diff --git "a/data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.Equiv.Basic.sym.json" "b/data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.Equiv.Basic.sym.json"
new file mode 100644--- /dev/null
+++ "b/data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.Equiv.Basic.sym.json"
@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["addMonoidHomLequivInt","_proof_5"],"typeFallback":"forall {A : Type.{u_1}} {B : Type.{u_2}} (R : Type.{u_3}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.13 : Semiring.{u_3} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16 : AddCommGroup.{u_1} A] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19 : AddCommGroup.{u_2} B] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.22 : Module.{u_3, u_2} R B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.13 (AddCommGroup.toAddCommMonoid.{u_2} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19)] (x._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.68 : R) (x._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.70 : AddMonoidHom.{u_1, u_2} A B (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (SubNegMonoid.toAddMonoid.{u_1} A (AddGroup.toSubNegMonoid.{u_1} A (AddCommGroup.toAddGroup.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16))))) (AddZeroClass.toAddZero.{u_2} B (AddMonoid.toAddZeroClass.{u_2} B (SubNegMonoid.toAddMonoid.{u_2} B (AddGroup.toSubNegMonoid.{u_2} B (AddCommGroup.toAddGroup.{u_2} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19)))))), Eq.{max (succ u_2) (succ u_1)} (LinearMap.{0, 0, u_1, u_2} Int Int Int.instSemiring Int.instSemiring (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int Int.instSemiring)) A B (AddCommGroup.toAddCommMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_2} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19) (AddCommGroup.toIntModule.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16) (AddCommGroup.toIntModule.{u_2} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19)) (AddMonoidHom.toIntLinearMap.{u_1, u_2} A B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19 (HSMul.hSMul.{u_3, max u_2 u_1, max u_2 u_1} R (AddMonoidHom.{u_1, u_2} A B (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (SubNegMonoid.toAddMonoid.{u_1} A (AddGroup.toSubNegMonoid.{u_1} A (AddCommGroup.toAddGroup.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16))))) (AddZeroClass.toAddZero.{u_2} B (AddMonoid.toAddZeroClass.{u_2} B (SubNegMonoid.toAddMonoid.{u_2} B (AddGroup.toSubNegMonoid.{u_2} B (AddCommGroup.toAddGroup.{u_2} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19)))))) (AddMonoidHom.{u_1, u_2} A B (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (SubNegMonoid.toAddMonoid.{u_1} A (AddGroup.toSubNegMonoid.{u_1} A (AddCommGroup.toAddGroup.{u_1} A 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(AddMonoidHom.instAddCommMonoid.{u_1, u_2} A B (AddMonoid.toAddZeroClass.{u_1} A (SubNegMonoid.toAddMonoid.{u_1} A (AddGroup.toSubNegMonoid.{u_1} A (AddCommGroup.toAddGroup.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16)))) (AddCommGroup.toAddCommMonoid.{u_2} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19)))))) (DistribSMul.toSMulZeroClass.{u_3, max u_2 u_1} R (AddMonoidHom.{u_1, u_2} A B (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (SubNegMonoid.toAddMonoid.{u_1} A (AddGroup.toSubNegMonoid.{u_1} A (AddCommGroup.toAddGroup.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16))))) (AddZeroClass.toAddZero.{u_2} B (AddMonoid.toAddZeroClass.{u_2} B (SubNegMonoid.toAddMonoid.{u_2} B (AddGroup.toSubNegMonoid.{u_2} B (AddCommGroup.toAddGroup.{u_2} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19)))))) (AddMonoid.toAddZeroClass.{max u_2 u_1} (AddMonoidHom.{u_1, u_2} A B (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (SubNegMonoid.toAddMonoid.{u_1} A (AddGroup.toSubNegMonoid.{u_1} A (AddCommGroup.toAddGroup.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16))))) (AddZeroClass.toAddZero.{u_2} B (AddMonoid.toAddZeroClass.{u_2} B (SubNegMonoid.toAddMonoid.{u_2} B (AddGroup.toSubNegMonoid.{u_2} B (AddCommGroup.toAddGroup.{u_2} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19)))))) (AddCommMonoid.toAddMonoid.{max u_2 u_1} (AddMonoidHom.{u_1, u_2} A B (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (SubNegMonoid.toAddMonoid.{u_1} A (AddGroup.toSubNegMonoid.{u_1} A (AddCommGroup.toAddGroup.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16))))) (AddZeroClass.toAddZero.{u_2} B (AddMonoid.toAddZeroClass.{u_2} B (SubNegMonoid.toAddMonoid.{u_2} B (AddGroup.toSubNegMonoid.{u_2} B (AddCommGroup.toAddGroup.{u_2} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19)))))) (AddMonoidHom.instAddCommMonoid.{u_1, u_2} A B (AddMonoid.toAddZeroClass.{u_1} A (SubNegMonoid.toAddMonoid.{u_1} A (AddGroup.toSubNegMonoid.{u_1} A (AddCommGroup.toAddGroup.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16)))) (AddCommGroup.toAddCommMonoid.{u_2} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19)))) (DistribMulAction.toDistribSMul.{u_3, max u_2 u_1} R (AddMonoidHom.{u_1, u_2} A B (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (SubNegMonoid.toAddMonoid.{u_1} A (AddGroup.toSubNegMonoid.{u_1} A (AddCommGroup.toAddGroup.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16))))) (AddZeroClass.toAddZero.{u_2} B (AddMonoid.toAddZeroClass.{u_2} B (SubNegMonoid.toAddMonoid.{u_2} B (AddGroup.toSubNegMonoid.{u_2} B (AddCommGroup.toAddGroup.{u_2} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19)))))) (MonoidWithZero.toMonoid.{u_3} R (Semiring.toMonoidWithZero.{u_3} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.13)) (AddCommMonoid.toAddMonoid.{max u_2 u_1} (AddMonoidHom.{u_1, u_2} A B (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (SubNegMonoid.toAddMonoid.{u_1} A (AddGroup.toSubNegMonoid.{u_1} A (AddCommGroup.toAddGroup.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16))))) (AddZeroClass.toAddZero.{u_2} B (AddMonoid.toAddZeroClass.{u_2} B (SubNegMonoid.toAddMonoid.{u_2} B (AddGroup.toSubNegMonoid.{u_2} B (AddCommGroup.toAddGroup.{u_2} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19)))))) (AddMonoidHom.instAddCommMonoid.{u_1, u_2} A B (AddMonoid.toAddZeroClass.{u_1} A (SubNegMonoid.toAddMonoid.{u_1} A (AddGroup.toSubNegMonoid.{u_1} A (AddCommGroup.toAddGroup.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16)))) (AddCommGroup.toAddCommMonoid.{u_2} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19))) (Module.toDistribMulAction.{u_3, max u_2 u_1} R (AddMonoidHom.{u_1, u_2} A B (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (SubNegMonoid.toAddMonoid.{u_1} A (AddGroup.toSubNegMonoid.{u_1} A (AddCommGroup.toAddGroup.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16))))) (AddZeroClass.toAddZero.{u_2} B (AddMonoid.toAddZeroClass.{u_2} B (SubNegMonoid.toAddMonoid.{u_2} B (AddGroup.toSubNegMonoid.{u_2} B (AddCommGroup.toAddGroup.{u_2} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19)))))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.13 (AddMonoidHom.instAddCommMonoid.{u_1, u_2} A B (AddMonoid.toAddZeroClass.{u_1} A (SubNegMonoid.toAddMonoid.{u_1} A (AddGroup.toSubNegMonoid.{u_1} A (AddCommGroup.toAddGroup.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16)))) (AddCommGroup.toAddCommMonoid.{u_2} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19)) (AddMonoidHom.instModule.{u_3, u_1, u_2} R A B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.13 (SubNegMonoid.toAddMonoid.{u_1} A (AddGroup.toSubNegMonoid.{u_1} A (AddCommGroup.toAddGroup.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16))) (AddCommGroup.toAddCommMonoid.{u_2} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.22)))))) x._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.68 x._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.70))","typeFull":"∀ {A : Type u_1} {B : Type u_2} (R : Type u_3) [inst : Semiring R] [inst_1 : AddCommGroup A] [inst_2 : AddCommGroup B]\n  [inst_3 : Module R B] (x : R) (x_1 : A →+ B), (x • x_1).toIntLinearMap = (x • x_1).toIntLinearMap","typeReadable":"∀ {A : Type u_1} {B : Type u_2} (R : Type u_3) [inst : Semiring R] [inst_1 : AddCommGroup A] [inst_2 : AddCommGroup B]\n  [inst_3 : Module R B] (x : R) (x_1 : A →+ B), (x • x_1).toIntLinearMap = (x • x_1).toIntLinearMap","typeReferences":[["Module"],["AddCommGroup","toAddGroup"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddMonoidHom","instModule"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["AddMonoidHom"],["MonoidWithZero","toMonoid"],["instHSMul"],["AddGroup","toSubNegMonoid"],["Eq"],["DistribSMul","toSMulZeroClass"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddMonoidHom","toIntLinearMap"],["AddCommGroup"],["LinearMap"],["AddZeroClass","toAddZero"],["AddCommGroup","toIntModule"],["Int"],["Module","toDistribMulAction"],["SubNegMonoid","toAddMonoid"],["Int","instSemiring"],["HSMul","hSMul"],["AddCommGroup","toAddCommMonoid"],["AddMonoidHom","instAddCommMonoid"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["AddCommGroup","toAddGroup"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddMonoidHom","instModule"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["AddMonoidHom"],["MonoidWithZero","toMonoid"],["instHSMul"],["AddGroup","toSubNegMonoid"],["DistribSMul","toSMulZeroClass"],["rfl"],["DistribMulAction","toDistribSMul"],["AddMonoidHom","toIntLinearMap"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["LinearMap"],["AddCommGroup","toIntModule"],["Int"],["Module","toDistribMulAction"],["SubNegMonoid","toAddMonoid"],["Int","instSemiring"],["HSMul","hSMul"],["AddCommGroup","toAddCommMonoid"],["AddMonoidHom","instAddCommMonoid"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","coe_toLinearMap_mul"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_5}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.19 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.25 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.19] {e₁ : LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10) 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.25) (instHMul.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.25) (DivInvMonoid.toMonoid.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.25) (Group.toDivInvMonoid.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.25) (LinearEquiv.automorphismGroup.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.25))))))) e₁ e₂)) (HMul.hMul.{u_5, u_5, u_5} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.25) (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.25) (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.25) (instHMul.{u_5} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.25) (Module.End.instMul.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.25)) (LinearEquiv.toLinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.25 e₁) (LinearEquiv.toLinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1759538277._hygCtx._hyg.25 e₂))","typeFull":"∀ {R : Type u_1} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  {e₁ e₂ : M ≃ₗ[R] M}, ↑(e₁ * e₂) = ↑e₁ * ↑e₂","typeReadable":"∀ {R : Type u_1} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  {e₁ e₂ : M ≃ₗ[R] M}, ↑(e₁ * e₂) = ↑e₁ * ↑e₂","typeReferences":[["MulOneClass","toMulOne"],["Module"],["HMul","hMul"],["LinearEquiv","toLinearMap"],["LinearEquiv"],["LinearMap"],["Module","End","instMul"],["LinearEquiv","automorphismGroup"],["AddCommMonoid"],["MulOne","toMul"],["Semiring","toNonAssocSemiring"],["DivInvMonoid","toMonoid"],["RingHom","id"],["Monoid","toMulOneClass"],["RingHomInvPair","ids"],["instHMul"],["Eq"],["Group","toDivInvMonoid"],["Semiring"]],"valueReferences":[["rfl"],["MulOneClass","toMulOne"],["HMul","hMul"],["LinearEquiv","toLinearMap"],["LinearMap"],["LinearEquiv"],["LinearEquiv","automorphismGroup"],["MulOne","toMul"],["Semiring","toNonAssocSemiring"],["DivInvMonoid","toMonoid"],["RingHom","id"],["Monoid","toMulOneClass"],["RingHomInvPair","ids"],["instHMul"],["Group","toDivInvMonoid"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","conj_conj_symm"],"typeFallback":"forall {R₁' : Type.{u_12}} {R₂' : Type.{u_13}} {M₁' : Type.{u_20}} {M₂' : Type.{u_21}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59 : CommSemiring.{u_12} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62 : CommSemiring.{u_13} R₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 : AddCommMonoid.{u_20} M₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 : AddCommMonoid.{u_21} M₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 : Module.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 : Module.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86] {σ₁'₂' : RingHom.{u_12, u_13} R₁' R₂' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59)) (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62))} {σ₂'₁' : RingHom.{u_13, u_12} R₂' R₁' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62)) (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59))} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.293 : RingHomInvPair.{u_12, u_13} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) σ₁'₂' σ₂'₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.297 : RingHomInvPair.{u_13, u_12} R₂' R₁' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) σ₂'₁' σ₁'₂'] (e : LinearEquiv.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.297 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114) (f : Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114), Eq.{succ u_21} (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114) (DFunLike.coe.{max (succ u_20) (succ u_21), succ u_20, succ u_21} (LinearEquiv.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.297 (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59)))) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62)))) (LinearMap.module.{u_12, u_12, u_12, u_20, u_20} R₁' R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62))) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114))))) (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110) => Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114) (EquivLike.toFunLike.{max (succ u_20) (succ u_21), succ u_20, succ u_21} (LinearEquiv.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.297 (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59)))) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62)))) (LinearMap.module.{u_12, u_12, u_12, u_20, u_20} R₁' R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62))) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114))))) (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114) (LinearEquiv.instEquivLike.{u_12, u_13, u_20, u_21} R₁' R₂' (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59)))) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62)))) (LinearMap.module.{u_12, u_12, u_12, u_20, u_20} R₁' R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62))) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114)))) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.297)) (LinearEquiv.conj.{u_12, u_13, u_20, u_21} R₁' R₂' M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.297 e) (DFunLike.coe.{max (succ u_20) (succ u_21), succ u_21, succ u_20} (LinearEquiv.{u_13, u_12, u_21, u_20} R₂' R₁' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) σ₂'₁' σ₁'₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.297 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.293 (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114) (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62)))) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62))) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114)))) (LinearMap.module.{u_12, u_12, u_12, u_20, u_20} R₁' R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110))))) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114) => Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110) (EquivLike.toFunLike.{max (succ u_20) (succ u_21), succ u_21, succ u_20} (LinearEquiv.{u_13, u_12, u_21, u_20} R₂' R₁' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) σ₂'₁' σ₁'₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.297 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.293 (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114) (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62)))) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62))) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114)))) (LinearMap.module.{u_12, u_12, u_12, u_20, u_20} R₁' R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114) (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110) (LinearEquiv.instEquivLike.{u_13, u_12, u_21, u_20} R₂' R₁' (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114) (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62)))) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62))) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114)))) (LinearMap.module.{u_12, u_12, u_12, u_20, u_20} R₁' R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110)))) σ₂'₁' σ₁'₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.297 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.293)) (LinearEquiv.conj.{u_13, u_12, u_21, u_20} R₂' R₁' M₂' M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 σ₂'₁' σ₁'₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.297 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.293 (LinearEquiv.symm.{u_12, u_13, u_20, u_21} R₁' R₂' M₁' M₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.114 σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2430078776._hygCtx._hyg.297 e)) f)) f","typeFull":"∀ {R₁' : Type u_12} {R₂' : Type u_13} {M₁' : Type u_20} {M₂' : Type u_21} [inst : CommSemiring R₁']\n  [inst_1 : CommSemiring R₂'] [inst_2 : AddCommMonoid M₁'] [inst_3 : AddCommMonoid M₂'] [inst_4 : Module R₁' M₁']\n  [inst_5 : Module R₂' M₂'] {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} [inst_6 : RingHomInvPair σ₁'₂' σ₂'₁']\n  [inst_7 : RingHomInvPair σ₂'₁' σ₁'₂'] (e : M₁' ≃ₛₗ[σ₁'₂'] M₂') (f : Module.End R₂' M₂'), e.conj (e.symm.conj f) = f","typeReadable":"∀ {R₁' : Type u_12} {R₂' : Type u_13} {M₁' : Type u_20} {M₂' : Type u_21} [inst : CommSemiring R₁']\n  [inst_1 : CommSemiring R₂'] [inst_2 : AddCommMonoid M₁'] [inst_3 : AddCommMonoid M₂'] [inst_4 : Module R₁' M₁']\n  [inst_5 : Module R₂' M₂'] {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} [inst_6 : RingHomInvPair σ₁'₂' σ₂'₁']\n  [inst_7 : RingHomInvPair σ₂'₁' σ₁'₂'] (e : M₁' ≃ₛₗ[σ₁'₂'] M₂') (f : Module.End R₂' M₂'), e.conj (e.symm.conj f) = f","typeReferences":[["smulCommClass_self"],["RingHom"],["Module","End"],["CommMonoid","toMonoid"],["Module"],["LinearMap","module"],["CommSemiring"],["CommSemiring","toSemiring"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["LinearEquiv","symm"],["DFunLike","coe"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["LinearEquiv","conj"],["Module","toDistribMulAction"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["EquivLike","toFunLike"],["DistribMulAction","toMulAction"],["LinearEquiv","instEquivLike"],["RingHomInvPair"],["Eq"]],"valueReferences":[["smulCommClass_self"],["CommMonoid","toMonoid"],["LinearMap","instFunLike"],["Eq","trans"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["DFunLike","coe"],["congrArg"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["LinearMap","ext"],["EquivLike","toFunLike"],["DistribMulAction","toMulAction"],["congrFun'"],["LinearEquiv","instEquivLike"],["Eq"],["Module","End"],["True"],["LinearMap","module"],["CommSemiring","toSemiring"],["LinearMap"],["LinearEquiv","symm"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["eq_self"],["Module","toDistribMulAction"],["LinearEquiv","conj"],["of_eq_true"],["LinearEquiv","apply_symm_apply"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","automorphismGroup","_proof_2"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 : Module.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19] (n : Nat) (x : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25), Eq.{succ u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (npowRecAuto.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Semigroup.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f)) (fun (x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.56 : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.58 : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.60 : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => rfl.{succ u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (HMul.hMul.{u_2, u_2, u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (instHMul.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f))) (HMul.hMul.{u_2, u_2, u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (instHMul.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f))) x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.56 x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.58) x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.60))) (One.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.refl.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x) (HMul.hMul.{u_2, u_2, u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (instHMul.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f))) (npowRecAuto.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Semigroup.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f)) (fun (x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.56 : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.58 : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.60 : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => rfl.{succ u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (HMul.hMul.{u_2, u_2, u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (instHMul.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f))) (HMul.hMul.{u_2, u_2, u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (instHMul.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f))) x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.56 x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.58) x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.60))) (One.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25)) n x) x)","typeFull":"∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (n : ℕ)\n  (x : M ≃ₗ[R] M), npowRecAuto (n + 1) x = npowRecAuto n x * x","typeReadable":"∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (n : ℕ)\n  (x : M ≃ₗ[R] M), npowRecAuto (n + 1) x = npowRecAuto n x * x","typeReferences":[["instAddNat"],["rfl"],["Mul","mk"],["instHAdd"],["RingHomCompTriple","ids"],["Module"],["One","mk"],["HMul","hMul"],["LinearEquiv"],["OfNat","ofNat"],["HAdd","hAdd"],["LinearEquiv","trans"],["AddCommMonoid"],["Nat"],["npowRecAuto"],["Semiring","toNonAssocSemiring"],["Semigroup","mk"],["instOfNatNat"],["RingHom","id"],["RingHomInvPair","ids"],["instHMul"],["Eq"],["LinearEquiv","refl"],["Semiring"]],"valueReferences":[["instAddNat"],["Mul","mk"],["rfl"],["instHAdd"],["RingHomCompTriple","ids"],["One","mk"],["HMul","hMul"],["LinearEquiv"],["OfNat","ofNat"],["HAdd","hAdd"],["LinearEquiv","trans"],["Nat"],["npowRecAuto"],["Semiring","toNonAssocSemiring"],["Semigroup","mk"],["instOfNatNat"],["RingHom","id"],["Eq","refl"],["RingHomInvPair","ids"],["instHMul"],["LinearEquiv","refl"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","automorphismGroup","toLinearMapMonoidHom_apply"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_5}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19] (e : LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25), Eq.{succ u_5} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (DFunLike.coe.{succ u_5, succ u_5, succ u_5} (MonoidHom.{u_5, u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (MulOneClass.toMulOne.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (Monoid.toMulOneClass.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (DivInvMonoid.toMonoid.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (Group.toDivInvMonoid.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (LinearEquiv.automorphismGroup.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25))))) (MulOneClass.toMulOne.{u_5} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (MulZeroOneClass.toMulOneClass.{u_5} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (NonAssocSemiring.toMulZeroOneClass.{u_5} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (Semiring.toNonAssocSemiring.{u_5} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (Module.End.instSemiring.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25)))))) (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) => LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (MonoidHom.instFunLike.{u_5, u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (MulOneClass.toMulOne.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (Monoid.toMulOneClass.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (DivInvMonoid.toMonoid.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (Group.toDivInvMonoid.