCommMonoid.toAddMonoid.{u_3} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22)) (DistribMulAction.toDistribSMul.{u_4, u_3} S M₂ (MonoidWithZero.toMonoid.{u_4} S (Semiring.toMonoidWithZero.{u_4} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (AddCommMonoid.toAddMonoid.{u_3} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22) (Module.toDistribMulAction.{u_4, u_3} S M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41))))) x (DFunLike.coe.{max (succ u_3) (succ u_2), succ u_2, succ u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M₂) (LinearMap.instFunLike.{u_1, u_1, u_2, u_3} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) f (OfNat.ofNat.{u_2} M 0 (Zero.toOfNat0.{u_2} M (AddZero.toZero.{u_2} M (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16))))))))","typeFull":"∀ {R : Type u_1} (S : Type u_4) {M : Type u_2} {M₂ : Type u_3} [inst : Semiring R] [inst_1 : Semiring S]\n  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R M₂]\n  [inst_6 : Module S M₂] [inst_7 : SMulCommClass R S M₂] (x : S) (f : M →ₗ[R] M₂), (x • f) 0 = x • f 0","typeReadable":"∀ {R : Type u_1} (S : Type u_4) {M : Type u_2} {M₂ : Type u_3} [inst : Semiring R] [inst_1 : Semiring S]\n  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R M₂]\n  [inst_6 : Module S M₂] [inst_7 : SMulCommClass R S M₂] (x : S) (f : M →ₗ[R] M₂), (x • f) 0 = x • f 0","typeReferences":[["LinearMap","instFunLike"],["Module"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["instHSMul"],["Zero","toOfNat0"],["Eq"],["DistribSMul","toSMulZeroClass"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["LinearMap"],["OfNat","ofNat"],["SMulCommClass"],["Module","toDistribMulAction"],["HSMul","hSMul"],["LinearMap","instSMul"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["Module","toDistribMulAction"],["Semiring","toNonAssocSemiring"],["LinearMap","smul_apply"],["RingHom","id"],["MonoidWithZero","toMonoid"],["Zero","toOfNat0"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["RingEquiv","moduleEndSelf","_proof_5"],"typeFallback":"forall 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_1, u_1, u_6, u_4} R R M₂ M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (LinearMap.module.{u_1, u_1, u_1, u_6, u_4} R R R M₂ M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22)))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (LinearMap.module.{u_1, u_1, u_1, u_6, u_4} R R R M₂ M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R 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(LinearMap.instSMulCommClass.{u_1, u_1, u_1, u_1, u_6, u_4} R R R R M₂ M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (DistribMulAction.toDistribSMul.{u_1, u_4} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22)) (smulCommClass_self.{u_1, u_4} R M (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_4} R M (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22))) (DistribMulAction.toDistribSMul.{u_1, u_4} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22)) (smulCommClass_self.{u_1, u_4} R M (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_4} R M (CommMonoid.toMonoid.{u_1} R 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(CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22)))))","typeFull":"{R : Type u_1} →\n  {M : Type u_4} →\n    {M₂ : Type u_6} →\n      [inst : CommSemiring R] →\n        [inst_1 : AddCommMonoid M] →\n          [inst_2 : AddCommMonoid M₂] →\n            [inst_3 : Module R M] → [inst_4 : Module R M₂] → (M₂ →ₗ[R] R) →ₗ[R] M →ₗ[R] M₂ →ₗ[R] M","typeReadable":"{R : Type u_1} →\n  {M : Type u_4} →\n    {M₂ : Type u_6} →\n      [inst : CommSemiring R] →\n        [inst_1 : AddCommMonoid M] →\n          [inst_2 : AddCommMonoid M₂] →\n            [inst_3 : Module R M] → [inst_4 : Module R M₂] → (M₂ →ₗ[R] R) →ₗ[R] M →ₗ[R] M₂ →ₗ[R] M","typeReferences":[["smulCommClass_self"],["CommMonoid","toMonoid"],["Module"],["CommSemiring"],["CommSemiring","toSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["LinearMap","module"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddCommMonoid","toAddMonoid"],["LinearMap"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["DistribMulAction","toMulAction"],["LinearMap","instSMulCommClass"],["Semiring","toModule"]],"valueReferences":[["LinearMap","smulRightₗ","_proof_4"],["LinearMap","applyₗ","_proof_1"],["LinearMap","smulRight"],["LinearMap","smulRightₗ","_proof_3"],["LinearMap","mk"],["AddHom","mk"],["CommSemiring","toSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["LinearMap","module"],["LinearMap","smulRightₗ","_proof_2"],["LinearMap"],["LinearMap","smulRightₗ","_proof_7"],["LinearMap","addCommMonoid"],["Semiring","toNonAssocSemiring"],["AddCommMonoid","toAddCommSemigroup"],["RingHom","id"],["LinearMap","smulRightₗ","_proof_5"],["LinearMap","smulRightₗ","_proof_6"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["LinearMap","smulRightₗ","_proof_1"],["Semiring","toModule"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","smulRight","_proof_1"],"typeFallback":"forall {R : Type.{u_4}} {S : Type.{u_2}} {M : Type.{u_1}} {M₁ : Type.{u_3}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10 : Semiring.{u_4} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.13 : AddCommMonoid.{u_1} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.16 : AddCommMonoid.{u_3} M₁] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.23 : Module.{u_4, u_3} R M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.27 : Semiring.{u_2} S] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.30 : Module.{u_4, u_2} R S inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.10 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S 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inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.30) (x : M) (x_1 : M₁) (y : M₁), Eq.{succ u_1} M (HSMul.hSMul.{u_2, u_1, u_1} S M M (instHSMul.{u_2, u_1} S M (SMulZeroClass.toSMul.{u_2, u_1} S M (AddZero.toZero.{u_1} M (AddZeroClass.toAddZero.{u_1} M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_2, u_1} S M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_2, u_1} S M (MonoidWithZero.toMonoid.{u_2} S (Semiring.toMonoidWithZero.{u_2} S inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.27)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.2414492958._hygCtx._hyg.13) 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inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_1, u_4, u_6} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.26 (smulCommClass_self.{u_1, u_6} R M₂ (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_6} R M₂ (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.938163380._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_6} M₂ 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Module R M₂] → M →ₗ[R] (M →ₗ[R] M₂) →ₗ[R] 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{R : Type.{u_1}} {S : Type.{u_3}} {M : Type.{u_4}} {M₁ : Type.{u_5}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.13 : AddCommMonoid.{u_4} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.16 : AddCommMonoid.{u_5} M₁] [inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.19 : Module.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.23 : Module.{u_1, u_5} R M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.27 : Semiring.{u_3} S] [inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.30 : Module.{u_1, u_3} R S inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.10 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.27)))] [inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.34 : Module.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.38 : IsScalarTower.{u_1, u_3, u_4} R S M (SMulZeroClass.toSMul.{u_1, u_3} R S (AddZero.toZero.{u_3} S (AddZeroClass.toAddZero.{u_3} S (AddMonoid.toAddZeroClass.{u_3} S (AddMonoidWithOne.toAddMonoid.{u_3} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_3} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.27))))))) (DistribSMul.toSMulZeroClass.{u_1, u_3} R S (AddMonoid.toAddZeroClass.{u_3} S (AddMonoidWithOne.toAddMonoid.{u_3} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_3} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.27))))) (DistribMulAction.toDistribSMul.{u_1, u_3} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.10)) (AddMonoidWithOne.toAddMonoid.{u_3} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_3} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.27)))) (Module.toDistribMulAction.{u_1, u_3} R S inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.10 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.27))) inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.30)))) (SMulZeroClass.toSMul.{u_3, u_4} S M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_3, u_4} S M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_3, u_4} S M (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.27)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.34)))) (SMulZeroClass.toSMul.