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (LinearEquiv.automorphismGroup.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25))))) (MulOneClass.toMulOne.{u_5} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (MulZeroOneClass.toMulOneClass.{u_5} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (NonAssocSemiring.toMulZeroOneClass.{u_5} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (Semiring.toNonAssocSemiring.{u_5} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (Module.End.instSemiring.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25)))))) (LinearEquiv.automorphismGroup.toLinearMapMonoidHom.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) e) (LinearEquiv.toLinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 e)","typeFull":"∀ {R : Type u_1} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (e : M ≃ₗ[R] M),\n  LinearEquiv.automorphismGroup.toLinearMapMonoidHom e = ↑e","typeReadable":"∀ {R : Type u_1} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (e : M ≃ₗ[R] M),\n  LinearEquiv.automorphismGroup.toLinearMapMonoidHom e = ↑e","typeReferences":[["MulOneClass","toMulOne"],["Module","End","instSemiring"],["LinearEquiv","automorphismGroup","toLinearMapMonoidHom"],["Module"],["MonoidHom"],["MonoidHom","instFunLike"],["LinearEquiv","toLinearMap"],["MulZeroOneClass","toMulOneClass"],["LinearEquiv"],["LinearMap"],["DFunLike","coe"],["LinearEquiv","automorphismGroup"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["DivInvMonoid","toMonoid"],["RingHom","id"],["Monoid","toMulOneClass"],["RingHomInvPair","ids"],["Eq"],["Group","toDivInvMonoid"],["NonAssocSemiring","toMulZeroOneClass"],["Semiring"]],"valueReferences":[["MulOneClass","toMulOne"],["Module","End","instSemiring"],["LinearEquiv","automorphismGroup","toLinearMapMonoidHom"],["MonoidHom"],["MonoidHom","instFunLike"],["MulZeroOneClass","toMulOneClass"],["LinearMap"],["LinearEquiv"],["DFunLike","coe"],["LinearEquiv","automorphismGroup"],["Semiring","toNonAssocSemiring"],["DivInvMonoid","toMonoid"],["RingHom","id"],["Eq","refl"],["Monoid","toMulOneClass"],["RingHomInvPair","ids"],["Group","toDivInvMonoid"],["NonAssocSemiring","toMulZeroOneClass"]]},{"isProp":true,"kind":"theorem","name":["Units","mulRightLinearEquiv_trans_mulRightLinearEquiv"],"typeFallback":"forall {R : Type.{u_9}} {A : Type.{u_10}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.285492511._hygCtx._hyg.12 : Semiring.{u_9} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.285492511._hygCtx._hyg.15 : Semiring.{u_10} A] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.285492511._hygCtx._hyg.18 : Module.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.285492511._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.285492511._hygCtx._hyg.15)))] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.285492511._hygCtx._hyg.22 : IsScalarTower.{u_9, u_10, u_10} R A A (SMulZeroClass.toSMul.{u_9, u_10} R A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.285492511._hygCtx._hyg.15))) (b : Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.285492511._hygCtx._hyg.15))), Eq.{succ u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.285492511._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.285492511._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.285492511._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.285492511._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.285492511._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.285492511._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.4207874633._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4207874633._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4207874633._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4207874633._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4207874633._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4207874633._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4207874633._hygCtx._hyg.25) (DivInvOneMonoid.toInvOneClass.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4207874633._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4207874633._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4207874633._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4207874633._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4207874633._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4207874633._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4207874633._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4207874633._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4207874633._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4207874633._hygCtx._hyg.25) (DivisionMonoid.toDivInvOneMonoid.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4207874633._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4207874633._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4207874633._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.4207874633._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4207874633._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4207874633._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4207874633._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4207874633._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4207874633._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4207874633._hygCtx._hyg.25) (LinearEquiv.automorphismGroup.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4207874633._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4207874633._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4207874633._hygCtx._hyg.25)))))))) (LinearMap.id.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4207874633._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4207874633._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4207874633._hygCtx._hyg.25)","typeFull":"∀ {R : Type u_1} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M], ↑1 = LinearMap.id","typeReadable":"∀ {R : Type u_1} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M], ↑1 = 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.27)) M (LinearMap.{u_1, u_1, u_1, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10))) 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.23 (LinearMap.module.{u_1, u_1, u_4, u_1, u_5} R R S R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.16 (Semiring.toModule.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.27) (RingHom.id.{u_4} S (Semiring.toNonAssocSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.13)) (RingHom.id.{u_4} S (Semiring.toNonAssocSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.13)) (RingHomInvPair.ids.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.13) (RingHomInvPair.ids.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.13))) (LinearEquiv.symm.{u_4, u_4, max u_5 u_1, u_5} S S (LinearMap.{u_1, u_1, u_1, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.27) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.23 (RingHom.id.{u_4} S (Semiring.toNonAssocSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.13)) (RingHom.id.{u_4} S (Semiring.toNonAssocSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.13)) (RingHomInvPair.ids.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.13) (RingHomInvPair.ids.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.13) (LinearMap.ringLmapEquivSelf.{u_1, u_4, u_5} R S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.27)) x) (LinearMap.smulRight.{u_1, u_1, u_5, u_1} R R M R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.16 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.19 (Semiring.toModule.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 (Semiring.toModule.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.19 (LinearMap.ringLmapEquivSelf._proof_5.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.19) (OfNat.ofNat.{u_1} (LinearMap.{u_1, u_1, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10)) R R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10))) (Semiring.toModule.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10) (Semiring.toModule.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10)) 1 (One.toOfNat1.{u_1} (LinearMap.{u_1, u_1, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10)) R R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10))) (Semiring.toModule.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10) (Semiring.toModule.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10)) (Module.End.instOne.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10))) (Semiring.toModule.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10)))) x)","typeFull":"∀ (R : Type u_1) (S : Type u_4) (M : Type u_5) [inst : Semiring R] [inst_1 : Semiring S] [inst_2 : AddCommMonoid M]\n  [inst_3 : Module R M] [inst_4 : Module S M] [inst_5 : SMulCommClass R S M] (x : M),\n  (LinearMap.ringLmapEquivSelf R S M).symm x = LinearMap.smulRight 1 x","typeReadable":"∀ (R : Type u_1) (S : Type u_4) (M : Type u_5) [inst : Semiring R] [inst_1 : Semiring S] [inst_2 : AddCommMonoid M]\n  [inst_3 : Module R M] [inst_4 : Module S M] [inst_5 : SMulCommClass R S M] (x : M),\n  (LinearMap.ringLmapEquivSelf R S M).symm x = LinearMap.smulRight 1 x","typeReferences":[["LinearMap","ringLmapEquivSelf","_proof_5"],["Module"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["DFunLike","coe"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["EquivLike","toFunLike"],["MonoidWithZero","toMonoid"],["Module","End","instOne"],["LinearMap","ringLmapEquivSelf"],["LinearEquiv","instEquivLike"],["Eq"],["Semiring","toModule"],["DistribSMul","toSMulZeroClass"],["LinearMap","smulRight"],["LinearMap","module"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["LinearMap"],["LinearEquiv","symm"],["OfNat","ofNat"],["LinearMap","addCommMonoid"],["SMulCommClass"],["Module","toDistribMulAction"],["One","toOfNat1"],["RingHomInvPair","ids"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["LinearMap","module"],["LinearMap"],["LinearEquiv"],["LinearEquiv","symm"],["DFunLike","coe"],["LinearMap","addCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Eq","refl"],["EquivLike","toFunLike"],["RingHomInvPair","ids"],["LinearMap","ringLmapEquivSelf"],["LinearEquiv","instEquivLike"],["Semiring","toModule"]]},{"isProp":false,"kind":"definition","name":["LinearEquiv","restrictScalars"],"typeFallback":"forall (R : Type.{u_1}) {S : Type.{u_4}} {M : Type.{u_5}} {M₂ : Type.{u_7}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 : Semiring.{u_4} S] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22 : AddCommMonoid.{u_7} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.25 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.29 : Module.{u_1, u_7} R M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.33 : Module.{u_4, u_5} S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.37 : Module.{u_4, u_7} S M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.41 : LinearMap.CompatibleSMul.{u_5, u_7, u_1, u_4} M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22 R S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 (SMulZeroClass.toSMul.{u_1, u_5} R M (AddZero.toZero.{u_5} M (AddZeroClass.toAddZero.{u_5} M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19)))) (DistribSMul.toSMulZeroClass.{u_1, u_5} R M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19)) (DistribMulAction.toDistribSMul.{u_1, u_5} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19) (Module.toDistribMulAction.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.25)))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.33 (SMulZeroClass.toSMul.{u_1, u_7} R M₂ (AddZero.toZero.{u_7} M₂ (AddZeroClass.toAddZero.{u_7} M₂ (AddMonoid.toAddZeroClass.{u_7} M₂ (AddCommMonoid.toAddMonoid.{u_7} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22)))) (DistribSMul.toSMulZeroClass.{u_1, u_7} R M₂ (AddMonoid.toAddZeroClass.{u_7} M₂ (AddCommMonoid.toAddMonoid.{u_7} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22)) (DistribMulAction.toDistribSMul.{u_1, u_7} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_7} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22) (Module.toDistribMulAction.{u_1, u_7} R M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.29)))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.37], (LinearEquiv.{u_4, u_4, u_5, u_7} S S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 (RingHom.id.{u_4} S (Semiring.toNonAssocSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13)) (RingHom.id.{u_4} S (Semiring.toNonAssocSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13)) (RingHomInvPair.ids.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13) (RingHomInvPair.ids.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13) M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.37) -> (LinearEquiv.{u_1, u_1, u_5, u_7} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10) M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.29)","typeFull":"(R : Type u_1) →\n  {S : Type u_4} →\n    {M : Type u_5} →\n      {M₂ : Type u_7} →\n        [inst : Semiring R] →\n          [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 M] →\n                      [inst_7 : Module S M₂] → [LinearMap.CompatibleSMul M M₂ R S] → (M ≃ₗ[S] M₂) → M ≃ₗ[R] M₂","typeReadable":"(R : Type u_1) →\n  {S : Type u_4} →\n    {M : Type u_5} →\n      {M₂ : Type u_7} →\n        [inst : Semiring R] →\n          [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 M] →\n                      [inst_7 : Module S M₂] → [LinearMap.CompatibleSMul M M₂ R S] → (M ≃ₗ[S] M₂) → M ≃ₗ[R] M₂","typeReferences":[["LinearMap","CompatibleSMul"],["Module"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["AddZeroClass","toAddZero"],["Module","toDistribMulAction"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["RingHomInvPair","ids"],["AddZero","toZero"],["Semiring"],["AddMonoid","toAddZeroClass"],["DistribSMul","toSMulZeroClass"]],"valueReferences":[["LinearMap","mk"],["AddHom","mk"],["LinearEquiv","restrictScalars","_proof_1"],["LinearEquiv","toLinearMap"],["LinearEquiv","restrictScalars","_proof_4"],["LinearEquiv"],["LinearEquiv","symm"],["DFunLike","coe"],["LinearEquiv","restrictScalars","_proof_2"],["Semiring","toNonAssocSemiring"],["AddCommMonoid","toAddCommSemigroup"],["RingHom","id"],["EquivLike","toFunLike"],["RingHomInvPair","ids"],["LinearEquiv","mk"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["LinearEquiv","restrictScalars","_proof_3"],["LinearEquiv","instEquivLike"],["LinearMap","restrictScalars"]]},{"isProp":true,"kind":"theorem","name":["addMonoidHomLequivInt","_proof_3"],"typeFallback":"forall {B : Type.{u_2}} (R : Type.{u_1}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.13 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19 : AddCommGroup.{u_2} B] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.22 : Module.{u_1, u_2} R B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.13 (AddCommGroup.toAddCommMonoid.{u_2} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19)], SMulCommClass.{0, u_1, u_2} Int R B (SubNegMonoid.toZSMul.{u_2} B (AddGroup.toSubNegMonoid.{u_2} B (AddCommGroup.toAddGroup.{u_2} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19))) (SMulZeroClass.toSMul.{u_1, u_2} R B (AddZero.toZero.{u_2} B (AddZeroClass.toAddZero.{u_2} B (AddMonoid.toAddZeroClass.{u_2} B (SubNegMonoid.toAddMonoid.{u_2} B (AddGroup.toSubNegMonoid.{u_2} B (AddCommGroup.toAddGroup.{u_2} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19)))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R B (AddMonoid.toAddZeroClass.{u_2} B (SubNegMonoid.toAddMonoid.{u_2} B (AddGroup.toSubNegMonoid.{u_2} B (AddCommGroup.toAddGroup.{u_2} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19)))) (DistribMulAction.toDistribSMul.{u_1, u_2} R B (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.13)) (SubNegMonoid.toAddMonoid.{u_2} B (AddGroup.toSubNegMonoid.{u_2} B (AddCommGroup.toAddGroup.{u_2} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19))) (Module.toDistribMulAction.{u_1, u_2} R B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.13 (AddCommGroup.toAddCommMonoid.{u_2} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.22))))","typeFull":"∀ {B : Type u_2} (R : Type u_1) [inst : Semiring R] [inst_1 : AddCommGroup B] [inst_2 : Module R B], SMulCommClass ℤ R B","typeReadable":"∀ {B : Type u_2} (R : Type u_1) [inst : Semiring R] [inst_1 : AddCommGroup B] [inst_2 : Module R B], SMulCommClass ℤ R B","typeReferences":[["Module"],["AddCommGroup","toAddGroup"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddCommGroup"],["SMulZeroClass","toSMul"],["AddZeroClass","toAddZero"],["Int"],["SMulCommClass"],["Module","toDistribMulAction"],["SubNegMonoid","toAddMonoid"],["MonoidWithZero","toMonoid"],["AddCommGroup","toAddCommMonoid"],["AddGroup","toSubNegMonoid"],["SubNegMonoid","toZSMul"],["AddZero","toZero"],["DistribSMul","toSMulZeroClass"],["Semiring"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["Module","toDistribMulAction"],["SubNegMonoid","toAddMonoid"],["AddCommGroup","toAddGroup"],["MonoidWithZero","toMonoid"],["AddCommGroup","toAddCommMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddGroup","toSubNegMonoid"],["AddGroup","int_smulCommClass"]]},{"isProp":false,"kind":"definition","name":["LinearEquiv","congrLeft"],"typeFallback":"forall (M : Type.{u_5}) {M₂ : Type.{u_7}} {M₃ : Type.{u_8}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 : AddCommMonoid.{u_7} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.19 : AddCommMonoid.{u_8} M₃] {R : Type.{u_9}} (S : Type.{u_10}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 : Semiring.{u_9} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.39 : Semiring.{u_10} S] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 : Module.{u_9, u_7} R M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.46 : Module.{u_9, u_8} R M₃ inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50 : Module.{u_9, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.54 : Module.{u_10, u_5} S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.58 : SMulCommClass.{u_9, u_10, u_5} R S M (SMulZeroClass.toSMul.{u_9, u_5} R M (AddZero.toZero.{u_5} M (AddZeroClass.toAddZero.{u_5} M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_9, u_5} R M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_9, u_5} R M (MonoidWithZero.toMonoid.{u_9} R (Semiring.toMonoidWithZero.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13) (Module.toDistribMulAction.{u_9, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50)))) (SMulZeroClass.toSMul.{u_10, u_5} S M (AddZero.toZero.{u_5} M (AddZeroClass.toAddZero.{u_5} M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_10, u_5} S M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_10, u_5} S M (MonoidWithZero.toMonoid.{u_10} S (Semiring.toMonoidWithZero.{u_10} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.39)) (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13) (Module.toDistribMulAction.{u_10, u_5} S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.54))))], (LinearEquiv.{u_9, u_9, u_7, u_8} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.39) (RingHomInvPair.ids.{u_10} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.39) (LinearMap.{u_9, u_9, u_7, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50) (LinearMap.{u_9, u_9, u_8, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) M₃ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50) (LinearMap.addCommMonoid.{u_9, u_9, u_7, u_5} R R M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36))) (LinearMap.addCommMonoid.{u_9, u_9, u_8, u_5} R R M₃ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36))) (LinearMap.module.{u_9, u_9, u_10, u_7, u_5} R R S M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.54 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.58) (LinearMap.module.{u_9, u_9, u_10, u_8, u_5} R R S M₃ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.54 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.58))","typeFull":"(M : Type u_5) →\n  {M₂ : Type u_7} →\n    {M₃ : Type u_8} →\n      [inst : AddCommMonoid M] →\n        [inst_1 : AddCommMonoid M₂] →\n          [inst_2 : AddCommMonoid M₃] →\n            {R : Type u_9} →\n              (S : Type u_10) →\n                [inst_3 : Semiring R] →\n                  [inst_4 : Semiring S] →\n                    [inst_5 : Module R M₂] →\n                      [inst_6 : Module R M₃] →\n                        [inst_7 : Module R M] →\n                          [inst_8 : Module S M] →\n                            [inst_9 : SMulCommClass R S M] → (M₂ ≃ₗ[R] M₃) → (M₂ →ₗ[R] M) ≃ₗ[S] M₃ →ₗ[R] M","typeReadable":"(M : Type u_5) →\n  {M₂ : Type u_7} →\n    {M₃ : Type u_8} →\n      [inst : AddCommMonoid M] →\n        [inst_1 : AddCommMonoid M₂] →\n          [inst_2 : AddCommMonoid M₃] →\n            {R : Type u_9} →\n              (S : Type u_10) →\n                [inst_3 : Semiring R] →\n                  [inst_4 : Semiring S] →\n                    [inst_5 : Module R M₂] →\n                      [inst_6 : Module R M₃] →\n                        [inst_7 : Module R M] →\n                          [inst_8 : Module S M] →\n                            [inst_9 : SMulCommClass R S M] → (M₂ ≃ₗ[R] M₃) → (M₂ →ₗ[R] M) ≃ₗ[S] M₃ →ₗ[R] M","typeReferences":[["Module"],["LinearMap","module"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["LinearMap"],["LinearEquiv"],["AddZeroClass","toAddZero"],["LinearMap","addCommMonoid"],["SMulCommClass"],["Module","toDistribMulAction"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["RingHomInvPair","ids"],["AddZero","toZero"],["Semiring"],["AddMonoid","toAddZeroClass"],["DistribSMul","toSMulZeroClass"]],"valueReferences":[["LinearEquiv","congrLeft","_proof_1"],["LinearMap","mk"],["LinearMap","module"],["AddHom","mk"],["LinearEquiv","automorphismGroup","_proof_7"],["AddEquiv","toEquiv"],["LinearMap"],["LinearMap","addCommMonoid"],["Semiring","toNonAssocSemiring"],["AddCommMonoid","toAddCommSemigroup"],["LinearEquiv","arrowCongrAddEquiv"],["Equiv","invFun"],["RingHom","id"],["LinearMap","instAdd"],["LinearEquiv","congrLeft","_proof_4"],["RingHomInvPair","ids"],["LinearEquiv","mk"],["LinearEquiv","congrLeft","_proof_3"],["Equiv","toFun"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["LinearEquiv","congrLeft","_proof_2"],["LinearEquiv","refl"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","arrowCongrAddEquiv_apply"],"typeFallback":"forall {R₁ : Type.{u_9}} {R₂ : Type.{u_10}} {R₁' : Type.{u_11}} {R₂' : Type.{u_12}} {M₁ : Type.{u_13}} {M₂ : Type.{u_14}} {M₁' : Type.{u_15}} {M₂' : Type.{u_16}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 : Semiring.{u_9} R₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 : Semiring.{u_10} R₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 : Semiring.{u_11} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 : Semiring.{u_12} R₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 : AddCommMonoid.{u_13} M₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 : AddCommMonoid.{u_14} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 : AddCommMonoid.{u_15} M₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 : AddCommMonoid.{u_16} M₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 : Module.{u_9, u_13} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 : Module.{u_10, u_14} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 : Module.{u_11, u_15} R₁' M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 : Module.{u_12, u_16} R₂' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39] {σ₁₂ : RingHom.{u_9, u_10} R₁ R₂ (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21)} {σ₂₁ : RingHom.{u_10, u_9} R₂ R₁ (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21) (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18)} {σ₁'₂' : RingHom.{u_11, u_12} R₁' R₂' (Semiring.toNonAssocSemiring.{u_11} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24) (Semiring.toNonAssocSemiring.{u_12} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27)} {σ₂'₁' : RingHom.{u_12, u_11} R₂' R₁' (Semiring.toNonAssocSemiring.{u_12} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27) (Semiring.toNonAssocSemiring.{u_11} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24)} {σ₁₁' : RingHom.{u_9, u_11} R₁ R₁' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_11} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24)} {σ₂₂' : RingHom.{u_10, u_12} R₂ R₂' (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21) (Semiring.toNonAssocSemiring.{u_12} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27)} {σ₂₁' : RingHom.{u_10, u_11} R₂ R₁' (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21) (Semiring.toNonAssocSemiring.{u_11} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24)} {σ₁₂' : RingHom.{u_9, u_12} R₁ R₂' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_12} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27)} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 : RingHomInvPair.