{u_1, u_4} R M (AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_1, u_4} R M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_1, u_4} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.19))))] (x : M), Eq.{max (succ u_4) (succ u_5)} (LinearMap.{u_1, u_1, u_5, u_4} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.10)) M₁ M inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.19) (LinearMap.smulRight.{u_1, u_3, u_4, u_5} R S M M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.34 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.38 (OfNat.ofNat.{max u_3 u_5} (LinearMap.{u_1, u_1, u_5, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.10)) M₁ S inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.27))) inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.30) 0 (Zero.toOfNat0.{max u_3 u_5} (LinearMap.{u_1, u_1, u_5, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.10)) M₁ S inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.27))) inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.30) (LinearMap.instZero.{u_1, u_1, u_5, u_3} R R M₁ S inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.27))) inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.30 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.10))))) x) (OfNat.ofNat.{max u_4 u_5} (LinearMap.{u_1, u_1, u_5, u_4} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.10)) M₁ M inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.19) 0 (Zero.toOfNat0.{max u_4 u_5} (LinearMap.{u_1, u_1, u_5, u_4} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.10)) M₁ M inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.19) (LinearMap.instZero.{u_1, u_1, u_5, u_4} R R M₁ M inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.4242374280._hygCtx._hyg.10)))))","typeFull":"∀ {R : Type u_1} {S : Type u_3} {M : Type u_4} {M₁ : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₁] [inst_3 : Module R M] [inst_4 : Module R M₁] [inst_5 : Semiring S] [inst_6 : Module R S]\n  [inst_7 : Module S M] [inst_8 : IsScalarTower R S M] (x : M), LinearMap.smulRight 0 x = 0","typeReadable":"∀ {R : Type u_1} {S : Type u_3} {M : Type u_4} {M₁ : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₁] [inst_3 : Module R M] [inst_4 : Module R M₁] [inst_5 : Semiring S] [inst_6 : Module R S]\n  [inst_7 : Module S M] [inst_8 : IsScalarTower R S M] (x : M), LinearMap.smulRight 0 x = 0","typeReferences":[["IsScalarTower"],["Module"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddMonoidWithOne","toAddMonoid"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["Zero","toOfNat0"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Eq"],["NonAssocSemiring","toAddCommMonoidWithOne"],["DistribSMul","toSMulZeroClass"],["LinearMap","instZero"],["LinearMap","smulRight"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["LinearMap"],["OfNat","ofNat"],["Module","toDistribMulAction"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["LinearMap","instFunLike"],["Eq","trans"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["congrArg"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["LinearMap","ext"],["Zero","toOfNat0"],["congrFun'"],["Eq"],["MulActionWithZero","toSMulWithZero"],["LinearMap","instZero"],["LinearMap","smulRight"],["True"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["Semiring","toMonoidWithZero"],["Module","toMulActionWithZero"],["LinearMap"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["eq_self"],["of_eq_true"],["zero_smul"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["Module","End","iterate_succ"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_4}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.13 : AddCommMonoid.{u_4} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.19 : Module.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.13] {f' : Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.19} (n : Nat), Eq.{succ u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.19) (HPow.hPow.{u_4, 0, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.19) Nat (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.19) (instHPow.{u_4, 0} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.19) Nat (Monoid.toPow.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.19) (Module.End.instMonoid.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.19))) f' (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (LinearMap.comp.{u_1, u_1, u_1, u_4, u_4, u_4} R R R M M M inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.10)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.10))) (HPow.hPow.{u_4, 0, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.19) Nat (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.19) (instHPow.{u_4, 0} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.19) Nat (Monoid.toPow.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.19) (Module.End.instMonoid.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.2137171166._hygCtx._hyg.19))) f' n) f')","typeFull":"∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  {f' : Module.End R M} (n : ℕ), f' ^ (n + 1) = (f' ^ n) ∘ₗ f'","typeReadable":"∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  {f' : Module.End R M} (n : ℕ), f' ^ (n + 1) = (f' ^ n) ∘ₗ f'","typeReferences":[["instHPow"],["instAddNat"],["Module","End"],["RingHomCompTriple","ids"],["Module"],["instHAdd"],["LinearMap","comp"],["HPow","hPow"],["OfNat","ofNat"],["HAdd","hAdd"],["AddCommMonoid"],["Nat"],["Semiring","toNonAssocSemiring"],["Monoid","toPow"],["RingHom","id"],["instOfNatNat"],["Module","End","instMonoid"],["Eq"],["Semiring"]],"valueReferences":[["instAddNat"],["MulOneClass","toMulOne"],["RingHomCompTriple","ids"],["LinearMap","comp"],["HMul","hMul"],["congrArg"],["MulOne","toMul"],["Semiring","toNonAssocSemiring"],["Monoid","toPow"],["pow_succ"],["instOfNatNat"],["RingHom","id"],["Monoid","toMulOneClass"],["Eq"],["instHPow"],["Module","End"],["instHAdd"],["HPow","hPow"],["OfNat","ofNat"],["Module","End","instMul"],["HAdd","hAdd"],["Nat"],["Eq","refl"],["id"],["instHMul"],["Module","End","mul_eq_comp"],["Module","End","instMonoid"],["Eq","mpr"]]},{"isProp":true,"kind":"theorem","name":["Module","End","natCast_def"],"typeFallback":"forall (R : Type.{u_1}) {N₁ : Type.{u_8}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.10 : Semiring.{u_1} R] (n : Nat) [inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.35 : AddCommMonoid.{u_8} N₁] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.38 : Module.{u_1, u_8} R N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.35], Eq.{succ u_8} (Module.End.{u_1, u_8} R N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.35 inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.38) (Nat.cast.{u_8} (Module.End.{u_1, u_8} R N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.35 inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.38) (AddMonoidWithOne.toNatCast.{u_8} (Module.End.{u_1, u_8} R N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.35 inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.38) (AddCommMonoidWithOne.toAddMonoidWithOne.{u_8} (Module.End.{u_1, u_8} R N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.35 inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.38) (NonAssocSemiring.toAddCommMonoidWithOne.{u_8} (Module.End.{u_1, u_8} R N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.35 inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.38) (Semiring.toNonAssocSemiring.{u_8} (Module.End.{u_1, u_8} R N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.35 inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.38) (Module.End.instSemiring.{u_1, u_8} R N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.35 inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.38))))) n) (DFunLike.coe.{max (succ u_8) 1, 1, succ u_8} (RingHom.{0, u_8} Nat (Module.End.{u_1, u_8} R N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.35 inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.38) (Semiring.toNonAssocSemiring.{0} Nat Nat.instSemiring) (Semiring.toNonAssocSemiring.{u_8} (Module.End.{u_1, u_8} R N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.35 inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.38) (Module.End.instSemiring.{u_1, u_8} R N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.35 inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.38))) Nat (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : Nat) => Module.End.{u_1, u_8} R N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.35 inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.38) (RingHom.instFunLike.{0, u_8} Nat (Module.End.{u_1, u_8} R N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.35 inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.38) (Semiring.toNonAssocSemiring.{0} Nat Nat.instSemiring) (Semiring.toNonAssocSemiring.{u_8} (Module.End.{u_1, u_8} R N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.35 inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.38) (Module.End.instSemiring.{u_1, u_8} R N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.35 inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.38))) (Module.toModuleEnd.{u_1, 0, u_8} R Nat N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.35 inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.38 Nat.instSemiring (AddCommMonoid.toNatModule.{u_8} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.35) (AddMonoid.nat_smulCommClass.{u_1, u_8} R N₁ (AddCommMonoid.toAddMonoid.{u_8} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.35) (DistribMulAction.toDistribSMul.{u_1, u_8} R N₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_8} N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.35) (Module.toDistribMulAction.{u_1, u_8} R N₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.35 inst._@.Mathlib.Algebra.Module.LinearMap.End.3284752934._hygCtx._hyg.38)))) n)","typeFull":"∀ (R : Type u_1) {N₁ : Type u_8} [inst : Semiring R] (n : ℕ) [inst_1 : AddCommMonoid N₁] [inst_2 : Module R N₁],\n  ↑n = (Module.toModuleEnd R N₁) n","typeReadable":"∀ (R : Type u_1) {N₁ : Type u_8} [inst : Semiring R] (n : ℕ) [inst_1 : AddCommMonoid N₁] [inst_2 : Module R N₁],\n  ↑n = (Module.toModuleEnd R N₁) 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Type.{u_1}} {S : Type.{u_3}} {M : Type.{u_4}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.13 : AddCommMonoid.{u_4} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.19 : Module.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.27 : Monoid.{u_3} S] [inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.30 : DistribMulAction.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.27 (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.13)] [inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.34 : SMulCommClass.{u_1, u_3, u_4} R S M (SMulZeroClass.toSMul.{u_1, 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(AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_3, u_4} S M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.27 (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.30)))] [inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.39 : SMul.{u_3, u_1} S R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.43 : IsScalarTower.{u_3, u_1, u_4} S R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.39 (SMulZeroClass.toSMul.{u_1, 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(AddZero.toZero.{u_4} M (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_3, u_4} S M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.27 (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.30)))], SMulCommClass.{u_4, u_3, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.19) S (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.19) (SMulZeroClass.toSMul.{u_4, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.19) (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.19) (AddZero.toZero.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.13 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inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.19)))))))) (DistribSMul.toSMulZeroClass.{u_4, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.19) (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.19) (AddMonoid.toAddZeroClass.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.19) (AddMonoidWithOne.toAddMonoid.{u_4} (Module.End.{u_1, u_4} R M 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(Semiring.toNonAssocSemiring.{u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.19) (Module.End.instSemiring.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.19)))))) (LinearMap.instSMul.{u_1, u_1, u_3, u_4, u_4} R R S M M inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.10)) (DistribMulAction.toDistribSMul.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.27 (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.30) inst._@.Mathlib.Algebra.Module.LinearMap.End.4034160367._hygCtx._hyg.34)","typeFull":"∀ {R : Type u_1} {S : Type u_3} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  [inst_3 : Monoid S] [inst_4 : DistribMulAction S M] [inst_5 : SMulCommClass R S M] [inst_6 : SMul S R]\n  [IsScalarTower S R M], SMulCommClass (Module.End R M) S (Module.End R M)","typeReadable":"∀ {R : Type u_1} {S : Type u_3} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] 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(x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (LinearMap.instFunLike.{u_1, u_1, u_4, u_4} R R M M inst._@.Mathlib.Algebra.Module.LinearMap.End.1751316427._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1751316427._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1751316427._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1751316427._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1751316427._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.1751316427._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1751316427._hygCtx._hyg.10))) (HPow.hPow.{u_4, 0, u_4} (Module.End.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.1751316427._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1751316427._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1751316427._hygCtx._hyg.19) Nat (Module.End.{u_1, u_4} R M 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1751316427._hygCtx._hyg.19))) f' n)))","typeFull":"∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  {f' : Module.End R M}, Function.Injective ⇑f' → ∀ (n : ℕ), Function.Injective ⇑(f' ^ n)","typeReadable":"∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  {f' : Module.End R M}, Function.Injective ⇑f' → ∀ (n : ℕ), Function.Injective ⇑(f' ^ 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(R : Type.{u_2}) {S : Type.{u_3}} (M : Type.{u_1}) [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 : Semiring.{u_2} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 : AddCommMonoid.{u_1} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16 : Module.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.20 : Monoid.{u_3} S] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.23 : DistribMulAction.{u_3, u_1} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.20 (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13)] [inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.27 : SMulCommClass.{u_3, u_2, u_1} S R M (SMulZeroClass.toSMul.{u_3, u_1} S M (AddZero.toZero.{u_1} M (AddZeroClass.toAddZero.{u_1} M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_3, u_1} S M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_3, u_1} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.20 (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.23))) (SMulZeroClass.toSMul.{u_2, u_1} R M (AddZero.toZero.{u_1} M (AddZeroClass.toAddZero.{u_1} M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_2, u_1} R M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_2, u_1} R M (MonoidWithZero.toMonoid.{u_2} R (Semiring.toMonoidWithZero.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13) (Module.toDistribMulAction.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16))))], Eq.{succ u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16) (DistribSMul.toLinearMap.{u_2, u_3, u_1} R S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16 (DistribMulAction.toDistribSMul.{u_3, u_1} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.20 (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.23) inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.27 (OfNat.ofNat.{u_3} S 1 (One.toOfNat1.{u_3} S (MulOne.toOne.{u_3} S (MulOneClass.toMulOne.{u_3} S (Monoid.toMulOneClass.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.20)))))) (OfNat.ofNat.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16) 1 (One.toOfNat1.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16) (MulOne.toOne.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16) (MulOneClass.toMulOne.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16) (MulZeroOneClass.toMulOneClass.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16) (NonAssocSemiring.toMulZeroOneClass.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16) (Semiring.toNonAssocSemiring.{u_1} (Module.End.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16) (Module.End.instSemiring.