{u_9, u_10} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 σ₁₂ σ₂₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 : RingHomInvPair.{u_10, u_9} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 σ₂₁ σ₁₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 : RingHomInvPair.{u_11, u_12} R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₁'₂' σ₂'₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 : RingHomInvPair.{u_12, u_11} R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₂'₁' σ₁'₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.114 : RingHomCompTriple.{u_9, u_11, u_12} R₁ R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₁₁' σ₁'₂' σ₁₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.119 : RingHomCompTriple.{u_10, u_9, u_12} R₂ R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₂₁ σ₁₂' σ₂₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.124 : RingHomCompTriple.{u_10, u_12, u_11} R₂ R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₂₂' σ₂'₁' σ₂₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.129 : RingHomCompTriple.{u_9, u_10, u_11} R₁ R₂ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₂ σ₂₁' σ₁₁'] (e₁ : LinearEquiv.{u_9, u_10, u_13, u_14} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46) (e₂ : LinearEquiv.{u_11, u_12, u_15, u_16} R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54) (f : LinearMap.{u_9, u_11, u_13, u_15} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50), Eq.{max (succ u_14) (succ u_16)} (LinearMap.{u_10, u_12, u_14, u_16} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54) (DFunLike.coe.{max (succ (max u_16 u_14)) (succ (max u_15 u_13)), succ (max u_15 u_13), succ (max u_16 u_14)} (AddEquiv.{max u_15 u_13, max u_16 u_14} (LinearMap.{u_9, u_11, u_13, u_15} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50) (LinearMap.{u_10, u_12, u_14, u_16} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54) (LinearMap.instAdd.{u_9, u_11, u_13, u_15} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 σ₁₁') (LinearMap.instAdd.{u_10, u_12, u_14, u_16} R₂ R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 σ₂₂')) (LinearMap.{u_9, u_11, u_13, u_15} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : LinearMap.{u_9, u_11, u_13, u_15} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50) => LinearMap.{u_10, u_12, u_14, u_16} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54) (EquivLike.toFunLike.{max (succ (max u_16 u_14)) (succ (max u_15 u_13)), succ (max u_15 u_13), succ (max u_16 u_14)} (AddEquiv.{max u_15 u_13, max u_16 u_14} (LinearMap.{u_9, u_11, u_13, u_15} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50) (LinearMap.{u_10, u_12, u_14, u_16} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54) (LinearMap.instAdd.{u_9, u_11, u_13, u_15} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 σ₁₁') (LinearMap.instAdd.{u_10, u_12, u_14, u_16} R₂ R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 σ₂₂')) (LinearMap.{u_9, u_11, u_13, u_15} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50) (LinearMap.{u_10, u_12, u_14, u_16} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54) (AddEquiv.instEquivLike.{max u_15 u_13, max u_16 u_14} (LinearMap.{u_9, u_11, u_13, u_15} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50) (LinearMap.{u_10, u_12, u_14, u_16} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54) (LinearMap.instAdd.{u_9, u_11, u_13, u_15} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 σ₁₁') (LinearMap.instAdd.{u_10, u_12, u_14, u_16} R₂ R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 σ₂₂'))) (LinearEquiv.arrowCongrAddEquiv.{u_9, u_10, u_11, u_12, u_13, u_14, u_15, u_16} R₁ R₂ R₁' R₂' M₁ M₂ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 σ₁₂ σ₂₁ σ₁'₂' σ₂'₁' σ₁₁' σ₂₂' σ₂₁' σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.119 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.124 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.129 e₁ e₂) f) (LinearMap.comp.{u_10, u_9, u_12, u_14, u_13, u_16} R₂ R₁ R₂' M₂ M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 σ₂₁ σ₁₂' σ₂₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.119 (LinearMap.comp.{u_9, u_11, u_12, u_13, u_15, u_16} R₁ R₁' R₂' M₁ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 σ₁₁' σ₁'₂' σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.114 (LinearEquiv.toLinearMap.{u_11, u_12, u_15, u_16} R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 e₂) f) (LinearEquiv.toLinearMap.{u_10, u_9, u_14, u_13} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 σ₂₁ σ₁₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 M₂ M₁ 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Type u_13} {M₂ : Type u_14}\n  {M₁' : Type u_15} {M₂' : Type u_16} [inst : Semiring R₁] [inst_1 : Semiring R₂] [inst_2 : Semiring R₁']\n  [inst_3 : Semiring R₂'] [inst_4 : AddCommMonoid M₁] [inst_5 : AddCommMonoid M₂] [inst_6 : AddCommMonoid M₁']\n  [inst_7 : AddCommMonoid M₂'] [inst_8 : Module R₁ M₁] [inst_9 : Module R₂ M₂] [inst_10 : Module R₁' M₁']\n  [inst_11 : Module R₂' M₂'] {σ₁₂ : R₁ →+* R₂} {σ₂₁ : R₂ →+* R₁} {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'}\n  {σ₁₁' : R₁ →+* R₁'} {σ₂₂' : R₂ →+* R₂'} {σ₂₁' : R₂ →+* R₁'} {σ₁₂' : R₁ →+* R₂'} [inst_12 : RingHomInvPair σ₁₂ σ₂₁]\n  [inst_13 : RingHomInvPair σ₂₁ σ₁₂] [inst_14 : RingHomInvPair σ₁'₂' σ₂'₁'] [inst_15 : RingHomInvPair σ₂'₁' σ₁'₂']\n  [inst_16 : RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_17 : RingHomCompTriple σ₂₁ σ₁₂' σ₂₂']\n  [inst_18 : RingHomCompTriple σ₂₂' σ₂'₁' σ₂₁'] [inst_19 : RingHomCompTriple σ₁₂ σ₂₁' σ₁₁'] (e₁ : M₁ ≃ₛₗ[σ₁₂] M₂)\n  (e₂ : M₁' ≃ₛₗ[σ₁'₂'] M₂') (f : M₁ →ₛₗ[σ₁₁'] M₁'), (e₁.arrowCongrAddEquiv e₂) f = (↑e₂ ∘ₛₗ f) ∘ₛₗ ↑e₁.symm","typeReadable":"∀ {R₁ : Type u_9} {R₂ : Type u_10} {R₁' : Type u_11} {R₂' : Type u_12} {M₁ : Type u_13} {M₂ : Type u_14}\n  {M₁' : Type u_15} {M₂' : Type u_16} [inst : Semiring R₁] [inst_1 : Semiring R₂] [inst_2 : Semiring R₁']\n  [inst_3 : Semiring R₂'] [inst_4 : AddCommMonoid M₁] [inst_5 : AddCommMonoid M₂] [inst_6 : AddCommMonoid M₁']\n  [inst_7 : AddCommMonoid M₂'] [inst_8 : Module R₁ M₁] [inst_9 : Module R₂ M₂] [inst_10 : Module R₁' M₁']\n  [inst_11 : Module R₂' M₂'] {σ₁₂ : R₁ →+* R₂} {σ₂₁ : R₂ →+* R₁} {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'}\n  {σ₁₁' : R₁ →+* R₁'} {σ₂₂' : R₂ →+* R₂'} {σ₂₁' : R₂ →+* R₁'} {σ₁₂' : R₁ →+* R₂'} [inst_12 : RingHomInvPair σ₁₂ σ₂₁]\n  [inst_13 : RingHomInvPair σ₂₁ σ₁₂] [inst_14 : RingHomInvPair σ₁'₂' σ₂'₁'] [inst_15 : RingHomInvPair σ₂'₁' σ₁'₂']\n  [inst_16 : RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_17 : RingHomCompTriple σ₂₁ σ₁₂' σ₂₂']\n  [inst_18 : RingHomCompTriple σ₂₂' σ₂'₁' σ₂₁'] [inst_19 : RingHomCompTriple σ₁₂ σ₂₁' σ₁₁'] (e₁ : M₁ ≃ₛₗ[σ₁₂] M₂)\n  (e₂ : M₁' ≃ₛₗ[σ₁'₂'] M₂') (f : M₁ →ₛₗ[σ₁₁'] M₁'), (e₁.arrowCongrAddEquiv e₂) f = (↑e₂ ∘ₛₗ f) ∘ₛₗ ↑e₁.symm","typeReferences":[["RingHom"],["Module"],["LinearMap","comp"],["LinearEquiv","toLinearMap"],["LinearEquiv"],["LinearMap"],["LinearEquiv","symm"],["DFunLike","coe"],["AddEquiv"],["AddEquiv","instEquivLike"],["RingHomCompTriple"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["LinearEquiv","arrowCongrAddEquiv"],["EquivLike","toFunLike"],["LinearMap","instAdd"],["RingHomInvPair"],["Eq"],["Semiring"]],"valueReferences":[["LinearEquiv","arrowCongrAddEquiv"],["Eq","refl"],["EquivLike","toFunLike"],["LinearMap","instAdd"],["LinearMap"],["AddEquiv"],["DFunLike","coe"],["AddEquiv","instEquivLike"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","arrowCongr","_proof_4"],"typeFallback":"forall {R₁ : Type.{u_5}} {R₂ : Type.{u_7}} {R₁' : Type.{u_6}} {R₂' : Type.{u_8}} {M₁ : Type.{u_2}} {M₂ : Type.{u_4}} {M₁' : Type.{u_1}} {M₂' : Type.{u_3}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 : Semiring.{u_5} R₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 : Semiring.{u_7} R₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59 : CommSemiring.{u_6} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62 : CommSemiring.{u_8} R₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 : AddCommMonoid.{u_2} M₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 : AddCommMonoid.{u_4} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 : AddCommMonoid.{u_1} M₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 : AddCommMonoid.{u_3} M₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 : Module.{u_5, u_2} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 : Module.{u_7, u_4} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 : Module.{u_6, u_1} R₁' M₁' (CommSemiring.toSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 : Module.{u_8, u_3} R₂' M₂' (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86] {σ₁₂ : RingHom.{u_5, u_7} R₁ R₂ (Semiring.toNonAssocSemiring.{u_5} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_7} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53)} {σ₂₁ : RingHom.{u_7, u_5} R₂ R₁ (Semiring.toNonAssocSemiring.{u_7} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53) (Semiring.toNonAssocSemiring.{u_5} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50)} {σ₁'₂' : RingHom.{u_6, u_8} R₁' R₂' (Semiring.toNonAssocSemiring.{u_6} R₁' (CommSemiring.toSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59)) (Semiring.toNonAssocSemiring.{u_8} R₂' (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62))} {σ₂'₁' : RingHom.{u_8, u_6} R₂' R₁' (Semiring.toNonAssocSemiring.{u_8} R₂' (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62)) (Semiring.toNonAssocSemiring.{u_6} R₁' (CommSemiring.toSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59))} {σ₁₁' : RingHom.{u_5, u_6} R₁ R₁' (Semiring.toNonAssocSemiring.{u_5} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_6} R₁' (CommSemiring.toSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59))} {σ₂₂' : RingHom.{u_7, u_8} R₂ R₂' (Semiring.toNonAssocSemiring.{u_7} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53) (Semiring.toNonAssocSemiring.{u_8} R₂' (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62))} {σ₂₁' : RingHom.{u_7, u_6} R₂ R₁' (Semiring.toNonAssocSemiring.{u_7} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53) (Semiring.toNonAssocSemiring.{u_6} R₁' (CommSemiring.toSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59))} {σ₁₂' : RingHom.{u_5, u_8} R₁ R₂' (Semiring.toNonAssocSemiring.{u_5} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_8} R₂' (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62))} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.285 : RingHomInvPair.{u_5, u_7} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 σ₁₂ σ₂₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.289 : RingHomInvPair.{u_7, u_5} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 σ₂₁ σ₁₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.293 : RingHomInvPair.{u_6, u_8} R₁' R₂' (CommSemiring.toSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₁'₂' σ₂'₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.297 : RingHomInvPair.{u_8, u_6} R₂' R₁' (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₂'₁' σ₁'₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.351 : RingHomCompTriple.{u_5, u_6, u_8} R₁ R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₁₁' σ₁'₂' σ₁₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.356 : RingHomCompTriple.{u_7, u_5, u_8} R₂ R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₁ σ₁₂' σ₂₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.361 : RingHomCompTriple.{u_7, u_8, u_6} R₂ R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₂₂' σ₂'₁' σ₂₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.366 : RingHomCompTriple.{u_5, u_7, u_6} R₁ R₂ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₂ σ₂₁' σ₁₁'] (e₁ : LinearEquiv.{u_5, u_7, u_2, u_4} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.285 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.289 M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102) (e₂ : LinearEquiv.{u_6, u_8, u_1, u_3} R₁' R₂' (CommSemiring.toSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.297 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114), Function.LeftInverse.{succ (max u_1 u_2), succ (max u_3 u_4)} (LinearMap.{u_5, u_6, u_2, u_1} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (LinearMap.{u_7, u_8, u_4, u_3} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (Equiv.invFun.{succ (max u_1 u_2), succ (max u_3 u_4)} (LinearMap.{u_5, u_6, u_2, u_1} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 σ₁₁') (LinearMap.instAdd.{u_7, u_8, u_4, u_3} R₂ R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 σ₂₂') (LinearEquiv.arrowCongrAddEquiv.{u_5, u_7, u_6, u_8, u_2, u_4, u_1, u_3} R₁ R₂ R₁' R₂' M₁ M₂ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 σ₁₂ σ₂₁ σ₁'₂' σ₂'₁' σ₁₁' σ₂₂' σ₂₁' σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.285 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.289 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.297 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.351 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.356 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.361 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.366 e₁ e₂)))","typeFull":"∀ {R₁ : Type u_5} {R₂ : Type u_7} {R₁' : Type u_6} {R₂' : Type u_8} {M₁ : Type u_2} {M₂ : Type u_4} {M₁' : Type u_1}\n  {M₂' : Type u_3} [inst : Semiring R₁] [inst_1 : Semiring R₂] [inst_2 : CommSemiring R₁'] [inst_3 : CommSemiring R₂']\n  [inst_4 : AddCommMonoid M₁] [inst_5 : AddCommMonoid M₂] [inst_6 : AddCommMonoid M₁'] [inst_7 : AddCommMonoid M₂']\n  [inst_8 : Module R₁ M₁] [inst_9 : Module R₂ M₂] [inst_10 : Module R₁' M₁'] [inst_11 : Module R₂' M₂']\n  {σ₁₂ : R₁ →+* R₂} {σ₂₁ : R₂ →+* R₁} {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} {σ₁₁' : R₁ →+* R₁'}\n  {σ₂₂' : R₂ →+* R₂'} {σ₂₁' : R₂ →+* R₁'} {σ₁₂' : R₁ →+* R₂'} [inst_12 : RingHomInvPair σ₁₂ σ₂₁]\n  [inst_13 : RingHomInvPair σ₂₁ σ₁₂] [inst_14 : RingHomInvPair σ₁'₂' σ₂'₁'] [inst_15 : RingHomInvPair σ₂'₁' σ₁'₂']\n  [inst_16 : RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_17 : RingHomCompTriple σ₂₁ σ₁₂' σ₂₂']\n  [inst_18 : RingHomCompTriple σ₂₂' σ₂'₁' σ₂₁'] [inst_19 : RingHomCompTriple σ₁₂ σ₂₁' σ₁₁'] (e₁ : M₁ ≃ₛₗ[σ₁₂] M₂)\n  (e₂ : M₁' ≃ₛₗ[σ₁'₂'] M₂'), Function.LeftInverse (e₁.arrowCongrAddEquiv e₂).invFun (e₁.arrowCongrAddEquiv e₂).toFun","typeReadable":"∀ {R₁ : Type u_5} {R₂ : Type u_7} {R₁' : Type u_6} {R₂' : Type u_8} {M₁ : Type u_2} {M₂ : Type u_4} {M₁' : Type u_1}\n  {M₂' : Type u_3} [inst : Semiring R₁] [inst_1 : Semiring R₂] [inst_2 : CommSemiring R₁'] [inst_3 : CommSemiring R₂']\n  [inst_4 : AddCommMonoid M₁] [inst_5 : AddCommMonoid M₂] [inst_6 : AddCommMonoid M₁'] [inst_7 : AddCommMonoid M₂']\n  [inst_8 : Module R₁ M₁] [inst_9 : Module R₂ M₂] [inst_10 : Module R₁' M₁'] [inst_11 : Module R₂' M₂']\n  {σ₁₂ : R₁ →+* R₂} {σ₂₁ : R₂ →+* R₁} {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} {σ₁₁' : R₁ →+* R₁'}\n  {σ₂₂' : R₂ →+* R₂'} {σ₂₁' : R₂ →+* R₁'} {σ₁₂' : R₁ →+* R₂'} [inst_12 : RingHomInvPair σ₁₂ σ₂₁]\n  [inst_13 : RingHomInvPair σ₂₁ σ₁₂] [inst_14 : RingHomInvPair σ₁'₂' σ₂'₁'] [inst_15 : RingHomInvPair σ₂'₁' σ₁'₂']\n  [inst_16 : RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_17 : RingHomCompTriple σ₂₁ σ₁₂' σ₂₂']\n  [inst_18 : RingHomCompTriple σ₂₂' σ₂'₁' σ₂₁'] [inst_19 : RingHomCompTriple σ₁₂ σ₂₁' σ₁₁'] (e₁ : M₁ ≃ₛₗ[σ₁₂] M₂)\n  (e₂ : M₁' ≃ₛₗ[σ₁'₂'] M₂'), Function.LeftInverse (e₁.arrowCongrAddEquiv e₂).invFun (e₁.arrowCongrAddEquiv e₂).toFun","typeReferences":[["RingHom"],["Module"],["CommSemiring"],["CommSemiring","toSemiring"],["AddEquiv","toEquiv"],["LinearEquiv"],["LinearMap"],["RingHomCompTriple"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["LinearEquiv","arrowCongrAddEquiv"],["Equiv","invFun"],["LinearMap","instAdd"],["Function","LeftInverse"],["Equiv","toFun"],["RingHomInvPair"],["Semiring"]],"valueReferences":[["Equiv","left_inv"],["LinearEquiv","arrowCongrAddEquiv"],["LinearMap","instAdd"],["CommSemiring","toSemiring"],["AddEquiv","toEquiv"],["LinearMap"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","curry","_proof_4"],"typeFallback":"forall (M : Type.{u_3}) (V : Type.{u_2}) (V₂ : Type.{u_1}), Function.RightInverse.{max (max (succ u_1) (succ u_2)) (succ u_3), max (succ u_2) (succ u_1) (succ u_3)} ((Prod.{u_2, u_1} V V₂) -> M) (V -> V₂ -> M) (Equiv.invFun.{max (max (succ u_1) (succ u_2)) (succ u_3), max (succ u_2) (succ u_1) (succ u_3)} ((Prod.{u_2, u_1} V V₂) -> M) (V -> V₂ -> M) 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114) (f : Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110) (g : Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110), Eq.{succ u_21} (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114) (DFunLike.coe.{max (succ u_20) (succ u_21), succ u_20, succ u_21} (LinearEquiv.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.297 (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59)))) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62)))) (LinearMap.module.{u_12, u_12, u_12, u_20, u_20} R₁' R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62))) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114))))) (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110) => Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114) (EquivLike.toFunLike.{max (succ u_20) (succ u_21), succ u_20, succ u_21} (LinearEquiv.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.297 (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59)))) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62)))) (LinearMap.module.{u_12, u_12, u_12, u_20, u_20} R₁' R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62))) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114))))) (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114) (LinearEquiv.instEquivLike.{u_12, u_13, u_20, u_21} R₁' R₂' (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59)))) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62)))) (LinearMap.module.{u_12, u_12, u_12, u_20, u_20} R₁' R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62))) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114)))) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.297)) (LinearEquiv.conj.{u_12, u_13, u_20, u_21} R₁' R₂' M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.297 e) (LinearMap.comp.{u_12, u_12, u_12, u_20, u_20, u_20} R₁' R₁' R₁' M₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59))) (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59))) (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59))) (RingHomCompTriple.ids.{u_12, u_12} R₁' R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59)))) g f)) (LinearMap.comp.{u_13, u_13, u_13, u_21, u_21, u_21} R₂' R₂' R₂' M₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62))) (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62))) (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62))) (RingHomCompTriple.ids.{u_13, u_13} R₂' R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62)))) (DFunLike.coe.{max (succ u_20) (succ u_21), succ u_20, succ u_21} (LinearEquiv.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.297 (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59)))) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62)))) (LinearMap.module.{u_12, u_12, u_12, u_20, u_20} R₁' R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62))) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114))))) (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110) => Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114) (EquivLike.toFunLike.{max (succ u_20) (succ u_21), succ u_20, succ u_21} (LinearEquiv.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.297 (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59)))) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62)))) (LinearMap.module.{u_12, u_12, u_12, u_20, u_20} R₁' R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62))) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114))))) (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114) (LinearEquiv.instEquivLike.{u_12, u_13, u_20, u_21} R₁' R₂' (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59)))) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62)))) (LinearMap.module.{u_12, u_12, u_12, u_20, u_20} R₁' R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62))) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114)))) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.297)) (LinearEquiv.conj.{u_12, u_13, u_20, u_21} R₁' R₂' M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.297 e) g) (DFunLike.coe.{max (succ u_20) (succ u_21), succ u_20, succ u_21} (LinearEquiv.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.297 (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59)))) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62)))) (LinearMap.module.{u_12, u_12, u_12, u_20, u_20} R₁' R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62))) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114))))) (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110) => Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114) (EquivLike.toFunLike.{max (succ u_20) (succ u_21), succ u_20, succ u_21} (LinearEquiv.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.297 (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59)))) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62)))) (LinearMap.module.{u_12, u_12, u_12, u_20, u_20} R₁' R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62))) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114))))) (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114) (LinearEquiv.instEquivLike.{u_12, u_13, u_20, u_21} R₁' R₂' (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59)))) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62)))) (LinearMap.module.{u_12, u_12, u_12, u_20, u_20} R₁' R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.110)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1547763226._hygCtx._hyg.86 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(g ∘ₗ f) = e.conj g ∘ₗ e.conj f","typeReferences":[["RingHom"],["smulCommClass_self"],["CommMonoid","toMonoid"],["Module"],["RingHomCompTriple","ids"],["CommSemiring"],["LinearMap","comp"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["DFunLike","coe"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["EquivLike","toFunLike"],["DistribMulAction","toMulAction"],["Eq"],["LinearEquiv","instEquivLike"],["Module","End"],["CommSemiring","toSemiring"],["LinearMap","module"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["LinearEquiv","conj"],["RingHomInvPair"]],"valueReferences":[["RingHomInvPair","triples₂"],["Semiring","toNonAssocSemiring"],["RingHomCompTriple","ids"],["RingHom","id"],["CommSemiring","toSemiring"],["LinearEquiv","arrowCongr_comp"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","sumPiEquivProdPi","_proof_1"],"typeFallback":"forall (S : Type.{u_1}) (T : Type.{u_2}) (A : (Sum.{u_1, u_2} S T) -> 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x_1 : (st : S ⊕ T) → A st), (Equiv.sumPiEquivProdPi A).toFun (x + x_1) = (Equiv.sumPiEquivProdPi A).toFun (x + x_1)","typeReadable":"∀ (S : Type u_1) (T : Type u_2) (A : S ⊕ T → Type u_3) [inst : (st : S ⊕ T) → AddCommMonoid (A st)]\n  (x x_1 : (st : S ⊕ T) → A st), (Equiv.sumPiEquivProdPi A).toFun (x + x_1) = (Equiv.sumPiEquivProdPi A).toFun (x + x_1)","typeReferences":[["Equiv","sumPiEquivProdPi"],["instHAdd"],["Pi","addCommMonoid"],["Sum"],["Prod"],["HAdd","hAdd"],["AddCommMonoid"],["Sum","inl"],["AddCommMonoid","toAddCommSemigroup"],["Equiv","toFun"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Eq"],["Sum","inr"]],"valueReferences":[["rfl"],["Equiv","sumPiEquivProdPi"],["instHAdd"],["Pi","addCommMonoid"],["Sum"],["Prod"],["HAdd","hAdd"],["Sum","inl"],["AddCommMonoid","toAddCommSemigroup"],["Equiv","toFun"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Sum","inr"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","congrLeft_apply"],"typeFallback":"forall (M : Type.{u_5}) {M₂ : Type.{u_7}} {M₃ : Type.{u_8}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 : AddCommMonoid.{u_7} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.19 : 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.54 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.58) (LinearMap.module.{u_9, u_9, u_10, u_8, u_5} R R S M₃ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.54 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.58)) (LinearMap.{u_9, u_9, u_7, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50) (fun 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50) (EquivLike.toFunLike.{max (succ (max u_5 u_7)) (succ (max u_5 u_8)), succ (max u_5 u_7), succ (max u_5 u_8)} (LinearEquiv.{u_10, u_10, max u_5 u_7, max u_5 u_8} S S inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.39 (RingHom.id.{u_10} S (Semiring.toNonAssocSemiring.{u_10} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.39)) (RingHom.id.{u_10} S (Semiring.toNonAssocSemiring.