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.3945395353._hygCtx._hyg.16))))))))","typeFull":"∀ (R : Type u_2) {S : Type u_3} (M : Type u_1) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  [inst_3 : Monoid S] [inst_4 : DistribMulAction S M] [inst_5 : SMulCommClass S R M], DistribSMul.toLinearMap R M 1 = 1","typeReadable":"∀ (R : Type u_2) {S : Type u_3} (M : Type u_1) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  [inst_3 : Monoid S] [inst_4 : DistribMulAction S M] [inst_5 : SMulCommClass S R M], DistribSMul.toLinearMap R M 1 = 1","typeReferences":[["MulOneClass","toMulOne"],["Module"],["MulZeroOneClass","toMulOneClass"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["DistribSMul","toLinearMap"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Monoid","toMulOneClass"],["MonoidWithZero","toMonoid"],["Eq"],["NonAssocSemiring","toMulZeroOneClass"],["DistribMulAction"],["DistribSMul","toSMulZeroClass"],["Module","End"],["Module","End","instSemiring"],["MulOne","toOne"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["LinearMap"],["OfNat","ofNat"],["SMulCommClass"],["Module","toDistribMulAction"],["One","toOfNat1"],["Monoid"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["MulOneClass","toMulOne"],["Module","End"],["Module","End","instSemiring"],["MulOne","toOne"],["DistribMulAction","toDistribSMul"],["MulZeroOneClass","toMulOneClass"],["AddCommMonoid","toAddMonoid"],["OfNat","ofNat"],["DistribSMul","toLinearMap"],["Semiring","toNonAssocSemiring"],["One","toOfNat1"],["RingHom","id"],["LinearMap","ext"],["one_smul"],["Monoid","toMulOneClass"],["DistribMulAction","toMulAction"],["NonAssocSemiring","toMulZeroOneClass"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","coe_smulRight"],"typeFallback":"forall {R : Type.{u_1}} {S : Type.{u_3}} {M : Type.{u_4}} {M₁ : Type.{u_5}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.13 : AddCommMonoid.{u_4} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.16 : AddCommMonoid.{u_5} M₁] [inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.19 : Module.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.23 : Module.{u_1, u_5} R M₁ inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.27 : Semiring.{u_3} S] [inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.30 : Module.{u_1, u_3} R S inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.10 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.27)))] [inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.34 : Module.{u_3, u_4} S M inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.38 : IsScalarTower.{u_1, u_3, u_4} R S M (SMulZeroClass.toSMul.{u_1, u_3} R S (AddZero.toZero.{u_3} S (AddZeroClass.toAddZero.{u_3} S (AddMonoid.toAddZeroClass.{u_3} S (AddMonoidWithOne.toAddMonoid.{u_3} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_3} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.27))))))) (DistribSMul.toSMulZeroClass.{u_1, u_3} R S (AddMonoid.toAddZeroClass.{u_3} S (AddMonoidWithOne.toAddMonoid.{u_3} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_3} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.27))))) (DistribMulAction.toDistribSMul.{u_1, u_3} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.10)) (AddMonoidWithOne.toAddMonoid.{u_3} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_3} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.27)))) (Module.toDistribMulAction.{u_1, u_3} R S inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.10 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inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.19))))] (f : LinearMap.{u_1, u_1, u_5, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.10)) M₁ S inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.27))) inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.30) (x : M), Eq.{max (succ u_4) (succ u_5)} (M₁ -> M) (DFunLike.coe.{max (succ u_4) (succ u_5), succ u_5, succ u_4} (LinearMap.{u_1, u_1, u_5, u_4} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.10)) M₁ M inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.19) M₁ (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M₁) => M) (LinearMap.instFunLike.{u_1, u_1, u_5, u_4} R R M₁ M 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inst._@.Mathlib.Algebra.Module.LinearMap.End.160980332._hygCtx._hyg.10))) f c) x)","typeFull":"∀ {R : Type u_1} {S : Type u_3} {M : Type u_4} {M₁ : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₁] [inst_3 : Module R M] [inst_4 : Module R M₁] [inst_5 : Semiring S] [inst_6 : Module R S]\n  [inst_7 : Module S M] [inst_8 : IsScalarTower R S M] (f : M₁ →ₗ[R] S) (x : M), ⇑(f.smulRight x) = fun c => f c • x","typeReadable":"∀ {R : Type u_1} {S : Type u_3} {M : Type u_4} {M₁ : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₁] [inst_3 : Module R M] [inst_4 : Module R M₁] [inst_5 : Semiring S] [inst_6 : Module R S]\n  [inst_7 : Module S M] [inst_8 : IsScalarTower R S M] (f : M₁ →ₗ[R] S) (x : M), ⇑(f.smulRight x) = fun c => f c • x","typeReferences":[["LinearMap","instFunLike"],["IsScalarTower"],["Module"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddMonoidWithOne","toAddMonoid"],["DFunLike","coe"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["instHSMul"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Eq"],["NonAssocSemiring","toAddCommMonoidWithOne"],["DistribSMul","toSMulZeroClass"],["LinearMap","smulRight"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["LinearMap"],["Module","toDistribMulAction"],["HSMul","hSMul"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["rfl"],["LinearMap","smulRight"],["Semiring","toNonAssocSemiring"],["LinearMap","instFunLike"],["RingHom","id"],["LinearMap"],["DFunLike","coe"]]},{"isProp":true,"kind":"theorem","name":["Module","End","instSemiring","_proof_3"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 : Module.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13] (x._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.60 : Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19) (x._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.62 : Module.End.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 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inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) (Module.End.instMul._proof_1.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10) x._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.60 x._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.64) (LinearMap.comp.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10)) (Module.End.instMul._proof_1.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.10) x._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.62 x._@.Mathlib.Algebra.Module.LinearMap.End.221733677._hygCtx._hyg.64))","typeFull":"∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  (x x_1 x_2 : Module.End R M), (x + x_1) ∘ₗ x_2 = x ∘ₗ x_2 + x_1 ∘ₗ x_2","typeReadable":"∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  (x x_1 x_2 : Module.End R M), (x + x_1) ∘ₗ x_2 = x ∘ₗ x_2 + x_1 ∘ₗ x_2","typeReferences":[["Module","End"],["Module"],["instHAdd"],["LinearMap","comp"],["LinearMap"],["HAdd","hAdd"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Module","End","instMul","_proof_1"],["LinearMap","instAdd"],["Eq"],["Semiring"]],"valueReferences":[["Semiring","toNonAssocSemiring"],["RingHom","id"],["Module","End","instMul","_proof_1"],["LinearMap","add_comp"]]},{"isProp":true,"kind":"theorem","name":["Module","End","instMul","_proof_1"],"typeFallback":"forall {R : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.3379617806._hygCtx._hyg.10 : Semiring.{u_1} R], RingHomCompTriple.{u_1, u_1, u_1} R R R inst._@.Mathlib.Algebra.Module.LinearMap.End.3379617806._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3379617806._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.3379617806._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3379617806._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3379617806._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.3379617806._hygCtx._hyg.10))","typeFull":"∀ {R : Type u_1} [inst : Semiring R], RingHomCompTriple (RingHom.id R) (RingHom.id R) (RingHom.id R)","typeReadable":"∀ {R : Type u_1} [inst : Semiring R], RingHomCompTriple (RingHom.id R) (RingHom.id R) (RingHom.id R)","typeReferences":[["Semiring","toNonAssocSemiring"],["RingHom","id"],["RingHomCompTriple"],["Semiring"]],"valueReferences":[["Semiring","toNonAssocSemiring"],["RingHom","id"],["RingHomCompTriple","ids"]]},{"isProp":false,"kind":"definition","name":["LinearMap","applyₗ'"],"typeFallback":"forall {R : Type.{u_1}} (S : Type.{u_3}) {M : Type.{u_4}} {M₂ : Type.{u_6}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 : Semiring.{u_3} S] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 : AddCommMonoid.{u_4} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 : AddCommMonoid.{u_6} M₂] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 : Module.{u_1, u_4} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 : Module.{u_1, u_6} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 : Module.{u_3, u_6} S M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50 : SMulCommClass.{u_1, u_3, u_6} R S M₂ (SMulZeroClass.toSMul.{u_1, u_6} R M₂ (AddZero.toZero.{u_6} M₂ (AddZeroClass.toAddZero.{u_6} M₂ (AddMonoid.toAddZeroClass.