{u_10} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.39)) (RingHomInvPair.ids.{u_10} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.39) (RingHomInvPair.ids.{u_10} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.39) (LinearMap.{u_9, u_9, u_7, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50) (LinearMap.{u_9, u_9, u_8, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) M₃ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50) (LinearMap.addCommMonoid.{u_9, u_9, u_7, u_5} R R M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36))) (LinearMap.addCommMonoid.{u_9, u_9, u_8, u_5} R R M₃ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36))) (LinearMap.module.{u_9, u_9, u_10, u_7, u_5} R R S M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.54 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.58)) (LinearMap.{u_9, u_9, u_7, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50) (LinearMap.{u_9, u_9, u_8, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19) (AddCommGroup.toIntModule.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16) (AddCommGroup.toIntModule.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19) (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int Int.instSemiring))) (AddMonoidHom.instModule.{u_11, u_9, u_10} R A B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.13 (SubNegMonoid.toAddMonoid.{u_9} A (AddGroup.toSubNegMonoid.{u_9} A (AddCommGroup.toAddGroup.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16))) (AddCommGroup.toAddCommMonoid.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.22) (LinearMap.module.{0, 0, u_11, u_9, u_10} Int Int R A B Int.instSemiring Int.instSemiring (AddCommGroup.toAddCommMonoid.{u_9} A 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(AddGroup.toSubNegMonoid.{u_10} B (AddCommGroup.toAddGroup.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19))) (Module.toDistribMulAction.{u_11, u_10} R B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.13 (AddCommGroup.toAddCommMonoid.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.22))))","typeFull":"{A : Type u_9} →\n  {B : Type u_10} →\n    (R : Type u_11) →\n      [inst : Semiring R] →\n        [inst_1 : AddCommGroup A] → [inst_2 : AddCommGroup B] → [inst_3 : Module R B] → (A →+ B) ≃ₗ[R] A →ₗ[ℤ] B","typeReadable":"{A : Type u_9} →\n  {B : Type u_10} →\n    (R : Type u_11) →\n      [inst : Semiring R] →\n        [inst_1 : AddCommGroup A] → [inst_2 : AddCommGroup B] → [inst_3 : Module R B] → (A →+ B) ≃ₗ[R] A →ₗ[ℤ] B","typeReferences":[["Module"],["AddCommGroup","toAddGroup"],["LinearEquiv"],["AddMonoidHom","instModule"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["AddMonoidHom"],["MonoidWithZero","toMonoid"],["AddGroup","toSubNegMonoid"],["AddGroup","int_smulCommClass"],["LinearMap","module"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddCommGroup"],["AddZeroClass","toAddZero"],["LinearMap"],["AddCommGroup","toIntModule"],["Int"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["SubNegMonoid","toAddMonoid"],["Int","instSemiring"],["RingHomInvPair","ids"],["AddCommGroup","toAddCommMonoid"],["AddMonoidHom","instAddCommMonoid"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["AddCommGroup","toAddGroup"],["LinearMap","mk"],["AddHom","mk"],["addMonoidHomLequivInt","_proof_1"],["addMonoidHomLequivInt","_proof_3"],["addMonoidHomLequivInt","_proof_4"],["AddMonoidHom","instModule"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["addMonoidHomLequivInt","_proof_5"],["AddMonoidHom"],["LinearEquiv","mk"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["AddGroup","toSubNegMonoid"],["LinearMap","toAddMonoidHom"],["LinearMap","module"],["AddMonoidHom","toIntLinearMap"],["LinearMap"],["AddZeroClass","toAddZero"],["AddCommGroup","toIntModule"],["Int"],["LinearMap","addCommMonoid"],["SubNegMonoid","toAddMonoid"],["AddCommMonoid","toAddCommSemigroup"],["Int","instSemiring"],["RingHomInvPair","ids"],["AddCommGroup","toAddCommMonoid"],["addMonoidHomLequivInt","_proof_2"],["AddMonoidHom","instAddCommMonoid"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","automorphismGroup","_proof_1"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 : Module.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19] (x : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25), Eq.{succ u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (npowRecAuto.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Semigroup.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f)) (fun (x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.56 : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.58 : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.60 : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => rfl.{succ u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (HMul.hMul.{u_2, u_2, u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (instHMul.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f))) (HMul.hMul.{u_2, u_2, u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (instHMul.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 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LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.refl.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25)) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) x) (OfNat.ofNat.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) 1 (One.toOfNat1.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (One.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.refl.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25))))","typeFull":"∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (x : M ≃ₗ[R] M),\n  npowRecAuto 0 x = 1","typeReadable":"∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (x : M ≃ₗ[R] M),\n  npowRecAuto 0 x = 1","typeReferences":[["rfl"],["Mul","mk"],["Module"],["RingHomCompTriple","ids"],["One","mk"],["HMul","hMul"],["LinearEquiv"],["OfNat","ofNat"],["LinearEquiv","trans"],["Nat"],["AddCommMonoid"],["npowRecAuto"],["Semiring","toNonAssocSemiring"],["Semigroup","mk"],["One","toOfNat1"],["instOfNatNat"],["RingHom","id"],["RingHomInvPair","ids"],["instHMul"],["Eq"],["LinearEquiv","refl"],["Semiring"]],"valueReferences":[["Mul","mk"],["rfl"],["RingHomCompTriple","ids"],["One","mk"],["HMul","hMul"],["LinearEquiv"],["OfNat","ofNat"],["LinearEquiv","trans"],["Nat"],["npowRecAuto"],["Semiring","toNonAssocSemiring"],["Semigroup","mk"],["instOfNatNat"],["RingHom","id"],["Eq","refl"],["RingHomInvPair","ids"],["instHMul"],["LinearEquiv","refl"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","ringLmapEquivSelf_apply"],"typeFallback":"forall (R : Type.{u_1}) (S : Type.{u_4}) (M : Type.{u_5}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.13 : Semiring.{u_4} S] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.16 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.19 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.23 : Module.{u_4, u_5} S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.27 : SMulCommClass.{u_1, u_4, u_5} R S M (SMulZeroClass.toSMul.{u_1, u_5} R M (AddZero.toZero.{u_5} M (AddZeroClass.toAddZero.{u_5} M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.16)))) 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u_5} S M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.16)) (DistribMulAction.toDistribSMul.{u_4, u_5} S M (MonoidWithZero.toMonoid.{u_4} S (Semiring.toMonoidWithZero.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.13)) (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.16) (Module.toDistribMulAction.{u_4, u_5} S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.23))))] (f : LinearMap.{u_1, u_1, u_1, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10)) 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{A : Type.{u_2}} {B : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.16 : AddCommMonoid.{u_2} A] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19 : AddCommMonoid.{u_1} B], Function.LeftInverse.{succ (max u_1 u_2), succ (max u_1 u_2)} (AddMonoidHom.{u_2, u_1} A B (AddZeroClass.toAddZero.{u_2} A (AddMonoid.toAddZeroClass.{u_2} A (AddCommMonoid.toAddMonoid.{u_2} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.16))) (AddZeroClass.toAddZero.{u_1} B (AddMonoid.toAddZeroClass.{u_1} B (AddCommMonoid.toAddMonoid.{u_1} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19)))) (LinearMap.{0, 0, u_2, u_1} Nat Nat Nat.instSemiring Nat.instSemiring (RingHom.id.{0} Nat Nat.instNonAssocSemiring) A B inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19 (AddCommMonoid.toNatModule.{u_2} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.16) (AddCommMonoid.toNatModule.{u_1} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19)) (LinearMap.toAddMonoidHom.{0, 0, u_2, u_1} Nat Nat A B Nat.instSemiring Nat.instSemiring inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19 (AddCommMonoid.toNatModule.{u_2} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.16) (AddCommMonoid.toNatModule.{u_1} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19) (RingHom.id.{0} Nat Nat.instNonAssocSemiring)) (AddMonoidHom.toNatLinearMap.{u_2, u_1} A B inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19)","typeFull":"∀ {A : Type u_2} {B : Type u_1} [inst : AddCommMonoid A] [inst_1 : AddCommMonoid B],\n  Function.LeftInverse LinearMap.toAddMonoidHom AddMonoidHom.toNatLinearMap","typeReadable":"∀ {A : Type u_2} {B : Type u_1} [inst : AddCommMonoid A] [inst_1 : AddCommMonoid B],\n  Function.LeftInverse LinearMap.toAddMonoidHom AddMonoidHom.toNatLinearMap","typeReferences":[["LinearMap","toAddMonoidHom"],["AddMonoidHom","toNatLinearMap"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["LinearMap"],["AddCommMonoid"],["Nat"],["Nat","instSemiring"],["Nat","instNonAssocSemiring"],["RingHom","id"],["AddMonoidHom"],["Function","LeftInverse"],["AddCommMonoid","toNatModule"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["Nat"],["LinearMap","toAddMonoidHom"],["Nat","instNonAssocSemiring"],["Nat","instSemiring"],["AddMonoidHom","toNatLinearMap"],["RingHom","id"],["AddMonoidHom"],["Eq","refl"],["AddCommMonoid","toNatModule"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","applyDistribMulAction","_proof_3"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 : Module.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19] (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25), Eq.{succ u_2} M (DFunLike.coe.{succ u_2, succ u_2, succ u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (EquivLike.toFunLike.{succ u_2, succ u_2, succ u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) M M (LinearEquiv.instEquivLike.{u_1, u_1, u_2, u_2} R R M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._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.Equiv.Basic.1747207001._hygCtx._hyg.19))))))) (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.Equiv.Basic.1747207001._hygCtx._hyg.19))))))","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  f 0 = 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  f 0 = 0","typeReferences":[["Module"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["LinearEquiv"],["DFunLike","coe"],["OfNat","ofNat"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["EquivLike","toFunLike"],["RingHomInvPair","ids"],["Zero","toOfNat0"],["Eq"],["LinearEquiv","instEquivLike"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["RingHom"],["AddMonoidHomClass","toZeroHomClass"],["Semiring","toMonoidWithZero"],["RingHom","instFunLike"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["AddZeroClass","toAddZero"],["DFunLike","coe"],["DistribMulActionSemiHomClass","toAddMonoidHomClass"],["LinearEquiv","instSemilinearEquivClass"],["SemilinearEquivClass","instSemilinearMapClass"],["Module","toDistribMulAction"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["EquivLike","toFunLike"],["RingHomInvPair","ids"],["map_zero"],["LinearEquiv","instEquivLike"],["AddZero","toZero"],["SemilinearMapClass","distribMulActionSemiHomClass"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","smulOfNeZero_symm_apply"],"typeFallback":"forall (K : Type.{u_3}) (M : Type.{u_5}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10 : Field.{u_3} K] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.13 : AddCommGroup.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.16 : Module.{u_3, u_5} K M (DivisionSemiring.toSemiring.{u_3} K (Semifield.toDivisionSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10))) (AddCommGroup.toAddCommMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.13)] (a : K) (ha : Ne.{succ u_3} K a (OfNat.ofNat.{u_3} K 0 (Zero.toOfNat0.{u_3} K (MulZeroClass.toZero.{u_3} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u_3} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_3} K (NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{u_3} K (NonUnitalCommRing.toNonUnitalNonAssocCommRing.{u_3} K (CommRing.toNonUnitalCommRing.{u_3} K (Field.toCommRing.{u_3} K 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10))))) (RingHomInvPair.ids.{u_3} K (DivisionSemiring.toSemiring.{u_3} K (Semifield.toDivisionSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10)))) (RingHomInvPair.ids.{u_3} K (DivisionSemiring.toSemiring.{u_3} K (Semifield.toDivisionSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10)))) M M (AddCommGroup.toAddCommMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.13) (AddCommGroup.toAddCommMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.16) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (EquivLike.toFunLike.{succ u_5, succ u_5, succ u_5} (LinearEquiv.{u_3, u_3, u_5, u_5} K K (DivisionSemiring.toSemiring.{u_3} K (Semifield.toDivisionSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10))) (DivisionSemiring.toSemiring.{u_3} K (Semifield.toDivisionSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10))) (RingHom.id.{u_3} K (Semiring.toNonAssocSemiring.{u_3} K (DivisionSemiring.toSemiring.{u_3} K (Semifield.toDivisionSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10))))) (RingHom.id.{u_3} K (Semiring.toNonAssocSemiring.{u_3} K (DivisionSemiring.toSemiring.{u_3} K (Semifield.toDivisionSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10))))) (RingHomInvPair.ids.{u_3} K (DivisionSemiring.toSemiring.{u_3} K (Semifield.toDivisionSemiring.{u_3} K (Field.toSemifield.{u_3} K 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10))) (AddCommGroup.toAddCommMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.13) (AddCommGroup.toAddCommMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.16 (RingHom.id.{u_3} K (Semiring.toNonAssocSemiring.{u_3} K (DivisionSemiring.toSemiring.{u_3} K (Semifield.toDivisionSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10))))) (RingHom.id.{u_3} K (Semiring.toNonAssocSemiring.{u_3} K (DivisionSemiring.toSemiring.{u_3} K (Semifield.toDivisionSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10))))) (RingHomInvPair.ids.{u_3} K (DivisionSemiring.toSemiring.{u_3} K (Semifield.toDivisionSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10)))) (RingHomInvPair.ids.{u_3} K (DivisionSemiring.toSemiring.{u_3} K (Semifield.toDivisionSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10)))))) (LinearEquiv.symm.{u_3, u_3, u_5, u_5} K K M M (DivisionSemiring.toSemiring.{u_3} K (Semifield.toDivisionSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10))) (DivisionSemiring.toSemiring.{u_3} K (Semifield.toDivisionSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10))) (AddCommGroup.toAddCommMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.13) (AddCommGroup.toAddCommMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.16 (RingHom.id.{u_3} K (Semiring.toNonAssocSemiring.{u_3} K (DivisionSemiring.toSemiring.{u_3} K (Semifield.toDivisionSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10))))) (RingHom.id.{u_3} K (Semiring.toNonAssocSemiring.{u_3} K (DivisionSemiring.toSemiring.{u_3} K (Semifield.toDivisionSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10))))) (RingHomInvPair.ids.{u_3} K (DivisionSemiring.toSemiring.{u_3} K (Semifield.toDivisionSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10)))) (RingHomInvPair.ids.{u_3} K (DivisionSemiring.toSemiring.{u_3} K (Semifield.toDivisionSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10)))) (LinearEquiv.smulOfNeZero.{u_3, u_5} K M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.16 a ha)) a._@._internal._hyg.0) (HSMul.hSMul.{u_3, u_5, u_5} (Units.{u_3} K (MonoidWithZero.toMonoid.{u_3} K (Semiring.toMonoidWithZero.{u_3} K (CommSemiring.toSemiring.{u_3} K (Semifield.toCommSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10)))))) M M (instHSMul.{u_3, u_5} (Units.{u_3} K (MonoidWithZero.toMonoid.{u_3} K (Semiring.toMonoidWithZero.{u_3} K (CommSemiring.toSemiring.{u_3} K (Semifield.toCommSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10)))))) M (SemigroupAction.toSMul.{u_3, u_5} (Units.{u_3} K (MonoidWithZero.toMonoid.{u_3} K (Semiring.toMonoidWithZero.{u_3} K (CommSemiring.toSemiring.{u_3} K (Semifield.toCommSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10)))))) M (Monoid.toSemigroup.{u_3} (Units.{u_3} K (MonoidWithZero.toMonoid.{u_3} K (Semiring.toMonoidWithZero.{u_3} K (CommSemiring.toSemiring.{u_3} K (Semifield.toCommSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10)))))) (DivInvMonoid.toMonoid.{u_3} (Units.{u_3} K (MonoidWithZero.toMonoid.{u_3} K (Semiring.toMonoidWithZero.{u_3} K (CommSemiring.toSemiring.{u_3} K (Semifield.toCommSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10)))))) (Group.toDivInvMonoid.{u_3} (Units.{u_3} K (MonoidWithZero.toMonoid.{u_3} K (Semiring.toMonoidWithZero.{u_3} K (CommSemiring.toSemiring.{u_3} K (Semifield.toCommSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10)))))) (Units.instGroup.{u_3} K (MonoidWithZero.toMonoid.{u_3} K (Semiring.toMonoidWithZero.{u_3} K (CommSemiring.toSemiring.{u_3} K (Semifield.toCommSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10))))))))) (MulAction.toSemigroupAction.{u_3, u_5} (Units.{u_3} K (MonoidWithZero.toMonoid.{u_3} K (Semiring.toMonoidWithZero.{u_3} K (CommSemiring.toSemiring.{u_3} K (Semifield.toCommSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10)))))) M (DivInvMonoid.toMonoid.{u_3} (Units.{u_3} K (MonoidWithZero.toMonoid.{u_3} K (Semiring.toMonoidWithZero.{u_3} K (CommSemiring.toSemiring.{u_3} K (Semifield.toCommSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10)))))) (Group.toDivInvMonoid.{u_3} (Units.{u_3} K (MonoidWithZero.toMonoid.{u_3} K (Semiring.toMonoidWithZero.{u_3} K (CommSemiring.toSemiring.{u_3} K (Semifield.toCommSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10)))))) (Units.instGroup.{u_3} K (MonoidWithZero.toMonoid.{u_3} K (Semiring.toMonoidWithZero.{u_3} K (CommSemiring.toSemiring.{u_3} K (Semifield.toCommSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10)))))))) (DistribMulAction.toMulAction.{u_3, u_5} (Units.{u_3} K (MonoidWithZero.toMonoid.{u_3} K (Semiring.toMonoidWithZero.{u_3} K (CommSemiring.toSemiring.{u_3} K (Semifield.toCommSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10)))))) M (DivInvMonoid.toMonoid.{u_3} (Units.{u_3} K (MonoidWithZero.toMonoid.{u_3} K (Semiring.toMonoidWithZero.{u_3} K (CommSemiring.toSemiring.{u_3} K (Semifield.toCommSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10)))))) (Group.toDivInvMonoid.{u_3} (Units.{u_3} K (MonoidWithZero.toMonoid.{u_3} K (Semiring.toMonoidWithZero.{u_3} K (CommSemiring.toSemiring.{u_3} K (Semifield.toCommSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10)))))) (Units.instGroup.{u_3} K (MonoidWithZero.toMonoid.{u_3} K (Semiring.toMonoidWithZero.{u_3} K (CommSemiring.toSemiring.{u_3} K (Semifield.toCommSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10)))))))) (AddCommMonoid.toAddMonoid.{u_5} M (AddCommGroup.toAddCommMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.13)) (Units.instDistribMulAction.{u_3, u_5} K M (MonoidWithZero.toMonoid.{u_3} K (Semiring.toMonoidWithZero.{u_3} K (CommSemiring.toSemiring.{u_3} K (Semifield.toCommSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10))))) (AddCommMonoid.toAddMonoid.{u_5} M (AddCommGroup.toAddCommMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.13)) (Module.toDistribMulAction.{u_3, u_5} K M (CommSemiring.toSemiring.{u_3} K (Semifield.toCommSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10))) (AddCommGroup.toAddCommMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.16)))))) (Inv.inv.{u_3} (Units.{u_3} K (MonoidWithZero.toMonoid.{u_3} K (Semiring.toMonoidWithZero.{u_3} K (CommSemiring.toSemiring.{u_3} K (Semifield.toCommSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10)))))) (InvOneClass.toInv.{u_3} (Units.{u_3} K (MonoidWithZero.toMonoid.{u_3} K (Semiring.toMonoidWithZero.{u_3} K (CommSemiring.toSemiring.{u_3} K (Semifield.toCommSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10)))))) (DivInvOneMonoid.toInvOneClass.{u_3} (Units.{u_3} K (MonoidWithZero.toMonoid.{u_3} K (Semiring.toMonoidWithZero.{u_3} K (CommSemiring.toSemiring.{u_3} K (Semifield.toCommSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10)))))) (DivisionMonoid.toDivInvOneMonoid.{u_3} (Units.{u_3} K (MonoidWithZero.toMonoid.{u_3} K (Semiring.toMonoidWithZero.{u_3} K (CommSemiring.toSemiring.{u_3} K (Semifield.toCommSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10)))))) (Group.toDivisionMonoid.{u_3} (Units.{u_3} K (MonoidWithZero.toMonoid.{u_3} K (Semiring.toMonoidWithZero.{u_3} K (CommSemiring.toSemiring.{u_3} K (Semifield.toCommSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10)))))) (Units.instGroup.{u_3} K (MonoidWithZero.toMonoid.{u_3} K (Semiring.toMonoidWithZero.{u_3} K (CommSemiring.toSemiring.{u_3} K (Semifield.toCommSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10)))))))))) (Units.mk0.{u_3} K (DivisionSemiring.toGroupWithZero.{u_3} K (Semifield.toDivisionSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10))) a ha)) a._@._internal._hyg.0)","typeFull":"∀ (K : Type u_3) (M : Type u_5) [inst : Field K] [inst_1 : AddCommGroup M] [inst_2 : Module K M] (a : K) (ha : a ≠ 0)\n  (a_1 : M), (LinearEquiv.smulOfNeZero K M a ha).symm a_1 = (Units.mk0 a ha)⁻¹ • a_1","typeReadable":"∀ (K : Type u_3) (M : Type u_5) [inst : Field K] [inst_1 : AddCommGroup M] [inst_2 : Module K M] (a : K) (ha : a ≠ 0)\n  (a_1 : M), (LinearEquiv.smulOfNeZero K M a ha).symm a_1 = (Units.mk0 a ha)⁻¹ • a_1","typeReferences":[["SemigroupAction","toSMul"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["NonUnitalNonAssocCommRing","toNonUnitalNonAssocRing"],["DistribMulAction","toMulAction"],["Semifield","toDivisionSemiring"],["Monoid","toSemigroup"],["Group","toDivInvMonoid"],["Units"],["Group","toDivisionMonoid"],["InvOneClass","toInv"],["NonUnitalCommRing","toNonUnitalNonAssocCommRing"],["DivisionSemiring","toGroupWithZero"],["DivisionSemiring","toSemiring"],["DivInvMonoid","toMonoid"],["HSMul","hSMul"],["RingHomInvPair","ids"],["AddCommGroup","toAddCommMonoid"],["DivisionMonoid","toDivInvOneMonoid"],["Semifield","toCommSemiring"],["Units","instGroup"],["Field"],["Module"],["CommRing","toNonUnitalCommRing"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["DFunLike","coe"],["EquivLike","toFunLike"],["MonoidWithZero","toMonoid"],["instHSMul"],["Zero","toOfNat0"],["LinearEquiv","instEquivLike"],["Eq"],["Inv","inv"],["Field","toCommRing"],["CommSemiring","toSemiring"],["Semiring","toMonoidWithZero"],["Units","mk0"],["AddCommGroup"],["LinearEquiv","symm"],["OfNat","ofNat"],["Module","toDistribMulAction"],["DivInvOneMonoid","toInvOneClass"],["Units","instDistribMulAction"],["MulZeroClass","toZero"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["Field","toSemifield"],["Ne"],["LinearEquiv","smulOfNeZero"],["MulAction","toSemigroupAction"]],"valueReferences":[["DivisionSemiring","toSemiring"],["LinearEquiv"],["DFunLike","coe"],["LinearEquiv","symm"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Eq","refl"],["EquivLike","toFunLike"],["Field","toSemifield"],["RingHomInvPair","ids"],["AddCommGroup","toAddCommMonoid"],["Semifield","toDivisionSemiring"],["LinearEquiv","instEquivLike"],["LinearEquiv","smulOfNeZero"]]},{"isProp":true,"kind":"theorem","name":["Units","symm_mulLeftLinearEquiv_apply"],"typeFallback":"forall (R : Type.{u_9}) {A : Type.{u_10}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12 : Semiring.{u_9} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.15 : Semiring.{u_10} A] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.18 : Module.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.15)))] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.22 : SMulCommClass.{u_9, u_10, u_10} R A A (SMulZeroClass.toSMul.{u_9, u_10} R A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_9, u_10} R A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.15))))) (DistribMulAction.toDistribSMul.{u_9, u_10} R A (MonoidWithZero.toMonoid.{u_9} R (Semiring.toMonoidWithZero.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12)) (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.15)))) (Module.toDistribMulAction.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.18)))) (SMulZeroClass.toSMul.{u_10, u_10} A A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_10, u_10} A A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.15))))) (instDistribSMul.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.15)))))] (a : Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.15))) (x : A), Eq.{succ u_10} A (DFunLike.coe.{succ u_10, succ u_10, succ u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.18) A (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : A) => A) (EquivLike.toFunLike.{succ u_10, succ u_10, succ u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.18) A A (LinearEquiv.instEquivLike.{u_9, u_9, u_10, u_10} R R A A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.18 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.18 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12) (DFunLike.coe.{succ u_10, succ u_10, succ u_10} (MonoidHom.{u_10, u_10} (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.15))) (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.18) (MulOneClass.toMulOne.{u_10} (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.15))) (Units.instMulOneClass.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.15)))) (MulOneClass.toMulOne.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.18) (DivInvMonoid.toMonoid.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.18) (Group.toDivInvMonoid.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.18) (LinearEquiv.automorphismGroup.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.18)))))) (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.15))) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.15))) => LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.18) (MonoidHom.instFunLike.{u_10, u_10} (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.15))) (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.372807256._hygCtx._hyg.18 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{R : Type.{u_1}} {M : Type.{u_5}} {M₂ : Type.{u_7}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555652._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555652._hygCtx._hyg.13 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555652._hygCtx._hyg.16 : AddCommMonoid.{u_7} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555652._hygCtx._hyg.22 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555652._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555652._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555652._hygCtx._hyg.26 : Module.{u_1, u_7} R M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555652._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555652._hygCtx._hyg.16] (e : AddEquiv.{u_5, u_7} M M₂ (AddCommMagma.toAdd.{u_5} M (AddCommSemigroup.toAddCommMagma.{u_5} M (AddCommMonoid.toAddCommSemigroup.{u_5} M 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(AddCommSemigroup.toAddCommMagma.{u_5} M (AddCommMonoid.toAddCommSemigroup.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555652._hygCtx._hyg.13))) (AddCommMagma.toAdd.{u_7} M₂ (AddCommSemigroup.toAddCommMagma.{u_7} M₂ (AddCommMonoid.toAddCommSemigroup.{u_7} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555652._hygCtx._hyg.16))))) e x))) -> (LinearEquiv.{u_1, u_1, u_5, u_7} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555652._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555652._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555652._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555652._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555652._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555652._hygCtx._hyg.10) M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555652._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555652._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555652._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555652._hygCtx._hyg.26)","typeFull":"{R : Type u_1} →\n  {M : Type u_5} →\n    {M₂ : Type u_7} →\n      [inst : Semiring R] →\n        [inst_1 : AddCommMonoid M] →\n          [inst_2 : AddCommMonoid M₂] →\n            [inst_3 : Module R M] →\n              [inst_4 : Module R M₂] → (e : M ≃+ M₂) → (∀ (c : R) (x : M), e (c • x) = c • e x) → M ≃ₗ[R] M₂","typeReadable":"{R : Type u_1} →\n  {M : Type u_5} →\n    {M₂ : Type u_7} →\n      [inst : Semiring R] →\n        [inst_1 : AddCommMonoid M] →\n          [inst_2 : AddCommMonoid M₂] →\n            [inst_3 : Module R M] →\n              [inst_4 : Module R M₂] → (e : M ≃+ M₂) → (∀ (c : R) (x : M), e (c • x) = c • e x) → M ≃ₗ[R] M₂","typeReferences":[["Module"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["DFunLike","coe"],["AddEquiv","instEquivLike"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["EquivLike","toFunLike"],["MonoidWithZero","toMonoid"],["instHSMul"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Eq"],["DistribSMul","toSMulZeroClass"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["AddEquiv"],["Module","toDistribMulAction"],["AddCommMonoid","toAddCommSemigroup"],["HSMul","hSMul"],["RingHomInvPair","ids"],["AddZero","toZero"],["Semiring"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["LinearMap","mk"],["AddHom","mk"],["AddEquiv","toEquiv"],["Semiring","toNonAssocSemiring"],["AddCommMonoid","toAddCommSemigroup"],["RingHom","id"],["Equiv","invFun"],["AddEquiv","toLinearEquiv","_proof_2"],["RingHomInvPair","ids"],["LinearEquiv","mk"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Equiv","toFun"],["AddEquiv","toLinearEquiv","_proof_1"],["AddEquiv","toLinearEquiv","_proof_3"]]},{"isProp":true,"kind":"theorem","name":["Units","mulLeftLinearEquiv_mul_apply"],"typeFallback":"forall {R : Type.{u_9}} {A : Type.{u_10}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 : Semiring.{u_9} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15 : Semiring.{u_10} A] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 : Module.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15)))] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.22 : SMulCommClass.{u_9, u_10, u_10} R A A (SMulZeroClass.toSMul.{u_9, u_10} R A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_9, u_10} R A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))))) (DistribMulAction.toDistribSMul.{u_9, u_10} R A (MonoidWithZero.toMonoid.{u_9} R (Semiring.toMonoidWithZero.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15)))) (Module.toDistribMulAction.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18)))) (SMulZeroClass.toSMul.{u_10, u_10} A A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_10, u_10} A A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))))) (instDistribSMul.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15)))))] (u : Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (v : Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (x : A), Eq.{succ u_10} A (DFunLike.coe.{succ u_10, succ u_10, succ u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18) A (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : A) => A) (EquivLike.toFunLike.{succ u_10, succ u_10, succ u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18) A A (LinearEquiv.instEquivLike.{u_9, u_9, u_10, u_10} R R A A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12))) (DFunLike.coe.{succ u_10, succ u_10, succ u_10} (MonoidHom.{u_10, u_10} (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18) (MulOneClass.toMulOne.{u_10} (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (Units.instMulOneClass.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15)))) (MulOneClass.toMulOne.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18) (Monoid.toMulOneClass.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18) (DivInvMonoid.toMonoid.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18) (Group.toDivInvMonoid.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18) (LinearEquiv.automorphismGroup.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18)))))) (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) => LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18) (MonoidHom.instFunLike.{u_10, u_10} (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18) 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18) (Monoid.toMulOneClass.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18) (DivInvMonoid.toMonoid.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18) (Group.toDivInvMonoid.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18) (LinearEquiv.automorphismGroup.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18)))))) (Units.mulLeftLinearEquiv.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.22) (HMul.hMul.{u_10, u_10, u_10} (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (instHMul.{u_10} (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (Units.instMul.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15)))) u v)) x) (DFunLike.coe.{succ u_10, succ u_10, succ u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18) A (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : A) => A) (EquivLike.toFunLike.{succ u_10, succ u_10, succ u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18) A A (LinearEquiv.instEquivLike.{u_9, u_9, u_10, u_10} R R A A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12))) (DFunLike.coe.{succ u_10, succ u_10, succ u_10} (MonoidHom.{u_10, u_10} (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18) (MulOneClass.toMulOne.{u_10} (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (Units.instMulOneClass.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15)))) (MulOneClass.toMulOne.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18) (Group.toDivInvMonoid.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (RingHom.id.{u_9} R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18) (LinearEquiv.automorphismGroup.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18)))))) (Units.mulLeftLinearEquiv.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.22) u) (DFunLike.coe.{succ u_10, succ u_10, succ u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18) A (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : A) => A) (EquivLike.toFunLike.{succ u_10, succ u_10, succ u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18) A A (LinearEquiv.instEquivLike.{u_9, u_9, u_10, u_10} R R A A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A 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(LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18) (MulOneClass.toMulOne.{u_10} (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (Units.instMulOneClass.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15)))) (MulOneClass.toMulOne.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18) (Monoid.toMulOneClass.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18) (DivInvMonoid.toMonoid.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18) (Group.toDivInvMonoid.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18) (LinearEquiv.automorphismGroup.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18)))))) (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) => LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18) (MonoidHom.instFunLike.{u_10, u_10} (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18) (MulOneClass.toMulOne.{u_10} (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (Units.instMulOneClass.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15)))) (MulOneClass.toMulOne.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18) (Monoid.toMulOneClass.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18) (DivInvMonoid.toMonoid.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18) (Group.toDivInvMonoid.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18) (LinearEquiv.automorphismGroup.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18)))))) (Units.mulLeftLinearEquiv.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.15 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3397224443._hygCtx._hyg.22) v) x))","typeFull":"∀ {R : Type u_9} {A : Type u_10} [inst : Semiring R] [inst_1 : Semiring A] [inst_2 : Module R A]\n  [inst_3 : SMulCommClass R A A] (u v : Aˣ) (x : A),\n  ((Units.mulLeftLinearEquiv R A) (u * v)) x = ((Units.mulLeftLinearEquiv R A) u) (((Units.mulLeftLinearEquiv R A) v) x)","typeReadable":"∀ {R : Type u_9} {A : Type u_10} [inst : Semiring R] [inst_1 : Semiring A] [inst_2 : Module R A]\n  [inst_3 : SMulCommClass R A A] (u v : Aˣ) (x : A),\n  ((Units.mulLeftLinearEquiv R A) (u * v)) x = ((Units.mulLeftLinearEquiv R A) u) (((Units.mulLeftLinearEquiv R A) v) x)","typeReferences":[["MulOneClass","toMulOne"],["Units","instMul"],["Module"],["MonoidHom"],["MonoidHom","instFunLike"],["HMul","hMul"],["SMulZeroClass","toSMul"],["AddMonoidWithOne","toAddMonoid"],["instDistribSMul"],["LinearEquiv"],["DFunLike","coe"],["LinearEquiv","automorphismGroup"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Monoid","toMulOneClass"],["EquivLike","toFunLike"],["MonoidWithZero","toMonoid"],["Units","mulLeftLinearEquiv"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["LinearEquiv","instEquivLike"],["Eq"],["Group","toDivInvMonoid"],["NonAssocSemiring","toAddCommMonoidWithOne"],["Units"],["DistribSMul","toSMulZeroClass"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["Units","instMulOneClass"],["AddZeroClass","toAddZero"],["SMulCommClass"],["Module","toDistribMulAction"],["DivInvMonoid","toMonoid"],["RingHomInvPair","ids"],["instHMul"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["MulOneClass","toMulOne"],["Units","instMul"],["Eq","trans"],["MonoidHom"],["MonoidHom","instFunLike"],["HMul","hMul"],["LinearEquiv"],["DFunLike","coe"],["congrArg"],["LinearEquiv","automorphismGroup"],["MulOne","toMul"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["EquivLike","toFunLike"],["MonoidWithZero","toMonoid"],["Monoid","toMulOneClass"],["congrFun'"],["Units","mulLeftLinearEquiv"],["LinearEquiv","instEquivLike"],["Eq"],["Group","toDivInvMonoid"],["Units"],["MonoidHomClass","toMulHomClass"],["True"],["NonUnitalNonAssocSemiring","toDistrib"],["Distrib","toMul"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["Semiring","toMonoidWithZero"],["Units","instMulOneClass"],["MonoidHom","instMonoidHomClass"],["eq_self"],["of_eq_true"],["DivInvMonoid","toMonoid"],["Units","val"],["map_mul"],["RingHomInvPair","ids"],["instHMul"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","conj_apply"],"typeFallback":"forall {R₁' : Type.{u_12}} {R₂' : Type.{u_13}} {M₁' : Type.{u_20}} {M₂' : Type.{u_21}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59 : CommSemiring.{u_12} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62 : CommSemiring.{u_13} R₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83 : AddCommMonoid.{u_20} M₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86 : AddCommMonoid.{u_21} M₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110 : Module.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.114 : Module.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86] {σ₁'₂' : RingHom.{u_12, u_13} R₁' R₂' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59)) (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62))} {σ₂'₁' : RingHom.{u_13, u_12} R₂' R₁' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62)) (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59))} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.293 : RingHomInvPair.{u_12, u_13} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) σ₁'₂' σ₂'₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.297 : RingHomInvPair.{u_13, u_12} R₂' R₁' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) σ₂'₁' σ₁'₂'] (e : LinearEquiv.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.297 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.114) (f : Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110), Eq.{succ u_21} (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.114) (DFunLike.coe.{max (succ u_20) (succ u_21), succ u_20, succ u_21} (LinearEquiv.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.297 (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.114) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59)))) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62)))) (LinearMap.module.{u_12, u_12, u_12, u_20, u_20} R₁' R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62))) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.114))))) (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110) => Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.114) (EquivLike.toFunLike.{max (succ u_20) (succ u_21), succ u_20, succ u_21} (LinearEquiv.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.297 (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.114) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59)))) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62)))) (LinearMap.module.{u_12, u_12, u_12, u_20, u_20} R₁' R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M���' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62))) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.114))))) (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.114) (LinearEquiv.instEquivLike.{u_12, u_13, u_20, u_21} R₁' R₂' (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.114) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59)))) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62)))) (LinearMap.module.{u_12, u_12, u_12, u_20, u_20} R₁' R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62))) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.114)))) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.297)) (LinearEquiv.conj.{u_12, u_13, u_20, u_21} R₁' R₂' M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.114 σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.297 e) f) (LinearMap.comp.{u_13, u_12, u_13, u_21, u_20, u_21} R₂' R₁' R₂' M₂' M₁' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.114 σ₂'₁' σ₁'₂' (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62))) (RingHomInvPair.triples₂.{u_12, u_13} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.293) (LinearMap.comp.{u_12, u_12, u_13, u_20, u_20, u_21} R₁' R₁' R₂' M₁' M₁' M₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.114 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59))) σ₁'₂' σ₁'₂' (RingHomCompTriple.ids.{u_12, u_13} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) σ₁'₂') (LinearEquiv.toLinearMap.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.297 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.114 e) f) (LinearEquiv.toLinearMap.{u_13, u_12, u_21, u_20} R₂' R₁' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) σ₂'₁' σ₁'₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.297 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.293 M₂' M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110 (LinearEquiv.symm.{u_12, u_13, u_20, u_21} R₁' R₂' M₁' M₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.114 σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1481765922._hygCtx._hyg.297 e)))","typeFull":"∀ {R₁' : Type u_12} {R₂' : Type u_13} {M₁' : Type u_20} {M₂' : Type u_21} [inst : CommSemiring R₁']\n  [inst_1 : CommSemiring R₂'] [inst_2 : AddCommMonoid M₁'] [inst_3 : AddCommMonoid M₂'] [inst_4 : Module R₁' M₁']\n  [inst_5 : Module R₂' M₂'] {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} [inst_6 : RingHomInvPair σ₁'₂' σ₂'₁']\n  [inst_7 : RingHomInvPair σ₂'₁' σ₁'₂'] (e : M₁' ≃ₛₗ[σ₁'₂'] M₂') (f : Module.End R₁' M₁'),\n  e.conj f = (↑e ∘ₛₗ f) ∘ₛₗ ↑e.symm","typeReadable":"∀ {R₁' : Type u_12} {R₂' : Type u_13} {M₁' : Type u_20} {M₂' : Type u_21} [inst : CommSemiring R₁']\n  [inst_1 : CommSemiring R₂'] [inst_2 : AddCommMonoid M₁'] [inst_3 : AddCommMonoid M₂'] [inst_4 : Module R₁' M₁']\n  [inst_5 : Module R₂' M₂'] {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} [inst_6 : RingHomInvPair σ₁'₂' σ₂'₁']\n  [inst_7 : RingHomInvPair σ₂'₁' σ₁'₂'] (e : M₁' ≃ₛₗ[σ₁'₂'] M₂') (f : Module.End R₁' M₁'),\n  e.conj f = (↑e ∘ₛₗ f) ∘ₛₗ ↑e.symm","typeReferences":[["RingHomInvPair","triples₂"],["RingHom"],["smulCommClass_self"],["CommMonoid","toMonoid"],["RingHomCompTriple","ids"],["Module"],["CommSemiring"],["LinearMap","comp"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["DFunLike","coe"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["EquivLike","toFunLike"],["DistribMulAction","toMulAction"],["Eq"],["LinearEquiv","instEquivLike"],["Module","End"],["CommSemiring","toSemiring"],["LinearMap","module"],["LinearEquiv","toLinearMap"],["LinearEquiv","symm"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["LinearEquiv","conj"],["RingHomInvPair"]],"valueReferences":[["rfl"],["smulCommClass_self"],["Module","End"],["CommMonoid","toMonoid"],["CommSemiring","toSemiring"],["LinearMap","module"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["DFunLike","coe"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["LinearEquiv","conj"],["Module","toDistribMulAction"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["EquivLike","toFunLike"],["DistribMulAction","toMulAction"],["LinearEquiv","instEquivLike"]]},{"isProp":true,"kind":"theorem","name":["Units","mulRightLinearEquiv_mul_apply"],"typeFallback":"forall {R : Type.{u_9}} {A : Type.{u_10}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12 : Semiring.{u_9} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15 : Semiring.{u_10} A] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.18 : Module.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15)))] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.22 : IsScalarTower.{u_9, u_10, u_10} R A A (SMulZeroClass.toSMul.{u_9, u_10} R A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_9, u_10} R A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15))))) (DistribMulAction.toDistribSMul.{u_9, u_10} R A (MonoidWithZero.toMonoid.{u_9} R (Semiring.toMonoidWithZero.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12)) (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15)))) (Module.toDistribMulAction.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.18)))) (SMulZeroClass.toSMul.{u_10, u_10} A A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_10, u_10} A A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15))))) (instDistribSMul.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15))))) (SMulZeroClass.toSMul.{u_9, u_10} R A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_9, u_10} R A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15))))) (DistribMulAction.toDistribSMul.{u_9, u_10} R A (MonoidWithZero.toMonoid.{u_9} R (Semiring.toMonoidWithZero.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12)) (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15)))) (Module.toDistribMulAction.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.18))))] (u : Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15))) (v : Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15))) (x : A), Eq.{succ u_10} A (DFunLike.coe.{succ u_10, succ u_10, succ u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.18) A (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : A) => A) (EquivLike.toFunLike.{succ u_10, succ u_10, succ u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.18) A A (LinearEquiv.instEquivLike.{u_9, u_9, u_10, u_10} R R A A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.18 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12))) (Units.mulRightLinearEquiv.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.22 (HMul.hMul.{u_10, u_10, u_10} (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15))) (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15))) (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15))) (instHMul.{u_10} (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15))) (Units.instMul.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15)))) u v)) x) (DFunLike.coe.{succ u_10, succ u_10, succ u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.18) A (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : A) => A) (EquivLike.toFunLike.{succ u_10, succ u_10, succ u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.18) A A (LinearEquiv.instEquivLike.{u_9, u_9, u_10, u_10} R R A A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.18 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12))) (Units.mulRightLinearEquiv.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.22 v) (DFunLike.coe.{succ u_10, succ u_10, succ u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.18) A (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : A) => A) (EquivLike.toFunLike.{succ u_10, succ u_10, succ u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.18 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12))) (Units.mulRightLinearEquiv.