{u_6} M₂ (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22)))) (DistribSMul.toSMulZeroClass.{u_1, u_6} R M₂ (AddMonoid.toAddZeroClass.{u_6} M₂ (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22)) (DistribMulAction.toDistribSMul.{u_1, u_6} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22) (Module.toDistribMulAction.{u_1, u_6} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33)))) (SMulZeroClass.toSMul.{u_3, u_6} S M₂ (AddZero.toZero.{u_6} M₂ (AddZeroClass.toAddZero.{u_6} M₂ (AddMonoid.toAddZeroClass.{u_6} M₂ (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22)))) (DistribSMul.toSMulZeroClass.{u_3, u_6} S M₂ (AddMonoid.toAddZeroClass.{u_6} M₂ (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22)) (DistribMulAction.toDistribSMul.{u_3, u_6} S M₂ (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (AddCommMonoid.toAddMonoid.{u_6} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22) (Module.toDistribMulAction.{u_3, u_6} S M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41))))], AddMonoidHom.{u_4, max u_6 u_4} M (LinearMap.{u_3, u_3, max u_6 u_4, u_6} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (LinearMap.{u_1, u_1, u_4, u_6} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_4, u_6} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_1, u_1, u_3, u_4, u_6} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41) (AddZeroClass.toAddZero.{u_4} M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16))) (AddZeroClass.toAddZero.{max u_4 u_6} (LinearMap.{u_3, u_3, max u_6 u_4, u_6} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (LinearMap.{u_1, u_1, u_4, u_6} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_4, u_6} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_1, u_1, u_3, u_4, u_6} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41) (AddMonoid.toAddZeroClass.{max u_4 u_6} (LinearMap.{u_3, u_3, max u_6 u_4, u_6} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (LinearMap.{u_1, u_1, u_4, u_6} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_4, u_6} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_1, u_1, u_3, u_4, u_6} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41) (AddCommMonoid.toAddMonoid.{max u_4 u_6} (LinearMap.{u_3, u_3, max u_6 u_4, u_6} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (LinearMap.{u_1, u_1, u_4, u_6} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (LinearMap.addCommMonoid.{u_1, u_1, u_4, u_6} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_1, u_1, u_3, u_4, u_6} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41) (LinearMap.addCommMonoid.{u_3, u_3, max u_4 u_6, u_6} S S (LinearMap.{u_1, u_1, u_4, u_6} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 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[inst_1 : Semiring S] →\n            [inst_2 : AddCommMonoid M] →\n              [inst_3 : AddCommMonoid M₂] →\n                [inst_4 : Module R M] →\n                  [inst_5 : Module R M₂] →\n                    [inst_6 : Module S M₂] → [inst_7 : SMulCommClass R S M₂] → M →+ (M →ₗ[R] M₂) →ₗ[S] M₂","typeReferences":[["Module"],["LinearMap","module"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["LinearMap"],["AddZeroClass","toAddZero"],["LinearMap","addCommMonoid"],["SMulCommClass"],["Module","toDistribMulAction"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["AddMonoidHom"],["MonoidWithZero","toMonoid"],["AddZero","toZero"],["Semiring"],["AddMonoid","toAddZeroClass"],["DistribSMul","toSMulZeroClass"]],"valueReferences":[["LinearMap","applyₗ'","_proof_8"],["LinearMap","instFunLike"],["LinearMap","applyₗ'","_proof_1"],["LinearMap","mk"],["LinearMap","module"],["AddHom","mk"],["LinearMap","applyₗ'","_proof_2"],["LinearMap","applyₗ'","_proof_5"],["AddMonoidHom","mk"],["AddCommMonoid","toAddMonoid"],["LinearMap"],["AddZeroClass","toAddZero"],["DFunLike","coe"],["LinearMap","addCommMonoid"],["Semiring","toNonAssocSemiring"],["AddCommMonoid","toAddCommSemigroup"],["RingHom","id"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["ZeroHom","mk"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["Module","End","one_apply"],"typeFallback":"forall 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22)))) (AddHom.mk.{u_1, max u_1 u_2} M (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) (AddCommMonoid.toAddCommSemigroup.{max u_1 u_2} (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))))))) (LinearMap.smulRight.{u_3, u_3, u_1, u_2} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (IsScalarTower.left.{u_3, u_1} R M (MonoidWithZero.toMonoid.{u_3} R (Semiring.toMonoidWithZero.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (DistribMulAction.toMulAction.{u_3, u_1} R M (MonoidWithZero.toMonoid.{u_3} R (Semiring.toMonoidWithZero.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22))) (HSMul.hSMul.{u_3, max u_3 u_2, max u_3 u_2} R (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (instHSMul.{u_3, max u_3 u_2} R (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (SMulZeroClass.toSMul.{u_3, max u_3 u_2} R (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddZero.toZero.{max u_3 u_2} (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddZeroClass.toAddZero.{max u_3 u_2} (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddMonoid.toAddZeroClass.{max u_3 u_2} (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{max u_3 u_2} (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_3} R R M₂ R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))))))) (DistribSMul.toSMulZeroClass.{u_3, max u_3 u_2} R (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddMonoid.toAddZeroClass.{max u_3 u_2} (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{max u_3 u_2} (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_3} R R M₂ R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))))) (DistribMulAction.toDistribSMul.{u_3, max u_3 u_2} R (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (MonoidWithZero.toMonoid.{u_3} R (Semiring.toMonoidWithZero.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{max u_3 u_2} (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))))) (Module.toDistribMulAction.{u_3, max u_3 u_2} R (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_3} R R M₂ R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) (LinearMap.module.{u_3, u_3, u_3, u_2, u_3} R R R M₂ R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (smulCommClass_self.{u_3, u_3} R R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_3} R R (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))))) (Module.toDistribMulAction.{u_3, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))))))))))) c f)) (fun (m : M) (m' : M) => LinearMap.smulRightₗ._proof_1.{u_1, u_2, u_3} R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (HSMul.hSMul.{u_3, max u_3 u_2, max u_3 u_2} R (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (instHSMul.{u_3, max u_3 u_2} R (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (SMulZeroClass.toSMul.{u_3, max u_3 u_2} R (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddZero.toZero.{max u_3 u_2} (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))))))) (DistribSMul.toSMulZeroClass.{u_3, max u_3 u_2} R (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) 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(RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{max u_3 u_2} (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_3} R R M₂ R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))))) (DistribMulAction.toDistribSMul.{u_3, max u_3 u_2} R (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (MonoidWithZero.toMonoid.{u_3} R (Semiring.toMonoidWithZero.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{max u_3 u_2} (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_3} R R M₂ R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))))) (Module.toDistribMulAction.{u_3, max u_3 u_2} R (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_3} R R M₂ R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) (LinearMap.module.{u_3, u_3, u_3, u_2, u_3} R R R M₂ R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (smulCommClass_self.{u_3, u_3} R R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_3} R R (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))))) (Module.toDistribMulAction.{u_3, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))))))))))) c f) m m')) (fun (c_1 : R) (m : M) => LinearMap.smulRightₗ._proof_2.{u_1, u_2, u_3} R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (HSMul.hSMul.{u_3, max u_3 u_2, max u_3 u_2} R (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (instHSMul.{u_3, max u_3 u_2} R (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (SMulZeroClass.toSMul.{u_3, max u_3 u_2} R (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddZero.toZero.