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.15 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3151611838._hygCtx._hyg.22 u) x))","typeFull":"∀ {R : Type u_9} {A : Type u_10} [inst : Semiring R] [inst_1 : Semiring A] [inst_2 : Module R A]\n  [inst_3 : IsScalarTower R A A] (u v : Aˣ) (x : A),\n  (Units.mulRightLinearEquiv R (u * v)) x = (Units.mulRightLinearEquiv R v) ((Units.mulRightLinearEquiv R u) x)","typeReadable":"∀ {R : Type u_9} {A : Type u_10} [inst : Semiring R] [inst_1 : Semiring A] [inst_2 : Module R A]\n  [inst_3 : IsScalarTower R A A] (u v : Aˣ) (x : A),\n  (Units.mulRightLinearEquiv R (u * v)) x = (Units.mulRightLinearEquiv R v) ((Units.mulRightLinearEquiv R u) x)","typeReferences":[["Units","instMul"],["IsScalarTower"],["Module"],["HMul","hMul"],["SMulZeroClass","toSMul"],["AddMonoidWithOne","toAddMonoid"],["instDistribSMul"],["LinearEquiv"],["DFunLike","coe"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["EquivLike","toFunLike"],["MonoidWithZero","toMonoid"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["LinearEquiv","instEquivLike"],["Eq"],["NonAssocSemiring","toAddCommMonoidWithOne"],["Units"],["DistribSMul","toSMulZeroClass"],["Units","mulRightLinearEquiv"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["Module","toDistribMulAction"],["RingHomInvPair","ids"],["instHMul"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["MulOneClass","toMulOne"],["Eq","trans"],["NonUnitalSemiring","toSemigroupWithZero"],["HMul","hMul"],["mul_assoc"],["LinearEquiv"],["DFunLike","coe"],["congrArg"],["Semigroup","toMul"],["MulOne","toMul"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["Monoid","toMulOneClass"],["EquivLike","toFunLike"],["Eq"],["LinearEquiv","instEquivLike"],["Semiring","toNonUnitalSemiring"],["Units","mulRightLinearEquiv"],["True"],["NonUnitalNonAssocSemiring","toDistrib"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["Distrib","toMul"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["Semiring","toMonoidWithZero"],["eq_self"],["of_eq_true"],["Units","val"],["RingHomInvPair","ids"],["instHMul"],["SemigroupWithZero","toSemigroup"]]},{"isProp":true,"kind":"theorem","name":["Module","compHom","toLinearEquiv","_proof_2"],"typeFallback":"forall {R : Type.{u_2}} {S : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.12 : Semiring.{u_2} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.15 : Semiring.{u_1} S] (g : RingEquiv.{u_2, u_1} R S (Distrib.toMul.{u_2} R (NonUnitalNonAssocSemiring.toDistrib.{u_2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.12)))) (Distrib.toMul.{u_1} S (NonUnitalNonAssocSemiring.toDistrib.{u_1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} S (Semiring.toNonAssocSemiring.{u_1} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.15)))) (Distrib.toAdd.{u_2} R (NonUnitalNonAssocSemiring.toDistrib.{u_2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.12)))) (Distrib.toAdd.{u_1} S (NonUnitalNonAssocSemiring.toDistrib.{u_1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} S (Semiring.toNonAssocSemiring.{u_1} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.15))))) (x : R) (y : R), Eq.{succ u_1} S (Equiv.toFun.{succ u_2, succ u_1} R S (RingEquiv.toEquiv.{u_2, u_1} R S (Distrib.toMul.{u_2} R (NonUnitalNonAssocSemiring.toDistrib.{u_2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.12)))) (Distrib.toMul.{u_1} S (NonUnitalNonAssocSemiring.toDistrib.{u_1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} S (Semiring.toNonAssocSemiring.{u_1} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.15)))) (Distrib.toAdd.{u_2} R (NonUnitalNonAssocSemiring.toDistrib.{u_2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f)) (Inv.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.symm.{u_1, u_1, u_2, u_2} R R M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) f)) (npowRec.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (One.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.refl.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25)) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f))) (OfNat.ofNat.{0} Int 0 (instOfNat 0)) a) (OfNat.ofNat.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) 1 (One.toOfNat1.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (One.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.refl.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25))))","typeFull":"∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (a : M ≃ₗ[R] M),\n  zpowRec npowRec 0 a = 1","typeReadable":"∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (a : M ≃ₗ[R] M),\n  zpowRec npowRec 0 a = 1","typeReferences":[["Mul","mk"],["RingHomCompTriple","ids"],["Module"],["Inv","mk"],["One","mk"],["LinearEquiv"],["LinearEquiv","symm"],["zpowRec"],["OfNat","ofNat"],["Int"],["LinearEquiv","trans"],["npowRec"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["One","toOfNat1"],["instOfNat"],["RingHom","id"],["RingHomInvPair","ids"],["Eq"],["Semiring"],["LinearEquiv","refl"]],"valueReferences":[["Mul","mk"],["RingHomCompTriple","ids"],["Inv","mk"],["One","mk"],["LinearEquiv"],["zpowRec"],["LinearEquiv","symm"],["OfNat","ofNat"],["Int"],["LinearEquiv","trans"],["npowRec"],["Semiring","toNonAssocSemiring"],["instOfNat"],["RingHom","id"],["Eq","refl"],["RingHomInvPair","ids"],["LinearEquiv","refl"]]},{"isProp":true,"kind":"theorem","name":["DistribMulAction","toModuleAut","_proof_2"],"typeFallback":"forall (R : Type.{u_2}) {S : Type.{u_3}} (M : Type.{u_1}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 : Semiring.{u_2} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13 : AddCommMonoid.{u_1} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.16 : Module.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.20 : Group.{u_3} S] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.23 : DistribMulAction.{u_3, u_1} S M (DivInvMonoid.toMonoid.{u_3} S (Group.toDivInvMonoid.{u_3} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.20)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13)] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._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.Equiv.Basic.4191798717._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.Equiv.Basic.4191798717._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_3, u_1} S M (DivInvMonoid.toMonoid.{u_3} S (Group.toDivInvMonoid.{u_3} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.20)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._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.Equiv.Basic.4191798717._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.Equiv.Basic.4191798717._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.Equiv.Basic.4191798717._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13) (Module.toDistribMulAction.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.16))))] (x._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.62 : S) (x._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.64 : S), Eq.{succ u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 (RingHom.id.{u_2} R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._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 (DivInvMonoid.toMonoid.{u_3} S (Group.toDivInvMonoid.{u_3} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.20)))))) x._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.62 x._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.64)) (HMul.hMul.{u_1, u_1, u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10)) (RingHom.id.{u_2} R 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(RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.16) (instHMul.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.16) (MulOneClass.toMulOne.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.16) (Monoid.toMulOneClass.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.16) (Group.toDivInvMonoid.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.16) (LinearEquiv.automorphismGroup.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.16))))))) (DistribMulAction.toLinearEquiv.{u_2, u_3, u_1} R S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.27 x._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.62) (DistribMulAction.toLinearEquiv.{u_2, u_3, u_1} R S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.27 x._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.64))","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 : Group S] [inst_4 : DistribMulAction S M] [inst_5 : SMulCommClass S R M] (x x_1 : S),\n  DistribMulAction.toLinearEquiv R M (x * x_1) =\n    DistribMulAction.toLinearEquiv R M x * DistribMulAction.toLinearEquiv 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 : Group S] [inst_4 : DistribMulAction S M] [inst_5 : SMulCommClass S R M] (x x_1 : S),\n  DistribMulAction.toLinearEquiv R M (x * x_1) =\n    DistribMulAction.toLinearEquiv R M x * DistribMulAction.toLinearEquiv R M 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M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3385283885._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3385283885._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3385283885._hygCtx._hyg.16) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3385283885._hygCtx._hyg.10))) (LinearMap.funLeft.{u_1, u_5, u_9, u_10} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3385283885._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3385283885._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3385283885._hygCtx._hyg.16 m n (DFunLike.coe.{max (succ u_10) (succ u_9), succ u_9, succ u_10} (Equiv.{succ u_9, succ u_10} m n) m (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : m) => n) (EquivLike.toFunLike.{max (succ u_10) (succ u_9), succ u_9, succ u_10} (Equiv.{succ u_9, succ u_10} m n) m n (Equiv.instEquivLike.{succ u_9, succ u_10} m n)) e)) x)","typeFull":"∀ (R : Type u_1) (M : Type u_5) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {m : Type u_9}\n  {n : Type u_10} (e : m ≃ n) (x : n → M), (LinearEquiv.funCongrLeft R M e) x = (LinearMap.funLeft R M ⇑e) x","typeReadable":"∀ (R : Type u_1) (M : Type u_5) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {m : Type u_9}\n  {n : Type u_10} (e : m ≃ n) (x : n → M), (LinearEquiv.funCongrLeft R M e) x = (LinearMap.funLeft R M ⇑e) x","typeReferences":[["Equiv","instEquivLike"],["LinearEquiv","funCongrLeft"],["LinearMap","instFunLike"],["Module"],["Pi","addCommMonoid"],["LinearMap"],["LinearEquiv"],["DFunLike","coe"],["Equiv"],["Pi","Function","module"],["LinearMap","funLeft"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["EquivLike","toFunLike"],["RingHomInvPair","ids"],["LinearEquiv","instEquivLike"],["Eq"],["Semiring"]],"valueReferences":[["rfl"],["LinearEquiv","funCongrLeft"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["EquivLike","toFunLike"],["Pi","addCommMonoid"],["RingHomInvPair","ids"],["LinearEquiv","instEquivLike"],["LinearEquiv"],["DFunLike","coe"],["Pi","Function","module"]]},{"isProp":false,"kind":"definition","name":["LinearEquiv","domMulActCongrRight"],"typeFallback":"forall {S : Type.{u_4}} {R₁ : Type.{u_9}} {R₁' : Type.{u_11}} {R₂' : Type.{u_12}} {M₁ : Type.{u_13}} {M₁' : Type.{u_15}} {M₂' : Type.{u_16}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 : Semiring.{u_9} R₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 : Semiring.{u_11} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 : Semiring.{u_12} R₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 : AddCommMonoid.{u_13} M₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 : AddCommMonoid.{u_15} M₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 : AddCommMonoid.{u_16} M₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 : Module.{u_9, u_13} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 : Module.{u_11, u_15} R₁' M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 : Module.{u_12, u_16} R₂' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39] {σ₁'₂' : RingHom.{u_11, u_12} R₁' R₂' (Semiring.toNonAssocSemiring.{u_11} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24) (Semiring.toNonAssocSemiring.{u_12} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27)} {σ₂'₁' : RingHom.{u_12, u_11} R₂' R₁' (Semiring.toNonAssocSemiring.{u_12} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27) (Semiring.toNonAssocSemiring.{u_11} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24)} {σ₁₁' : RingHom.{u_9, u_11} R₁ R₁' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_11} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24)} {σ₁₂' : RingHom.{u_9, u_12} R₁ R₂' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_12} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27)} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.106 : RingHomInvPair.{u_11, u_12} R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁'₂' σ₂'₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.110 : RingHomInvPair.{u_12, u_11} R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₂'₁' σ₁'₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.114 : RingHomCompTriple.{u_9, u_11, u_12} R₁ R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₁' σ₁'₂' σ₁₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134 : Semiring.{u_4} S] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.137 : Module.{u_4, u_13} S M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.141 : SMulCommClass.{u_9, u_4, u_13} R₁ S M₁ (SMulZeroClass.toSMul.{u_9, u_13} R₁ M₁ (AddZero.toZero.{u_13} M₁ (AddZeroClass.toAddZero.{u_13} M₁ (AddMonoid.toAddZeroClass.{u_13} M₁ (AddCommMonoid.toAddMonoid.{u_13} M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30)))) (DistribSMul.toSMulZeroClass.{u_9, u_13} R₁ M₁ (AddMonoid.toAddZeroClass.{u_13} M₁ (AddCommMonoid.toAddMonoid.{u_13} M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30)) (DistribMulAction.toDistribSMul.{u_9, u_13} R₁ M₁ (MonoidWithZero.toMonoid.{u_9} R₁ (Semiring.toMonoidWithZero.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18)) (AddCommMonoid.toAddMonoid.{u_13} M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30) (Module.toDistribMulAction.{u_9, u_13} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42)))) (SMulZeroClass.toSMul.{u_4, u_13} S M₁ (AddZero.toZero.{u_13} M₁ (AddZeroClass.toAddZero.{u_13} M₁ (AddMonoid.toAddZeroClass.{u_13} M₁ (AddCommMonoid.toAddMonoid.{u_13} M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30)))) (DistribSMul.toSMulZeroClass.{u_4, u_13} S M₁ (AddMonoid.toAddZeroClass.{u_13} M₁ (AddCommMonoid.toAddMonoid.{u_13} M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30)) (DistribMulAction.toDistribSMul.{u_4, u_13} S M₁ (MonoidWithZero.toMonoid.{u_4} S (Semiring.toMonoidWithZero.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)) (AddCommMonoid.toAddMonoid.{u_13} M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30) (Module.toDistribMulAction.{u_4, u_13} S M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.137))))] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.146 : RingHomCompTriple.{u_9, u_12, u_11} R₁ R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₂' σ₂'₁' σ₁₁'], (LinearEquiv.{u_11, u_12, u_15, u_16} R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.110 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) -> (LinearEquiv.{u_4, u_4, max u_15 u_13, max u_16 u_13} (DomMulAct.{u_4} S) (DomMulAct.{u_4} S) (DomMulAct.instSemiringOfMulOpposite.{u_4} S (MulOpposite.instSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)) (DomMulAct.instSemiringOfMulOpposite.{u_4} S (MulOpposite.instSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)) (RingHom.id.{u_4} (DomMulAct.{u_4} S) (DomMulAct.instNonAssocSemiringOfMulOpposite.{u_4} S (MulOpposite.instNonAssocSemiring.{u_4} S (Semiring.toNonAssocSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)))) (RingHom.id.{u_4} (DomMulAct.{u_4} S) (Semiring.toNonAssocSemiring.{u_4} (DomMulAct.{u_4} S) (DomMulAct.instSemiringOfMulOpposite.{u_4} S (MulOpposite.instSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)))) (RingHomInvPair.ids.{u_4} (DomMulAct.{u_4} S) (DomMulAct.instSemiringOfMulOpposite.{u_4} S (MulOpposite.instSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134))) (RingHomInvPair.ids.{u_4} (DomMulAct.{u_4} S) (DomMulAct.instSemiringOfMulOpposite.{u_4} S (MulOpposite.instSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134))) (LinearMap.{u_9, u_11, u_13, u_15} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.{u_9, u_12, u_13, u_16} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (LinearMap.addCommMonoid.{u_9, u_11, u_13, u_15} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁') (LinearMap.addCommMonoid.{u_9, u_12, u_13, u_16} R₁ R₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂') (LinearMap.instModuleDomMulActOfSMulCommClass.{u_9, u_11, u_4, u_13, u_15} R₁ R₁' S M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.137 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.141) (LinearMap.instModuleDomMulActOfSMulCommClass.{u_9, u_12, u_4, u_13, u_16} R₁ R₂' S M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.137 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.141))","typeFull":"{S : Type u_4} →\n  {R₁ : Type u_9} →\n    {R₁' : Type u_11} →\n      {R₂' : Type u_12} →\n        {M₁ : Type u_13} →\n          {M₁' : Type u_15} →\n            {M₂' : Type u_16} →\n              [inst : Semiring R₁] →\n                [inst_1 : Semiring R₁'] →\n                  [inst_2 : Semiring R₂'] →\n                    [inst_3 : AddCommMonoid M₁] →\n                      [inst_4 : AddCommMonoid M₁'] →\n                        [inst_5 : AddCommMonoid M₂'] →\n                          [inst_6 : Module R₁ M₁] →\n                            [inst_7 : Module R₁' M₁'] →\n                              [inst_8 : Module R₂' M₂'] →\n                                {σ₁'₂' : R₁' →+* R₂'} →\n                                  {σ₂'₁' : R₂' →+* R₁'} →\n                                    {σ₁₁' : R₁ →+* R₁'} →\n                                      {σ₁₂' : R₁ →+* R₂'} →\n                                        [inst_9 : RingHomInvPair σ₁'₂' σ₂'₁'] →\n                                          [inst_10 : RingHomInvPair σ₂'₁' σ₁'₂'] →\n                                            [RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] →\n                                              [inst_12 : Semiring S] →\n                                                [inst_13 : Module S M₁] →\n                                                  [inst_14 : SMulCommClass R₁ S M₁] →\n                                                    [RingHomCompTriple σ₁₂' σ₂'₁' σ₁₁'] →\n                                                      (M₁' ≃ₛₗ[σ₁'₂'] M₂') →\n                                                        (M₁ →ₛₗ[σ₁₁'] M₁') ≃ₗ[Sᵈᵐᵃ] M₁ →ₛₗ[σ₁₂'] M₂'","typeReadable":"{S : Type u_4} →\n  {R₁ : Type u_9} →\n    {R₁' : Type u_11} →\n      {R₂' : Type u_12} →\n        {M₁ : Type u_13} →\n          {M₁' : Type u_15} →\n            {M₂' : Type u_16} →\n              [inst : Semiring R₁] →\n                [inst_1 : Semiring R₁'] →\n                  [inst_2 : Semiring R₂'] →\n                    [inst_3 : AddCommMonoid M₁] →\n                      [inst_4 : AddCommMonoid M₁'] →\n                        [inst_5 : AddCommMonoid M₂'] →\n                          [inst_6 : Module R₁ M₁] →\n                            [inst_7 : Module R₁' M₁'] →\n                              [inst_8 : Module R₂' M₂'] →\n                                {σ₁'₂' : R₁' →+* R₂'} →\n                                  {σ₂'₁' : R₂' →+* R₁'} →\n                                    {σ₁₁' : R₁ →+* R₁'} →\n                                      {σ₁₂' : R₁ →+* R₂'} →\n                                        [inst_9 : RingHomInvPair σ₁'₂' σ₂'₁'] →\n                                          [inst_10 : RingHomInvPair σ₂'₁' σ₁'₂'] →\n                                            [RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] →\n                                              [inst_12 : Semiring S] →\n                                                [inst_13 : Module S M₁] →\n                                                  [inst_14 : SMulCommClass R₁ S M₁] →\n                                                    [RingHomCompTriple σ₁₂' σ₂'₁' σ₁₁'] →\n                                                      (M₁' ≃ₛₗ[σ₁'₂'] M₂') →\n                                                        (M₁ →ₛₗ[σ₁₁'] M₁') ≃ₗ[Sᵈᵐᵃ] M₁ →ₛₗ[σ₁₂'] M₂'","typeReferences":[["RingHom"],["Module"],["DomMulAct","instNonAssocSemiringOfMulOpposite"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["RingHomCompTriple"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["MulOpposite","instSemiring"],["DistribSMul","toSMulZeroClass"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["DomMulAct"],["LinearMap"],["AddZeroClass","toAddZero"],["LinearMap","instModuleDomMulActOfSMulCommClass"],["LinearMap","addCommMonoid"],["SMulCommClass"],["Module","toDistribMulAction"],["RingHomInvPair","ids"],["MulOpposite","instNonAssocSemiring"],["RingHomInvPair"],["AddZero","toZero"],["DomMulAct","instSemiringOfMulOpposite"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["RingHomCompTriple","ids"],["LinearMap","mk"],["AddHom","mk"],["LinearEquiv","domMulActCongrRight","_proof_1"],["DomMulAct","instNonAssocSemiringOfMulOpposite"],["LinearEquiv","domMulActCongrRight","_proof_5"],["LinearEquiv","domMulActCongrRight","_proof_6"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["LinearMap","instAdd"],["LinearEquiv","mk"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Equiv","toFun"],["MulOpposite","instSemiring"],["DomMulAct"],["LinearMap"],["AddEquiv","toEquiv"],["LinearEquiv","domMulActCongrRight","_proof_4"],["LinearMap","instModuleDomMulActOfSMulCommClass"],["LinearMap","addCommMonoid"],["LinearEquiv","arrowCongrAddEquiv"],["AddCommMonoid","toAddCommSemigroup"],["Equiv","invFun"],["MulOpposite","instNonAssocSemiring"],["RingHomInvPair","ids"],["LinearEquiv","domMulActCongrRight","_proof_3"],["DomMulAct","instSemiringOfMulOpposite"],["LinearEquiv","refl"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","domMulActCongrRight_apply"],"typeFallback":"forall {S : Type.{u_4}} {R₁ : Type.{u_9}} {R₁' : Type.{u_11}} {R₂' : Type.{u_12}} {M₁ : Type.{u_13}} {M₁' : Type.{u_15}} {M₂' : Type.{u_16}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 : Semiring.{u_9} R₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 : Semiring.{u_11} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 : Semiring.{u_12} R₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 : AddCommMonoid.{u_13} M₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 : AddCommMonoid.{u_15} M₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 : AddCommMonoid.{u_16} M₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 : Module.{u_9, u_13} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 : Module.{u_11, u_15} R₁' M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 : Module.{u_12, u_16} R₂' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39] {σ₁'₂' : RingHom.{u_11, u_12} R₁' R₂' (Semiring.toNonAssocSemiring.{u_11} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24) (Semiring.toNonAssocSemiring.{u_12} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27)} {σ₂'₁' : RingHom.{u_12, u_11} R₂' R₁' (Semiring.toNonAssocSemiring.{u_12} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27) (Semiring.toNonAssocSemiring.{u_11} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24)} {σ₁₁' : RingHom.{u_9, u_11} R₁ R₁' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_11} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24)} {σ₁₂' : RingHom.{u_9, u_12} R₁ R₂' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_12} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27)} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.106 : RingHomInvPair.{u_11, u_12} R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁'₂' σ₂'₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.110 : RingHomInvPair.{u_12, u_11} R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₂'₁' σ₁'₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.114 : RingHomCompTriple.{u_9, u_11, u_12} R₁ R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₁' σ₁'₂' σ₁₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134 : Semiring.{u_4} S] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.137 : Module.{u_4, u_13} S M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.141 : SMulCommClass.{u_9, u_4, u_13} R₁ S M₁ (SMulZeroClass.toSMul.{u_9, u_13} R₁ M₁ (AddZero.toZero.{u_13} M₁ (AddZeroClass.toAddZero.{u_13} M₁ (AddMonoid.toAddZeroClass.{u_13} M₁ (AddCommMonoid.toAddMonoid.{u_13} M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30)))) (DistribSMul.toSMulZeroClass.{u_9, u_13} R₁ M₁ (AddMonoid.toAddZeroClass.{u_13} M₁ (AddCommMonoid.toAddMonoid.{u_13} M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30)) (DistribMulAction.toDistribSMul.{u_9, u_13} R₁ M₁ (MonoidWithZero.toMonoid.{u_9} R₁ (Semiring.toMonoidWithZero.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18)) (AddCommMonoid.toAddMonoid.