{max u_3 u_2} (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddZeroClass.toAddZero.{max u_3 u_2} (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddMonoid.toAddZeroClass.{max u_3 u_2} (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{max u_3 u_2} (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_3} R R M₂ R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))))))) (DistribSMul.toSMulZeroClass.{u_3, max u_3 u_2} R (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddMonoid.toAddZeroClass.{max u_3 u_2} (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{max u_3 u_2} (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_3} R R M₂ R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))))) (DistribMulAction.toDistribSMul.{u_3, max u_3 u_2} R (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (MonoidWithZero.toMonoid.{u_3} R (Semiring.toMonoidWithZero.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{max u_3 u_2} (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_3} R R M₂ R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))))) (Module.toDistribMulAction.{u_3, max u_3 u_2} R (LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_3} R R M₂ R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (RingHom.id.{u_3} R 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R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))))))))))) c f) c_1 m)) (HSMul.hSMul.{u_3, max u_1 u_2, max u_1 u_2} R (LinearMap.{u_3, u_3, u_1, max u_1 u_2} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22))))) (LinearMap.{u_3, u_3, u_1, max u_1 u_2} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22))))) (instHSMul.{u_3, max u_1 u_2} R (LinearMap.{u_3, u_3, u_1, max u_1 u_2} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22))))) (SMulZeroClass.toSMul.{u_3, max u_1 u_2} R (LinearMap.{u_3, u_3, u_1, max u_1 u_2} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22))))) (AddZero.toZero.{max u_1 u_2} (LinearMap.{u_3, u_3, u_1, max u_1 u_2} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22))))) (AddZeroClass.toAddZero.{max u_1 u_2} (LinearMap.{u_3, u_3, u_1, max u_1 u_2} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22))))) (AddMonoid.toAddZeroClass.{max u_1 u_2} (LinearMap.{u_3, u_3, u_1, max u_1 u_2} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22))))) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (LinearMap.{u_3, u_3, u_1, max u_1 u_2} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22)))) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))))))) (DistribSMul.toSMulZeroClass.{u_3, max u_1 u_2} R (LinearMap.{u_3, u_3, u_1, max u_1 u_2} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22))))) (AddMonoid.toAddZeroClass.{max u_1 u_2} (LinearMap.{u_3, u_3, u_1, max u_1 u_2} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22))))) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (LinearMap.{u_3, u_3, u_1, max u_1 u_2} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22))))) (LinearMap.addCommMonoid.{u_3, u_3, u_1, max u_1 u_2} R R M (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22)))) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))))) (DistribMulAction.toDistribSMul.{u_3, max u_1 u_2} R (LinearMap.{u_3, u_3, u_1, max u_1 u_2} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22))))) (MonoidWithZero.toMonoid.{u_3} R (Semiring.toMonoidWithZero.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (LinearMap.{u_3, u_3, u_1, max u_1 u_2} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22))))) (LinearMap.addCommMonoid.{u_3, u_3, u_1, max u_1 u_2} R R M (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22)))) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))))) (Module.toDistribMulAction.{u_3, max u_1 u_2} R (LinearMap.{u_3, u_3, u_1, max u_1 u_2} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22))))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (LinearMap.addCommMonoid.{u_3, u_3, u_1, max u_1 u_2} R R M (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R 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(CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22)))) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) (LinearMap.module.{u_3, u_3, u_3, u_1, max u_1 u_2} R R R M (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22)))) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22)))) (LinearMap.instSMulCommClass.{u_3, u_3, u_3, u_3, u_2, u_1} R R R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (DistribMulAction.toDistribSMul.{u_3, u_1} R M (MonoidWithZero.toMonoid.{u_3} R (Semiring.toMonoidWithZero.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22)) (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22))) (DistribMulAction.toDistribSMul.{u_3, u_1} R M (MonoidWithZero.toMonoid.{u_3} R (Semiring.toMonoidWithZero.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22)) (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22))) (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22)))))))))) (DFunLike.coe.{succ u_3, succ u_3, succ u_3} (RingHom.{u_3, u_3} R R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) R (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : R) => R) (RingHom.instFunLike.{u_3, u_3} R R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) c) (LinearMap.mk.{u_3, u_3, u_1, max u_1 u_2} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (LinearMap.module.{u_3, u_3, u_3, u_2, u_1} R R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (smulCommClass_self.{u_3, u_1} R M (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_3, u_1} R M (CommMonoid.toMonoid.{u_3} R (CommSemiring.toCommMonoid.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22)))) (AddHom.mk.{u_1, max u_1 u_2} M (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) (AddCommMagma.toAdd.{u_1} M (AddCommSemigroup.toAddCommMagma.{u_1} M (AddCommMonoid.toAddCommSemigroup.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13))) (AddCommMagma.toAdd.{max u_1 u_2} (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) (AddCommSemigroup.toAddCommMagma.{max u_1 u_2} (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) (AddCommMonoid.toAddCommSemigroup.{max u_1 u_2} (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))))))) (LinearMap.smulRight.{u_3, u_3, u_1, u_2} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (IsScalarTower.left.{u_3, u_1} R M (MonoidWithZero.toMonoid.{u_3} R (Semiring.toMonoidWithZero.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (DistribMulAction.toMulAction.{u_3, u_1} R M (MonoidWithZero.toMonoid.{u_3} R (Semiring.toMonoidWithZero.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22))) f) (fun (m : M) (m' : M) => LinearMap.smulRightₗ._proof_1.{u_1, u_2, u_3} R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 f m m')) (fun (c : R) (m : M) => LinearMap.smulRightₗ._proof_2.{u_1, u_2, u_3} R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 f c m)))","typeFull":"∀ {R : Type u_3} {M : Type u_1} {M₂ : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₂] [inst_3 : Module R M] [inst_4 : Module R M₂] (c : R) (f : M₂ →ₗ[R] R),\n  { toFun := (c • f).smulRight, map_add' := ⋯, map_smul' := ⋯ } =\n    (RingHom.id R) c • { toFun := f.smulRight, map_add' := ⋯, map_smul' := ⋯ }","typeReadable":"∀ {R : Type u_3} {M : Type u_1} {M₂ : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₂] [inst_3 : Module R M] [inst_4 : Module R M₂] (c : R) (f : M₂ →ₗ[R] R),\n  { toFun := (c • f).smulRight, map_add' := ⋯, map_smul' := ⋯ } =\n    (RingHom.id R) c • { toFun := f.smulRight, map_add' := ⋯, map_smul' := ⋯ 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[inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 : Module.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 : Module.{u_3, u_2} R M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16] (f : LinearMap.{u_3, u_3, u_2, u_3} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) (LinearMap.smulRight.{u_3, u_3, u_1, u_2} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (Semiring.toModule.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (IsScalarTower.left.{u_3, u_1} R M (MonoidWithZero.toMonoid.{u_3} R (Semiring.toMonoidWithZero.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (DistribMulAction.toMulAction.{u_3, u_1} R M (MonoidWithZero.toMonoid.{u_3} R (Semiring.toMonoidWithZero.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22))) f (HSMul.hSMul.{u_3, u_1, u_1} R M M (instHSMul.{u_3, u_1} R M (SMulZeroClass.toSMul.{u_3, u_1} R M (AddZero.toZero.{u_1} M (AddZeroClass.toAddZero.{u_1} M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_3, u_1} R M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_3, u_1} R M (MonoidWithZero.toMonoid.{u_3} R (Semiring.toMonoidWithZero.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13) (Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22))))) c m)) (HSMul.hSMul.