{u_13} M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30) (Module.toDistribMulAction.{u_9, u_13} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42)))) (SMulZeroClass.toSMul.{u_4, u_13} S M₁ (AddZero.toZero.{u_13} M₁ (AddZeroClass.toAddZero.{u_13} M₁ (AddMonoid.toAddZeroClass.{u_13} M₁ (AddCommMonoid.toAddMonoid.{u_13} M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30)))) (DistribSMul.toSMulZeroClass.{u_4, u_13} S M₁ (AddMonoid.toAddZeroClass.{u_13} M₁ (AddCommMonoid.toAddMonoid.{u_13} M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30)) (DistribMulAction.toDistribSMul.{u_4, u_13} S M₁ (MonoidWithZero.toMonoid.{u_4} S (Semiring.toMonoidWithZero.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)) (AddCommMonoid.toAddMonoid.{u_13} M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30) (Module.toDistribMulAction.{u_4, u_13} S M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.137))))] 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (LinearMap.addCommMonoid.{u_9, u_11, u_13, u_15} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁') (LinearMap.addCommMonoid.{u_9, u_12, u_13, u_16} R₁ R₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂') (LinearMap.instModuleDomMulActOfSMulCommClass.{u_9, u_11, u_4, u_13, u_15} R₁ R₁' S M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.137 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.141) (LinearMap.instModuleDomMulActOfSMulCommClass.{u_9, u_12, u_4, u_13, u_16} R₁ R₂' S M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.137 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.141)) (LinearMap.{u_9, u_11, u_13, u_15} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : LinearMap.{u_9, u_11, u_13, u_15} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) => LinearMap.{u_9, u_12, u_13, u_16} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (EquivLike.toFunLike.{max (succ (max u_15 u_13)) (succ (max u_16 u_13)), succ (max u_15 u_13), succ (max u_16 u_13)} (LinearEquiv.{u_4, u_4, max u_15 u_13, max u_16 u_13} (DomMulAct.{u_4} S) (DomMulAct.{u_4} S) (DomMulAct.instSemiringOfMulOpposite.{u_4} S (MulOpposite.instSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)) (DomMulAct.instSemiringOfMulOpposite.{u_4} S (MulOpposite.instSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)) (RingHom.id.{u_4} (DomMulAct.{u_4} S) (DomMulAct.instNonAssocSemiringOfMulOpposite.{u_4} S (MulOpposite.instNonAssocSemiring.{u_4} S (Semiring.toNonAssocSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)))) (RingHom.id.{u_4} (DomMulAct.{u_4} S) (Semiring.toNonAssocSemiring.{u_4} (DomMulAct.{u_4} S) (DomMulAct.instSemiringOfMulOpposite.{u_4} S (MulOpposite.instSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)))) (RingHomInvPair.ids.{u_4} (DomMulAct.{u_4} S) (DomMulAct.instSemiringOfMulOpposite.{u_4} S (MulOpposite.instSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134))) (RingHomInvPair.ids.{u_4} (DomMulAct.{u_4} S) (DomMulAct.instSemiringOfMulOpposite.{u_4} S (MulOpposite.instSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134))) (LinearMap.{u_9, u_11, u_13, u_15} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.{u_9, u_12, u_13, u_16} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (LinearMap.addCommMonoid.{u_9, u_11, u_13, u_15} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁') (LinearMap.addCommMonoid.{u_9, u_12, u_13, u_16} R₁ R₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂') (LinearMap.instModuleDomMulActOfSMulCommClass.{u_9, u_11, u_4, u_13, u_15} R₁ R₁' S M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.137 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.141) (LinearMap.instModuleDomMulActOfSMulCommClass.{u_9, u_12, u_4, u_13, u_16} R₁ R₂' S M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.137 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.141)) (LinearMap.{u_9, u_11, u_13, u_15} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.{u_9, u_12, u_13, u_16} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (LinearEquiv.instEquivLike.{u_4, u_4, max u_15 u_13, max u_16 u_13} (DomMulAct.{u_4} S) (DomMulAct.{u_4} S) (LinearMap.{u_9, u_11, u_13, u_15} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.{u_9, u_12, u_13, u_16} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (DomMulAct.instSemiringOfMulOpposite.{u_4} S (MulOpposite.instSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)) (DomMulAct.instSemiringOfMulOpposite.{u_4} S (MulOpposite.instSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)) (LinearMap.addCommMonoid.{u_9, u_11, u_13, u_15} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁') (LinearMap.addCommMonoid.{u_9, u_12, u_13, u_16} R₁ R₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂') (LinearMap.instModuleDomMulActOfSMulCommClass.{u_9, u_11, u_4, u_13, u_15} R₁ R₁' S M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.137 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.141) (LinearMap.instModuleDomMulActOfSMulCommClass.{u_9, u_12, u_4, u_13, u_16} R₁ R₂' S M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.137 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.141) (RingHom.id.{u_4} (DomMulAct.{u_4} S) (DomMulAct.instNonAssocSemiringOfMulOpposite.{u_4} S (MulOpposite.instNonAssocSemiring.{u_4} S (Semiring.toNonAssocSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)))) (RingHom.id.{u_4} (DomMulAct.{u_4} S) (Semiring.toNonAssocSemiring.{u_4} (DomMulAct.{u_4} S) (DomMulAct.instSemiringOfMulOpposite.{u_4} S (MulOpposite.instSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)))) (RingHomInvPair.ids.{u_4} (DomMulAct.{u_4} S) (DomMulAct.instSemiringOfMulOpposite.{u_4} S (MulOpposite.instSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134))) (RingHomInvPair.ids.{u_4} (DomMulAct.{u_4} S) (DomMulAct.instSemiringOfMulOpposite.{u_4} S (MulOpposite.instSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134))))) (LinearEquiv.domMulActCongrRight.{u_4, u_9, u_11, u_12, u_13, u_15, u_16} S R₁ R₁' R₂' M₁ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁'₂' σ₂'₁' σ₁₁' σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.137 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.141 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.146 e₂) a._@._internal._hyg.0) (Equiv.toFun.{succ (max u_15 u_13), succ (max u_16 u_13)} (LinearMap.{u_9, u_11, u_13, u_15} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.{u_9, u_12, u_13, u_16} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (AddEquiv.toEquiv.{max u_15 u_13, max u_16 u_13} (LinearMap.{u_9, u_11, u_13, u_15} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.{u_9, u_12, u_13, u_16} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (LinearMap.instAdd.{u_9, u_11, u_13, u_15} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁') (LinearMap.instAdd.{u_9, u_12, u_13, u_16} R₁ R₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂') (LinearEquiv.arrowCongrAddEquiv.{u_9, u_9, u_11, u_12, u_13, u_13, u_15, u_16} R₁ R₁ R₁' R₂' M₁ M₁ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 (RingHom.id.{u_9} R₁ (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18)) (RingHom.id.{u_9} R₁ (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18)) σ₁'₂' σ₂'₁' σ₁₁' σ₁₂' σ₁₁' σ₁₂' (RingHomInvPair.ids.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) (RingHomInvPair.ids.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.114 (RingHomCompTriple.ids.{u_9, u_12} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂') inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.146 (RingHomCompTriple.ids.{u_9, u_11} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁') (LinearEquiv.refl.{u_9, u_13} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42) e₂)) a._@._internal._hyg.0)","typeFull":"∀ {S : Type u_4} {R₁ : Type u_9} {R₁' : Type u_11} {R₂' : Type u_12} {M₁ : Type u_13} {M₁' : Type u_15}\n  {M₂' : Type u_16} [inst : Semiring R₁] [inst_1 : Semiring R₁'] [inst_2 : Semiring R₂'] [inst_3 : AddCommMonoid M₁]\n  [inst_4 : AddCommMonoid M₁'] [inst_5 : AddCommMonoid M₂'] [inst_6 : Module R₁ M₁] [inst_7 : Module R₁' M₁']\n  [inst_8 : Module R₂' M₂'] {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} {σ₁₁' : R₁ →+* R₁'} {σ₁₂' : R₁ →+* R₂'}\n  [inst_9 : RingHomInvPair σ₁'₂' σ₂'₁'] [inst_10 : RingHomInvPair σ₂'₁' σ₁'₂']\n  [inst_11 : RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_12 : Semiring S] [inst_13 : Module S M₁]\n  [inst_14 : SMulCommClass R₁ S M₁] [inst_15 : RingHomCompTriple σ₁₂' σ₂'₁' σ₁₁'] (e₂ : M₁' ≃ₛₗ[σ₁'₂'] M₂')\n  (a : M₁ →ₛₗ[σ₁₁'] M₁'), e₂.domMulActCongrRight a = ((LinearEquiv.refl R₁ M₁).arrowCongrAddEquiv e₂).toFun a","typeReadable":"∀ {S : Type u_4} {R₁ : Type u_9} {R₁' : Type u_11} {R₂' : Type u_12} {M₁ : Type u_13} {M₁' : Type u_15}\n  {M₂' : Type u_16} [inst : Semiring R₁] [inst_1 : Semiring R₁'] [inst_2 : Semiring R₂'] [inst_3 : AddCommMonoid M₁]\n  [inst_4 : AddCommMonoid M₁'] [inst_5 : AddCommMonoid M₂'] [inst_6 : Module R₁ M₁] [inst_7 : Module R₁' M₁']\n  [inst_8 : Module R₂' M₂'] {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} {σ₁₁' : R₁ →+* R₁'} {σ₁₂' : R₁ →+* R₂'}\n  [inst_9 : RingHomInvPair σ₁'₂' σ₂'₁'] [inst_10 : RingHomInvPair σ₂'₁' σ₁'₂']\n  [inst_11 : RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_12 : Semiring S] [inst_13 : Module S M₁]\n  [inst_14 : SMulCommClass R₁ S M₁] [inst_15 : RingHomCompTriple σ₁₂' σ₂'₁' σ₁₁'] (e₂ : M₁' ≃ₛₗ[σ₁'₂'] M₂')\n  (a : M₁ →ₛₗ[σ₁₁'] M₁'), e₂.domMulActCongrRight a = ((LinearEquiv.refl R₁ M₁).arrowCongrAddEquiv e₂).toFun a","typeReferences":[["RingHom"],["RingHomCompTriple","ids"],["Module"],["DomMulAct","instNonAssocSemiringOfMulOpposite"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["DFunLike","coe"],["RingHomCompTriple"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["LinearMap","instAdd"],["EquivLike","toFunLike"],["MonoidWithZero","toMonoid"],["Equiv","toFun"],["LinearEquiv","instEquivLike"],["Eq"],["MulOpposite","instSemiring"],["DistribSMul","toSMulZeroClass"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["DomMulAct"],["AddEquiv","toEquiv"],["AddZeroClass","toAddZero"],["LinearMap"],["LinearMap","instModuleDomMulActOfSMulCommClass"],["LinearMap","addCommMonoid"],["SMulCommClass"],["Module","toDistribMulAction"],["LinearEquiv","arrowCongrAddEquiv"],["RingHomInvPair","ids"],["MulOpposite","instNonAssocSemiring"],["RingHomInvPair"],["LinearEquiv","domMulActCongrRight"],["AddZero","toZero"],["DomMulAct","instSemiringOfMulOpposite"],["LinearEquiv","refl"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["DomMulAct","instNonAssocSemiringOfMulOpposite"],["DomMulAct"],["LinearMap"],["LinearEquiv"],["DFunLike","coe"],["LinearMap","instModuleDomMulActOfSMulCommClass"],["LinearMap","addCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Eq","refl"],["EquivLike","toFunLike"],["MulOpposite","instNonAssocSemiring"],["RingHomInvPair","ids"],["LinearEquiv","instEquivLike"],["LinearEquiv","domMulActCongrRight"],["DomMulAct","instSemiringOfMulOpposite"],["MulOpposite","instSemiring"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","apply_faithfulSMul"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_5}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.19 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.25 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.19], FaithfulSMul.{u_5, u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.25) M (SMulZeroClass.toSMul.{u_5, u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.25) M (AddZero.toZero.{u_5} M (AddZeroClass.toAddZero.{u_5} M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.19)))) (DistribSMul.toSMulZeroClass.{u_5, u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.25) M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.19)) (DistribMulAction.toDistribSMul.{u_5, u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.25) M (DivInvMonoid.toMonoid.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.25) (LinearEquiv.automorphismGroup.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.711589862._hygCtx._hyg.25))) (AddCommMonoid.toAddMonoid.{u_5} M 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R₁' (Semiring.toNonAssocSemiring.{u_14} R₃' (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.65)) (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.59))} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.293 : RingHomInvPair.{u_12, u_13} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.62) σ₁'₂' σ₂'₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.297 : RingHomInvPair.{u_13, u_12} R₂' R₁' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.59) σ₂'₁' σ₁'₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.309 : RingHomInvPair.{u_13, u_14} R₂' R₃' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.65) σ₂'₃' σ₃'₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.313 : RingHomInvPair.{u_14, u_13} R₃' R₂' (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.65) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.62) σ₃'₂' σ₂'₃'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.325 : RingHomInvPair.{u_12, u_14} R₁' R₃' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.65) σ₁'₃' σ₃'₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.329 : RingHomInvPair.{u_14, u_12} R₃' R₁' (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.65) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.59) σ₃'₁' σ₁'₃'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.461 : RingHomCompTriple.{u_12, u_13, u_14} R₁' R₂' R₃' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.65) σ₁'₂' σ₂'₃' σ₁'₃'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.466 : RingHomCompTriple.{u_14, u_13, u_12} R₃' R₂' R₁' (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.65) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.59) σ₃'₂' σ₂'₁' σ₃'₁'] (e₁ : LinearEquiv.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.297 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.114) (e₂ : LinearEquiv.{u_13, u_14, u_21, u_22} R₂' R₃' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.65) σ₂'₃' σ₃'₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.309 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.313 M₂' M₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.89 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.118), Eq.{max (succ u_20) (succ u_22)} (LinearEquiv.{u_12, u_14, u_20, u_22} R₁' R₃' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.65) σ₁'₃' σ₃'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.325 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.329 (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.110) (Module.End.{u_14, u_22} R₃' M₃' (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.65) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.89 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.118) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.59)))) (LinearMap.addCommMonoid.{u_14, u_14, u_22, u_22} R₃' R₃' M₃' M₃' (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.65) (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.65) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.89 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.89 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.118 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.118 (RingHom.id.{u_14} R₃' (Semiring.toNonAssocSemiring.{u_14} R₃' (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.65)))) (LinearMap.module.{u_12, u_12, u_12, u_20, u_20} R₁' R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.110)))) (LinearMap.module.{u_14, u_14, u_14, u_22, u_22} R₃' R₃' R₃' M₃' M₃' (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.65) (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.65) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.89 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.89 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.118 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.118 (RingHom.id.{u_14} R₃' (Semiring.toNonAssocSemiring.{u_14} R₃' (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.65))) (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.65) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.118 (smulCommClass_self.{u_14, u_22} R₃' M₃' (CommSemiring.toCommMonoid.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.65) (DistribMulAction.toMulAction.{u_14, u_22} R₃' M₃' (CommMonoid.toMonoid.{u_14} R₃' (CommSemiring.toCommMonoid.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.65)) (AddCommMonoid.toAddMonoid.{u_22} M₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.89) (Module.toDistribMulAction.{u_14, u_22} R₃' M₃' (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.65) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.89 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.118))))) (LinearEquiv.trans.{u_12, u_13, u_14, u_20, u_21, u_22} R₁' R₂' R₃' (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.114) (Module.End.{u_14, u_22} R₃' M₃' (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.65) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.89 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.118) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.65) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.59)))) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.62)))) (LinearMap.addCommMonoid.{u_14, u_14, u_22, u_22} R₃' R₃' M₃' M₃' (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.65) (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.65) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.89 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.89 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.118 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.118 (RingHom.id.{u_14} R₃' (Semiring.toNonAssocSemiring.{u_14} R₃' (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.65)))) (LinearMap.module.{u_12, u_12, u_12, u_20, u_20} R₁' R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.110)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.62))) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1728039567._hygCtx._hyg.114 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.114) (f : Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.110) (x : M₂'), Eq.{succ u_21} M₂' (DFunLike.coe.{succ u_21, succ u_21, succ u_21} (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.114) M₂' (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M₂') => M₂') (LinearMap.instFunLike.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.62)))) (DFunLike.coe.{max (succ u_20) (succ u_21), succ u_20, succ u_21} (LinearEquiv.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.297 (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.114) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.59)))) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.62)))) (LinearMap.module.{u_12, u_12, u_12, u_20, u_20} R₁' R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.110)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.62))) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.114))))) (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.110) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.110) => Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.114) (EquivLike.toFunLike.{max (succ u_20) (succ u_21), succ u_20, succ u_21} (LinearEquiv.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.297 (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.114) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.59)))) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.62)))) (LinearMap.module.{u_12, u_12, u_12, u_20, u_20} R₁' R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.110)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.62))) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.114))))) (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.114) (LinearEquiv.instEquivLike.{u_12, u_13, u_20, u_21} R₁' R₂' (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.114) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.62) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.59)))) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1077355515._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' 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[inst_7 : RingHomInvPair σ₂'₁' σ₁'₂'] (e : M₁' ≃ₛₗ[σ₁'₂'] M₂') (f : Module.End R₁' M₁') (x : M₂'),\n  (e.conj f) x = e (f (e.symm x))","typeReadable":"∀ {R₁' : Type u_12} {R₂' : Type u_13} {M₁' : Type u_20} {M₂' : Type u_21} [inst : CommSemiring R₁']\n  [inst_1 : CommSemiring R₂'] [inst_2 : AddCommMonoid M₁'] [inst_3 : AddCommMonoid M₂'] [inst_4 : Module R₁' M₁']\n  [inst_5 : Module R₂' M₂'] {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} [inst_6 : RingHomInvPair σ₁'₂' σ₂'₁']\n  [inst_7 : RingHomInvPair σ₂'₁' σ₁'₂'] (e : M₁' ≃ₛₗ[σ₁'₂'] M₂') (f : Module.End R₁' M₁') (x : M₂'),\n  (e.conj f) x = e (f (e.symm x))","typeReferences":[["RingHom"],["smulCommClass_self"],["LinearMap","instFunLike"],["CommMonoid","toMonoid"],["Module"],["CommSemiring"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["DFunLike","coe"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["EquivLike","toFunLike"],["DistribMulAction","toMulAction"],["Eq"],["LinearEquiv","instEquivLike"],["Module","End"],["CommSemiring","toSemiring"],["LinearMap","module"],["LinearEquiv","symm"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["LinearEquiv","conj"],["RingHomInvPair"]],"valueReferences":[["rfl"],["smulCommClass_self"],["Module","End"],["CommMonoid","toMonoid"],["LinearMap","instFunLike"],["CommSemiring","toSemiring"],["LinearMap","module"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["DFunLike","coe"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["LinearEquiv","conj"],["Module","toDistribMulAction"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["EquivLike","toFunLike"],["DistribMulAction","toMulAction"],["LinearEquiv","instEquivLike"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","sumPiEquivProdPi","_proof_4"],"typeFallback":"forall 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.instAdd.{u_1, u_2, u_3, u_4} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁')) x y)) (HAdd.hAdd.{max u_5 u_3, max u_5 u_3, max u_5 u_3} (LinearMap.{u_1, u_6, u_3, u_5} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (LinearMap.{u_1, u_6, u_3, u_5} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (LinearMap.{u_1, u_6, u_3, u_5} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (instHAdd.{max u_5 u_3} (LinearMap.{u_1, u_6, u_3, u_5} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (LinearMap.instAdd.{u_1, u_6, u_3, u_5} R₁ R₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂')) (Equiv.toFun.{succ (max u_4 u_3), succ (max u_5 u_3)} (LinearMap.{u_1, u_2, u_3, u_4} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.{u_1, u_6, u_3, u_5} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (AddEquiv.toEquiv.{max u_4 u_3, max u_5 u_3} (LinearMap.{u_1, u_2, u_3, u_4} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.{u_1, u_6, u_3, u_5} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (LinearMap.instAdd.{u_1, u_2, u_3, u_4} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁') (LinearMap.instAdd.{u_1, u_6, u_3, u_5} R₁ R₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂') (LinearEquiv.arrowCongrAddEquiv.{u_1, u_1, u_2, u_6, u_3, u_3, u_4, u_5} R₁ R₁ R₁' R₂' M₁ M₁ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 (RingHom.id.{u_1} R₁ (Semiring.toNonAssocSemiring.{u_1} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18)) (RingHom.id.{u_1} R₁ (Semiring.toNonAssocSemiring.{u_1} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18)) σ₁'₂' σ₂'₁' σ₁₁' σ₁₂' σ₁₁' σ₁₂' (RingHomInvPair.ids.{u_1} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) (RingHomInvPair.ids.{u_1} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.114 (RingHomCompTriple.ids.{u_1, u_6} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂') inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.146 (RingHomCompTriple.ids.{u_1, u_2} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁') (LinearEquiv.refl.{u_1, u_3} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42) e₂)) x) (Equiv.toFun.{succ (max u_4 u_3), succ (max u_5 u_3)} (LinearMap.{u_1, u_2, u_3, u_4} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.{u_1, u_6, u_3, u_5} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (AddEquiv.toEquiv.{max u_4 u_3, max u_5 u_3} (LinearMap.{u_1, u_2, u_3, u_4} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.{u_1, u_6, u_3, u_5} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (LinearMap.instAdd.{u_1, u_2, u_3, u_4} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁') (LinearMap.instAdd.{u_1, u_6, u_3, u_5} R₁ R₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂') (LinearEquiv.arrowCongrAddEquiv.{u_1, u_1, u_2, u_6, u_3, u_3, u_4, u_5} R₁ R₁ R₁' R₂' M₁ M₁ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 (RingHom.id.