{u_3, max u_1 u_2, max u_1 u_2} R (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) (SMulZeroClass.toSMul.{u_3, max u_1 u_2} R (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) (AddZero.toZero.{max u_1 u_2} (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) (AddZeroClass.toAddZero.{max u_1 u_2} (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) (AddMonoid.toAddZeroClass.{max u_1 u_2} (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))))))) (DistribSMul.toSMulZeroClass.{u_3, max u_1 u_2} R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))))) (DistribMulAction.toDistribSMul.{u_3, max u_1 u_2} R 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22) (LinearMap.addCommMonoid.{u_3, u_3, u_2, u_1} R R M₂ M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))))) (Module.toDistribMulAction.{u_3, max u_1 u_2} R (LinearMap.{u_3, u_3, u_2, u_1} R R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) M₂ M inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 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inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) R (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : R) => R) (RingHom.instFunLike.{u_3, u_3} R R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)) (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))) c) (LinearMap.smulRight.{u_3, u_3, u_1, u_2} R R M M₂ (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.16 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(Module.toDistribMulAction.{u_3, u_1} R M (CommSemiring.toSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.22))) f m))","typeFull":"∀ {R : Type u_3} {M : Type u_1} {M₂ : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₂] [inst_3 : Module R M] [inst_4 : Module R M₂] (f : M₂ →ₗ[R] R) (c : R) (m : M),\n  f.smulRight (c • m) = (RingHom.id R) c • f.smulRight m","typeReadable":"∀ {R : Type u_3} {M : Type u_1} {M₂ : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₂] [inst_3 : Module R M] [inst_4 : Module R M₂] (f : M₂ →ₗ[R] R) (c : R) (m : M),\n  f.smulRight (c • m) = (RingHom.id R) c • f.smulRight m","typeReferences":[["RingHom"],["smulCommClass_self"],["CommMonoid","toMonoid"],["Module"],["CommSemiring"],["RingHom","instFunLike"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["DistribMulAction","toMulAction"],["instHSMul"],["Eq"],["Semiring","toModule"],["DistribSMul","toSMulZeroClass"],["LinearMap","smulRight"],["IsScalarTower","left"],["LinearMap","module"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["CommSemiring","toSemiring"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["LinearMap"],["AddZeroClass","toAddZero"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["HSMul","hSMul"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["RingHom"],["smulCommClass_self"],["LinearMap","instFunLike"],["CommMonoid","toMonoid"],["RingHom","instFunLike"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["SMulCommClass","smul_comm"],["DFunLike","coe"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["LinearMap","ext"],["MonoidWithZero","toMonoid"],["DistribMulAction","toMulAction"],["instHSMul"],["Semiring","toModule"],["DistribSMul","toSMulZeroClass"],["LinearMap","smulRight"],["IsScalarTower","left"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["CommSemiring","toSemiring"],["LinearMap","module"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["LinearMap"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["HSMul","hSMul"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","applyₗ'","_proof_3"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_2}} {M₂ : Type.{u_3}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 : AddCommMonoid.{u_3} M₂] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 : Module.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 : Module.{u_1, u_3} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22] (f : LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 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inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) f (OfNat.ofNat.{u_2} M 0 (Zero.toOfNat0.{u_2} M (AddZero.toZero.{u_2} M (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16))))))) (DFunLike.coe.{max (succ u_3) (succ u_2), succ u_2, succ u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M₂) (LinearMap.instFunLike.{u_1, u_1, u_2, u_3} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) g (OfNat.ofNat.{u_2} M 0 (Zero.toOfNat0.{u_2} M (AddZero.toZero.{u_2} M (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16))))))))","typeFull":"∀ {R : Type u_1} {M : Type u_2} {M₂ : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₂] [inst_3 : Module R M] [inst_4 : Module R M₂] (f g : M →ₗ[R] M₂), (f + g) 0 = f 0 + g 0","typeReadable":"∀ {R : Type u_1} {M : Type u_2} {M₂ : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₂] [inst_3 : Module R M] [inst_4 : Module R M₂] (f g : M →ₗ[R] M₂), (f + g) 0 = f 0 + g 0","typeReferences":[["LinearMap","instFunLike"],["Module"],["instHAdd"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["LinearMap"],["DFunLike","coe"],["OfNat","ofNat"],["HAdd","hAdd"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["AddCommMonoid","toAddCommSemigroup"],["RingHom","id"],["LinearMap","instAdd"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Zero","toOfNat0"],["Eq"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["Semiring","toNonAssocSemiring"],["RingHom","id"],["Zero","toOfNat0"],["LinearMap","add_apply"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["AddZero","toZero"],["OfNat","ofNat"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","applyₗ'","_proof_8"],"typeFallback":"forall {R : Type.{u_4}} (S : Type.{u_3}) {M : Type.{u_2}} {M₂ : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 : Semiring.{u_4} R] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 : Semiring.{u_3} S] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 : AddCommMonoid.{u_1} M₂] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 : Module.{u_4, u_2} R M inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 : Module.{u_4, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 : Module.{u_3, u_1} S M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50 : SMulCommClass.{u_4, u_3, u_1} R S M₂ (SMulZeroClass.toSMul.{u_4, u_1} R M₂ (AddZero.toZero.{u_1} M₂ (AddZeroClass.toAddZero.{u_1} M₂ (AddMonoid.toAddZeroClass.{u_1} M₂ (AddCommMonoid.toAddMonoid.{u_1} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22)))) (DistribSMul.toSMulZeroClass.{u_4, u_1} R M₂ (AddMonoid.toAddZeroClass.{u_1} M₂ (AddCommMonoid.toAddMonoid.{u_1} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22)) (DistribMulAction.toDistribSMul.{u_4, u_1} R M₂ (MonoidWithZero.toMonoid.{u_4} R (Semiring.toMonoidWithZero.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22) (Module.toDistribMulAction.{u_4, u_1} R M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33)))) (SMulZeroClass.toSMul.{u_3, u_1} S M₂ (AddZero.toZero.{u_1} M₂ (AddZeroClass.toAddZero.{u_1} M₂ (AddMonoid.toAddZeroClass.{u_1} M₂ (AddCommMonoid.toAddMonoid.{u_1} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22)))) (DistribSMul.toSMulZeroClass.{u_3, u_1} S M₂ (AddMonoid.toAddZeroClass.{u_1} M₂ (AddCommMonoid.toAddMonoid.{u_1} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22)) (DistribMulAction.toDistribSMul.{u_3, u_1} S M₂ (MonoidWithZero.toMonoid.{u_3} S (Semiring.toMonoidWithZero.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (AddCommMonoid.toAddMonoid.{u_1} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22) (Module.toDistribMulAction.{u_3, u_1} S M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41))))] (x._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.119 : M) (x._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.121 : M), Eq.{max (succ u_1) (succ (max u_2 u_1))} (LinearMap.{u_3, u_3, max u_2 u_1, u_1} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (LinearMap.addCommMonoid.{u_4, u_4, u_2, u_1} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_4, u_4, u_3, u_2, u_1} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41) (LinearMap.mk.{u_3, u_3, max u_2 u_1, u_1} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (LinearMap.addCommMonoid.{u_4, u_4, u_2, u_1} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_4, u_4, u_3, u_2, u_1} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 (AddHom.mk.{max u_2 u_1, u_1} (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (AddCommMagma.toAdd.{max u_2 u_1} (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) (AddCommSemigroup.toAddCommMagma.{max u_2 u_1} (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) (AddCommMonoid.toAddCommSemigroup.{max u_2 u_1} (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) (LinearMap.addCommMonoid.{u_4, u_4, u_2, u_1} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)))))) (AddCommMagma.toAdd.{u_1} M₂ (AddCommSemigroup.toAddCommMagma.{u_1} M₂ (AddCommMonoid.toAddCommSemigroup.{u_1} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22))) (fun (f : LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) => DFunLike.coe.{max (succ u_2) (succ u_1), succ u_2, succ u_1} (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M₂) (LinearMap.instFunLike.{u_4, u_4, u_2, u_1} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) f (HAdd.hAdd.{u_2, u_2, u_2} M M M (instHAdd.{u_2} M (AddZero.toAdd.{u_2} M (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16))))) x._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.119 x._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.121)) (LinearMap.applyₗ'._proof_6.{u_4, u_2, u_1} R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 x._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.119 x._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.121)) (LinearMap.applyₗ'._proof_7.{u_4, u_2, u_1, u_3} R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50 x._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.119 x._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.121)) (HAdd.hAdd.{max u_2 u_1, max u_2 u_1, max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (LinearMap.addCommMonoid.{u_4, u_4, u_2, u_1} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_4, u_4, u_3, u_2, u_1} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41) (LinearMap.{u_3, u_3, max u_1 u_2, u_1} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (LinearMap.addCommMonoid.{u_4, u_4, u_2, u_1} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_4, u_4, u_3, u_2, u_1} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41) (LinearMap.{u_3, u_3, max u_1 u_2, u_1} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (LinearMap.addCommMonoid.{u_4, u_4, u_2, u_1} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_4, u_4, u_3, u_2, u_1} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41) (instHAdd.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (LinearMap.addCommMonoid.{u_4, u_4, u_2, u_1} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_4, u_4, u_3, u_2, u_1} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41) (AddZero.toAdd.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (LinearMap.addCommMonoid.{u_4, u_4, u_2, u_1} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_4, u_4, u_3, u_2, u_1} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41) (AddZeroClass.toAddZero.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (LinearMap.addCommMonoid.{u_4, u_4, u_2, u_1} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_4, u_4, u_3, u_2, u_1} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41) (AddMonoid.toAddZeroClass.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (LinearMap.addCommMonoid.{u_4, u_4, u_2, u_1} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_4, u_4, u_3, u_2, u_1} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41) (AddCommMonoid.toAddMonoid.{max u_2 u_1} (LinearMap.{u_3, u_3, max u_1 u_2, u_1} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (LinearMap.addCommMonoid.{u_4, u_4, u_2, u_1} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_4, u_4, u_3, u_2, u_1} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41) (LinearMap.addCommMonoid.{u_3, u_3, max u_2 u_1, u_1} S S (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_4, u_4, u_2, u_1} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_4, u_4, u_3, u_2, u_1} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)))))))) (LinearMap.mk.{u_3, u_3, max u_2 u_1, u_1} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (LinearMap.addCommMonoid.{u_4, u_4, u_2, u_1} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_4, u_4, u_3, u_2, u_1} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 (AddHom.mk.{max u_2 u_1, u_1} (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (AddCommMagma.toAdd.{max u_2 u_1} (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) (AddCommSemigroup.toAddCommMagma.{max u_2 u_1} (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) (AddCommMonoid.toAddCommSemigroup.{max u_2 u_1} (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) (LinearMap.addCommMonoid.{u_4, u_4, u_2, u_1} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)))))) (AddCommMagma.toAdd.{u_1} M₂ (AddCommSemigroup.toAddCommMagma.{u_1} M₂ (AddCommMonoid.toAddCommSemigroup.{u_1} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22))) (fun (f : LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) => DFunLike.coe.{max (succ u_2) (succ u_1), succ u_2, succ u_1} (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M₂) (LinearMap.instFunLike.{u_4, u_4, u_2, u_1} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) f x._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.119) (LinearMap.applyₗ'._proof_1.{u_4, u_2, u_1} R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 x._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.119)) (LinearMap.applyₗ'._proof_2.{u_4, u_2, u_1, u_3} R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50 x._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.119)) (LinearMap.mk.{u_3, u_3, max u_2 u_1, u_1} S S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13)) (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (LinearMap.addCommMonoid.{u_4, u_4, u_2, u_1} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 (LinearMap.module.{u_4, u_4, u_3, u_2, u_1} R R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 (AddHom.mk.{max u_2 u_1, u_1} (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M₂ (AddCommMagma.toAdd.{max u_2 u_1} (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) (AddCommSemigroup.toAddCommMagma.{max u_2 u_1} (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) (AddCommMonoid.toAddCommSemigroup.{max u_2 u_1} (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) (LinearMap.addCommMonoid.{u_4, u_4, u_2, u_1} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)))))) (AddCommMagma.toAdd.{u_1} M₂ (AddCommSemigroup.toAddCommMagma.{u_1} M₂ (AddCommMonoid.toAddCommSemigroup.{u_1} M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22))) (fun (f : LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) => DFunLike.coe.{max (succ u_2) (succ u_1), succ u_2, succ u_1} (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M₂) (LinearMap.instFunLike.{u_4, u_4, u_2, u_1} R R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10))) f x._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.121) (LinearMap.applyₗ'._proof_1.{u_4, u_2, u_1} R M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 x._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.121)) (LinearMap.applyₗ'._proof_2.{u_4, u_2, u_1, u_3} R S M M₂ inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.50 x._@.Mathlib.Algebra.Module.LinearMap.End.26689465._hygCtx._hyg.121)))","typeFull":"∀ {R : Type u_4} (S : Type u_3) {M : Type u_2} {M₂ : Type u_1} [inst : Semiring R] [inst_1 : Semiring S]\n  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R M₂]\n  [inst_6 : Module S M₂] [inst_7 : SMulCommClass R S M₂] (x x_1 : M),\n  { toFun := fun f => f (x + x_1), map_add' := ⋯, map_smul' := ⋯ } =\n    { toFun := fun f => f x, map_add' := ⋯, map_smul' := ⋯ } +\n      { toFun := fun f => f x_1, map_add' := ⋯, map_smul' := ⋯ }","typeReadable":"∀ {R : Type u_4} (S : Type u_3) {M : Type u_2} {M₂ : Type u_1} [inst : Semiring R] [inst_1 : Semiring S]\n  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R M₂]\n  [inst_6 : Module S M₂] [inst_7 : SMulCommClass R S M₂] (x x_1 : M),\n  { toFun := fun f => f (x + x_1), map_add' := ⋯, map_smul' := ⋯ } =\n    { toFun := fun f => f x, map_add' := ⋯, map_smul' := ⋯ } +\n      { toFun := fun f => f x_1, map_add' := ⋯, map_smul' := ⋯ 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(Module.toDistribMulAction.{u_1, u_1} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10)))) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LinearMap.End.1046452819._hygCtx._hyg.10))))))","typeFull":"∀ {R : Type u_1} [inst : CommSemiring R], SMulCommClass R R R","typeReadable":"∀ {R : Type u_1} [inst : CommSemiring R], SMulCommClass R R R","typeReferences":[["CommMonoid","toMonoid"],["CommSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["CommSemiring","toSemiring"],["SemigroupAction","toSMul"],["AddCommMonoid","toAddMonoid"],["CommSemiring","toCommMonoid"],["SMulCommClass"],["Module","toDistribMulAction"],["Semiring","toNonAssocSemiring"],["DistribMulAction","toMulAction"],["Monoid","toSemigroup"],["Semiring","toModule"],["MulAction","toSemigroupAction"]],"valueReferences":[["smulCommClass_self"],["Module","toDistribMulAction"],["Semiring","toNonAssocSemiring"],["CommMonoid","toMonoid"],["CommSemiring","toSemiring"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["DistribMulAction","toMulAction"],["AddCommMonoid","toAddMonoid"],["Semiring","toModule"],["CommSemiring","toCommMonoid"]]}]