{u_1} R₁ (Semiring.toNonAssocSemiring.{u_1} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18)) (RingHom.id.{u_1} R₁ (Semiring.toNonAssocSemiring.{u_1} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18)) σ₁'₂' σ₂'₁' σ₁₁' σ₁₂' σ₁₁' σ₁₂' (RingHomInvPair.ids.{u_1} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) (RingHomInvPair.ids.{u_1} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.114 (RingHomCompTriple.ids.{u_1, u_6} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂') inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.146 (RingHomCompTriple.ids.{u_1, u_2} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁') (LinearEquiv.refl.{u_1, u_3} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42) e₂)) y))","typeFull":"∀ {R₁ : Type u_1} {R₁' : Type u_2} {R₂' : Type u_6} {M₁ : Type u_3} {M₁' : Type u_4} {M₂' : Type u_5}\n  [inst : Semiring R₁] [inst_1 : Semiring R₁'] [inst_2 : Semiring R₂'] [inst_3 : AddCommMonoid M₁]\n  [inst_4 : AddCommMonoid M₁'] [inst_5 : AddCommMonoid M₂'] [inst_6 : Module R₁ M₁] [inst_7 : Module R₁' M₁']\n  [inst_8 : Module R₂' M₂'] {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} {σ₁₁' : R₁ →+* R₁'} {σ₁₂' : R₁ →+* R₂'}\n  [inst_9 : RingHomInvPair σ₁'₂' σ₂'₁'] [inst_10 : RingHomInvPair σ₂'₁' σ₁'₂']\n  [inst_11 : RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_12 : RingHomCompTriple σ₁₂' σ₂'₁' σ₁₁'] (e₂ : M₁' ≃ₛₗ[σ₁'₂'] M₂')\n  (x y : M₁ →ₛₗ[σ₁₁'] M₁'),\n  ((LinearEquiv.refl R₁ M₁).arrowCongrAddEquiv e₂).toFun (x + y) =\n    ((LinearEquiv.refl R₁ M₁).arrowCongrAddEquiv e₂).toFun x + ((LinearEquiv.refl R₁ M₁).arrowCongrAddEquiv e₂).toFun y","typeReadable":"∀ {R₁ : Type u_1} {R₁' : Type u_2} {R₂' : Type u_6} {M₁ : Type u_3} {M₁' : Type u_4} {M₂' : Type u_5}\n  [inst : Semiring R₁] [inst_1 : Semiring R₁'] [inst_2 : Semiring R₂'] [inst_3 : AddCommMonoid M₁]\n  [inst_4 : AddCommMonoid M₁'] [inst_5 : AddCommMonoid M₂'] [inst_6 : Module R₁ M₁] [inst_7 : Module R₁' M₁']\n  [inst_8 : Module R₂' M₂'] {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} {σ₁₁' : R₁ →+* R₁'} {σ₁₂' : R₁ →+* R₂'}\n  [inst_9 : RingHomInvPair σ₁'₂' σ₂'₁'] [inst_10 : RingHomInvPair σ₂'₁' σ₁'₂']\n  [inst_11 : RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_12 : RingHomCompTriple σ₁₂' σ₂'₁' σ₁₁'] (e₂ : M₁' ≃ₛₗ[σ₁'₂'] M₂')\n  (x y : M₁ →ₛₗ[σ₁₁'] M₁'),\n  ((LinearEquiv.refl R₁ M₁).arrowCongrAddEquiv e₂).toFun (x + y) =\n    ((LinearEquiv.refl R₁ M₁).arrowCongrAddEquiv e₂).toFun x + ((LinearEquiv.refl R₁ M₁).arrowCongrAddEquiv e₂).toFun y","typeReferences":[["RingHom"],["instHAdd"],["RingHomCompTriple","ids"],["Module"],["LinearEquiv"],["LinearMap"],["AddEquiv","toEquiv"],["RingHomCompTriple"],["HAdd","hAdd"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["LinearEquiv","arrowCongrAddEquiv"],["RingHom","id"],["LinearMap","instAdd"],["RingHomInvPair","ids"],["Equiv","toFun"],["RingHomInvPair"],["Eq"],["LinearEquiv","refl"],["Semiring"]],"valueReferences":[["Semiring","toNonAssocSemiring"],["LinearEquiv","arrowCongrAddEquiv"],["RingHomCompTriple","ids"],["RingHom","id"],["LinearMap","instAdd"],["RingHomInvPair","ids"],["AddEquiv","map_add'"],["LinearMap"],["LinearEquiv","refl"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","smul_def"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_5}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.19 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.25 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.19] (f : LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.25) (a : M), Eq.{succ u_5} M (HSMul.hSMul.{u_5, u_5, u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.25) M M (instHSMul.{u_5, u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.25) M (SMulZeroClass.toSMul.{u_5, u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.25) M (AddZero.toZero.{u_5} M (AddZeroClass.toAddZero.{u_5} M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.19)))) (DistribSMul.toSMulZeroClass.{u_5, u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.25) M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.19)) (DistribMulAction.toDistribSMul.{u_5, u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.25) M (DivInvMonoid.toMonoid.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.25) (Group.toDivInvMonoid.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.25) (LinearEquiv.automorphismGroup.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.25))) (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.19) (LinearEquiv.applyDistribMulAction.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.25))))) f a) (DFunLike.coe.{succ u_5, succ u_5, succ u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.25) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (EquivLike.toFunLike.{succ u_5, succ u_5, succ u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.25) M M (LinearEquiv.instEquivLike.{u_1, u_1, u_5, u_5} R R M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1925582909._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R 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(R : Type.{u_1}) {S : Type.{u_4}} (M : Type.{u_5}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.16 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.20 : Group.{u_4} S] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.23 : DistribMulAction.{u_4, u_5} S M (DivInvMonoid.toMonoid.{u_4} S (Group.toDivInvMonoid.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.20)) (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13)] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.27 : SMulCommClass.{u_4, 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(DivInvMonoid.toMonoid.{u_4} S (Group.toDivInvMonoid.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.20)) (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.23)))) s a._@._internal._hyg.0)","typeFull":"∀ (R : Type u_1) {S : Type u_4} (M : Type u_5) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  [inst_3 : Group S] [inst_4 : DistribMulAction S M] [inst_5 : SMulCommClass S R M] (s : S) (a : M),\n  (DistribMulAction.toLinearEquiv R M s) a = s • a","typeReadable":"∀ (R : Type u_1) {S : Type u_4} (M : Type u_5) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  [inst_3 : Group S] [inst_4 : DistribMulAction S M] [inst_5 : SMulCommClass S R M] (s : S) (a : M),\n  (DistribMulAction.toLinearEquiv R M s) a = s • 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{R : Type.{u_1}} {S : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.12 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.15 : Semiring.{u_2} S] (g : RingEquiv.{u_1, u_2} R S (Distrib.toMul.{u_1} R (NonUnitalNonAssocSemiring.toDistrib.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.12)))) (Distrib.toMul.{u_2} S (NonUnitalNonAssocSemiring.toDistrib.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.15)))) (Distrib.toAdd.{u_1} R (NonUnitalNonAssocSemiring.toDistrib.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.12)))) (Distrib.toAdd.{u_2} S (NonUnitalNonAssocSemiring.toDistrib.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.15))))), Function.LeftInverse.{succ u_1, succ u_2} R S (Equiv.invFun.{succ u_1, succ u_2} R S (RingEquiv.toEquiv.{u_1, u_2} R S (Distrib.toMul.{u_1} R (NonUnitalNonAssocSemiring.toDistrib.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.12)))) (Distrib.toMul.{u_2} S (NonUnitalNonAssocSemiring.toDistrib.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.15)))) (Distrib.toAdd.{u_1} R (NonUnitalNonAssocSemiring.toDistrib.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R 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(AddCommGroup.toAddCommMonoid.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19) (AddCommGroup.toIntModule.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16) (AddCommGroup.toIntModule.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19) (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int Int.instSemiring))) (AddMonoidHom.instModule.{u_11, u_9, u_10} R A B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.13 (SubNegMonoid.toAddMonoid.{u_9} A (AddGroup.toSubNegMonoid.{u_9} A (AddCommGroup.toAddGroup.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16))) (AddCommGroup.toAddCommMonoid.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.22) (LinearMap.module.{0, 0, u_11, u_9, u_10} Int Int R A B Int.instSemiring Int.instSemiring (AddCommGroup.toAddCommMonoid.{u_9} A 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.22)) f) (LinearMap.toAddMonoidHom.{0, 0, u_9, u_10} Int Int A B Int.instSemiring Int.instSemiring (AddCommGroup.toAddCommMonoid.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19) (AddCommGroup.toIntModule.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16) (AddCommGroup.toIntModule.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19) (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int Int.instSemiring)) f)","typeFull":"∀ {A : Type u_9} {B : Type u_10} (R : Type u_11) [inst : Semiring R] [inst_1 : AddCommGroup A] [inst_2 : AddCommGroup B]\n  [inst_3 : Module R B] (f : A →ₗ[ℤ] B), (addMonoidHomLequivInt R).symm f = f.toAddMonoidHom","typeReadable":"∀ {A : Type u_9} {B : Type u_10} (R : Type u_11) [inst : Semiring R] [inst_1 : AddCommGroup A] [inst_2 : AddCommGroup B]\n  [inst_3 : Module R B] (f : A →ₗ[ℤ] B), (addMonoidHomLequivInt R).symm f = f.toAddMonoidHom","typeReferences":[["Module"],["AddCommGroup","toAddGroup"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["DFunLike","coe"],["AddMonoidHom","instModule"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["AddMonoidHom"],["EquivLike","toFunLike"],["MonoidWithZero","toMonoid"],["addMonoidHomLequivInt"],["AddGroup","toSubNegMonoid"],["LinearEquiv","instEquivLike"],["Eq"],["AddGroup","int_smulCommClass"],["LinearMap","toAddMonoidHom"],["LinearMap","module"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddCommGroup"],["AddZeroClass","toAddZero"],["LinearMap"],["LinearEquiv","symm"],["AddCommGroup","toIntModule"],["Int"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["SubNegMonoid","toAddMonoid"],["Int","instSemiring"],["AddCommGroup","toAddCommMonoid"],["RingHomInvPair","ids"],["AddMonoidHom","instAddCommMonoid"],["Semiring"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["AddCommGroup","toAddGroup"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["DFunLike","coe"],["AddMonoidHom","instModule"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["AddMonoidHom"],["EquivLike","toFunLike"],["MonoidWithZero","toMonoid"],["addMonoidHomLequivInt"],["AddGroup","toSubNegMonoid"],["LinearEquiv","instEquivLike"],["AddGroup","int_smulCommClass"],["LinearMap","module"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["LinearMap"],["AddZeroClass","toAddZero"],["LinearEquiv","symm"],["AddCommGroup","toIntModule"],["Int"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["SubNegMonoid","toAddMonoid"],["Int","instSemiring"],["Eq","refl"],["RingHomInvPair","ids"],["AddCommGroup","toAddCommMonoid"],["AddMonoidHom","instAddCommMonoid"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["Units","mulLeftLinearEquiv","_proof_4"],"typeFallback":"forall 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(Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18))))) m x)) (HSMul.hSMul.{u_2, u_1, u_1} R A A (instHSMul.{u_2, u_1} R A (SMulZeroClass.toSMul.{u_2, u_1} R A (AddZero.toZero.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddCommMonoid.toAddMonoid.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_2, u_1} R A (AddMonoid.toAddZeroClass.{u_1} A (AddCommMonoid.toAddMonoid.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))))) (DistribMulAction.toDistribSMul.{u_2, 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.25) 1 (One.toOfNat1.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.25) (InvOneClass.toOne.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.25) (DivInvOneMonoid.toInvOneClass.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.25) (DivisionMonoid.toDivInvOneMonoid.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.25) (Group.toDivisionMonoid.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.25) (LinearEquiv.automorphismGroup.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.25))))))) (LinearEquiv.refl.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.277502174._hygCtx._hyg.25)","typeFull":"∀ {R : Type u_1} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],\n  1 = LinearEquiv.refl R M","typeReadable":"∀ {R : Type u_1} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],\n  1 = LinearEquiv.refl R M","typeReferences":[["Group","toDivisionMonoid"],["Module"],["InvOneClass","toOne"],["LinearEquiv"],["OfNat","ofNat"],["LinearEquiv","automorphismGroup"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["DivInvOneMonoid","toInvOneClass"],["One","toOfNat1"],["RingHom","id"],["RingHomInvPair","ids"],["Eq"],["DivisionMonoid","toDivInvOneMonoid"],["LinearEquiv","refl"],["Semiring"]],"valueReferences":[["LinearEquiv","automorphismGroup"],["rfl"],["Group","toDivisionMonoid"],["DivInvOneMonoid","toInvOneClass"],["Semiring","toNonAssocSemiring"],["One","toOfNat1"],["RingHom","id"],["InvOneClass","toOne"],["RingHomInvPair","ids"],["LinearEquiv"],["DivisionMonoid","toDivInvOneMonoid"],["OfNat","ofNat"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","arrowCongr","_proof_5"],"typeFallback":"forall {R₁ : Type.{u_5}} {R₂ : Type.{u_7}} {R₁' : Type.{u_6}} {R₂' : Type.{u_8}} {M₁ : Type.{u_2}} {M₂ : Type.{u_4}} {M₁' : Type.{u_1}} {M₂' : Type.{u_3}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 : Semiring.{u_5} R₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 : Semiring.{u_7} R₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59 : CommSemiring.{u_6} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62 : CommSemiring.{u_8} R₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 : AddCommMonoid.{u_2} M₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 : AddCommMonoid.{u_4} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 : AddCommMonoid.{u_1} M₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 : AddCommMonoid.{u_3} M₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 : Module.{u_5, u_2} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 : Module.{u_7, u_4} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 : Module.{u_6, u_1} R₁' M₁' (CommSemiring.toSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 : Module.{u_8, u_3} R₂' M₂' (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86] {σ₁₂ : RingHom.{u_5, u_7} R₁ R₂ (Semiring.toNonAssocSemiring.{u_5} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_7} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53)} {σ₂₁ : RingHom.{u_7, u_5} R₂ R₁ (Semiring.toNonAssocSemiring.{u_7} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53) (Semiring.toNonAssocSemiring.{u_5} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50)} {σ₁'₂' : RingHom.{u_6, u_8} R₁' R₂' (Semiring.toNonAssocSemiring.{u_6} R₁' (CommSemiring.toSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59)) (Semiring.toNonAssocSemiring.{u_8} R₂' (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62))} {σ₂'₁' : RingHom.{u_8, u_6} R₂' R₁' (Semiring.toNonAssocSemiring.{u_8} R₂' (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62)) (Semiring.toNonAssocSemiring.{u_6} R₁' (CommSemiring.toSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59))} {σ₁₁' : RingHom.{u_5, u_6} R₁ R₁' (Semiring.toNonAssocSemiring.{u_5} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_6} R₁' (CommSemiring.toSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59))} {σ₂₂' : RingHom.{u_7, u_8} R₂ R₂' (Semiring.toNonAssocSemiring.{u_7} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53) (Semiring.toNonAssocSemiring.{u_8} R₂' (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62))} {σ₂₁' : RingHom.{u_7, u_6} R₂ R₁' (Semiring.toNonAssocSemiring.{u_7} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53) (Semiring.toNonAssocSemiring.{u_6} R₁' (CommSemiring.toSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59))} {σ₁₂' : RingHom.{u_5, u_8} R₁ R₂' (Semiring.toNonAssocSemiring.{u_5} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_8} R₂' (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62))} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.285 : RingHomInvPair.{u_5, u_7} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 σ₁₂ σ₂₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.289 : RingHomInvPair.{u_7, u_5} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 σ₂₁ σ₁₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.293 : RingHomInvPair.{u_6, u_8} R₁' R₂' (CommSemiring.toSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₁'₂' σ₂'₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.297 : RingHomInvPair.{u_8, u_6} R₂' R₁' (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₂'₁' σ₁'₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.351 : RingHomCompTriple.{u_5, u_6, u_8} R₁ R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₁₁' σ₁'₂' σ₁₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.356 : RingHomCompTriple.{u_7, u_5, u_8} R₂ R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₁ σ₁₂' σ₂₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.361 : RingHomCompTriple.{u_7, u_8, u_6} R₂ R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₂₂' σ₂'₁' σ₂₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.366 : RingHomCompTriple.{u_5, u_7, u_6} R₁ R₂ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₂ σ₂₁' σ₁₁'] (e₁ : LinearEquiv.{u_5, u_7, u_2, u_4} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.285 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.289 M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102) (e₂ : LinearEquiv.{u_6, u_8, u_1, u_3} R₁' R₂' (CommSemiring.toSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.297 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114), Function.RightInverse.{succ (max u_1 u_2), succ (max u_3 u_4)} (LinearMap.{u_5, u_6, u_2, u_1} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (LinearMap.{u_7, u_8, u_4, u_3} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (Equiv.invFun.{succ (max u_1 u_2), succ (max u_3 u_4)} (LinearMap.{u_5, u_6, u_2, u_1} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (LinearMap.{u_7, u_8, u_4, u_3} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (LinearMap.instAdd.{u_5, u_6, u_2, u_1} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 σ₁₁') (LinearMap.instAdd.{u_7, u_8, u_4, u_3} R₂ R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 σ₂₂') (LinearEquiv.arrowCongrAddEquiv.{u_5, u_7, u_6, u_8, u_2, u_4, u_1, u_3} R₁ R₂ R₁' R₂' M₁ M₂ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 σ₁₂ σ₂₁ σ₁'₂' σ₂'₁' σ₁₁' σ₂₂' σ₂₁' σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.285 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.289 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.297 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.351 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.356 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.361 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.366 e₁ e₂))) (Equiv.toFun.{succ (max u_1 u_2), succ (max u_3 u_4)} (LinearMap.{u_5, u_6, u_2, u_1} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (LinearMap.{u_7, u_8, u_4, u_3} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (AddEquiv.toEquiv.{max u_1 u_2, max u_3 u_4} (LinearMap.{u_5, u_6, u_2, u_1} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (LinearMap.{u_7, u_8, u_4, u_3} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (LinearMap.instAdd.{u_5, u_6, u_2, u_1} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 σ₁₁') (LinearMap.instAdd.{u_7, u_8, u_4, u_3} R₂ R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 σ₂₂') (LinearEquiv.arrowCongrAddEquiv.{u_5, u_7, u_6, u_8, u_2, u_4, u_1, u_3} R₁ R₂ R₁' R₂' M₁ M₂ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 σ₁₂ σ₂₁ σ₁'₂' σ₂'₁' σ₁₁' σ₂₂' σ₂₁' σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.285 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.289 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.297 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.351 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.356 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.361 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.366 e₁ e₂)))","typeFull":"∀ {R₁ : Type u_5} {R₂ : Type u_7} {R₁' : Type u_6} {R₂' : Type u_8} {M₁ : Type u_2} {M₂ : Type u_4} {M₁' : Type u_1}\n  {M₂' : Type u_3} [inst : Semiring R₁] [inst_1 : Semiring R₂] [inst_2 : CommSemiring R₁'] [inst_3 : CommSemiring R₂']\n  [inst_4 : AddCommMonoid M₁] [inst_5 : AddCommMonoid M₂] [inst_6 : AddCommMonoid M₁'] [inst_7 : AddCommMonoid M₂']\n  [inst_8 : Module R₁ M₁] [inst_9 : Module R₂ M₂] [inst_10 : Module R₁' M₁'] [inst_11 : Module R₂' M₂']\n  {σ₁₂ : R₁ →+* R₂} {σ₂₁ : R₂ →+* R₁} {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} {σ₁₁' : R₁ →+* R₁'}\n  {σ₂₂' : R₂ →+* R₂'} {σ₂₁' : R₂ →+* R₁'} {σ₁₂' : R₁ →+* R₂'} [inst_12 : RingHomInvPair σ₁₂ σ₂₁]\n  [inst_13 : RingHomInvPair σ₂₁ σ₁₂] [inst_14 : RingHomInvPair σ₁'₂' σ₂'₁'] [inst_15 : RingHomInvPair σ₂'₁' σ₁'₂']\n  [inst_16 : RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_17 : RingHomCompTriple σ₂₁ σ₁₂' σ₂₂']\n  [inst_18 : RingHomCompTriple σ₂₂' σ₂'₁' σ₂₁'] [inst_19 : RingHomCompTriple σ₁₂ σ₂₁' σ₁₁'] (e₁ : M₁ ≃ₛₗ[σ₁₂] M₂)\n  (e₂ : M₁' ≃ₛₗ[σ₁'₂'] M₂'), Function.RightInverse (e₁.arrowCongrAddEquiv e₂).invFun (e₁.arrowCongrAddEquiv e₂).toFun","typeReadable":"∀ {R₁ : Type u_5} {R₂ : Type u_7} {R₁' : Type u_6} {R₂' : Type u_8} {M₁ : Type u_2} {M₂ : Type u_4} {M₁' : Type u_1}\n  {M₂' : Type u_3} [inst : Semiring R₁] [inst_1 : Semiring R₂] [inst_2 : CommSemiring R₁'] [inst_3 : CommSemiring R₂']\n  [inst_4 : AddCommMonoid M₁] [inst_5 : AddCommMonoid M₂] [inst_6 : AddCommMonoid M₁'] [inst_7 : AddCommMonoid M₂']\n  [inst_8 : Module R₁ M₁] [inst_9 : Module R₂ M₂] [inst_10 : Module R₁' M₁'] [inst_11 : Module R₂' M₂']\n  {σ₁₂ : R₁ →+* R₂} {σ₂₁ : R₂ →+* R₁} {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} {σ₁₁' : R₁ →+* R₁'}\n  {σ₂₂' : R₂ →+* R₂'} {σ₂₁' : R₂ →+* R₁'} {σ₁₂' : R₁ →+* R₂'} [inst_12 : RingHomInvPair σ₁₂ σ₂₁]\n  [inst_13 : RingHomInvPair σ₂₁ σ₁₂] [inst_14 : RingHomInvPair σ₁'₂' σ₂'₁'] [inst_15 : RingHomInvPair σ₂'₁' σ₁'₂']\n  [inst_16 : RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_17 : RingHomCompTriple σ₂₁ σ₁₂' σ₂₂']\n  [inst_18 : RingHomCompTriple σ₂₂' σ₂'₁' σ₂₁'] [inst_19 : RingHomCompTriple σ₁₂ σ₂₁' σ₁₁'] (e₁ : M₁ ≃ₛₗ[σ₁₂] M₂)\n  (e₂ : M₁' ≃ₛₗ[σ₁'₂'] M₂'), Function.RightInverse (e₁.arrowCongrAddEquiv e₂).invFun (e₁.arrowCongrAddEquiv e₂).toFun","typeReferences":[["RingHom"],["Module"],["CommSemiring"],["CommSemiring","toSemiring"],["AddEquiv","toEquiv"],["LinearEquiv"],["LinearMap"],["RingHomCompTriple"],["Function","RightInverse"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["LinearEquiv","arrowCongrAddEquiv"],["Equiv","invFun"],["LinearMap","instAdd"],["Equiv","toFun"],["RingHomInvPair"],["Semiring"]],"valueReferences":[["LinearEquiv","arrowCongrAddEquiv"],["Equiv","right_inv"],["LinearMap","instAdd"],["CommSemiring","toSemiring"],["AddEquiv","toEquiv"],["LinearMap"]]},{"isProp":true,"kind":"theorem","name":["Module","compHom","toLinearEquiv_apply"],"typeFallback":"forall {R : Type.{u_9}} {S : Type.{u_10}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.12 : Semiring.{u_9} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.15 : Semiring.{u_10} S] (g : RingEquiv.{u_9, u_10} R S (Distrib.toMul.{u_9} R (NonUnitalNonAssocSemiring.toDistrib.{u_9} R 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{R₁ : Type.{u_7}} {R₂ : Type.{u_3}} {R₁' : Type.{u_8}} {R₂' : Type.{u_4}} {M₁ : Type.{u_6}} {M₂ : Type.{u_1}} {M₁' : Type.{u_5}} {M₂' : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 : Semiring.{u_7} R₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 : Semiring.{u_3} R₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59 : CommSemiring.{u_8} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62 : CommSemiring.{u_4} R₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 : AddCommMonoid.{u_6} M₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 : AddCommMonoid.{u_1} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 : AddCommMonoid.{u_5} M₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 : AddCommMonoid.{u_2} M₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 : Module.{u_7, u_6} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 : Module.{u_3, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 : Module.{u_8, u_5} R₁' M₁' (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 : Module.{u_4, u_2} R₂' M₂' (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86] {σ₁₂ : RingHom.{u_7, u_3} R₁ R₂ (Semiring.toNonAssocSemiring.{u_7} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_3} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53)} {σ₂₁ : RingHom.{u_3, u_7} R₂ R₁ (Semiring.toNonAssocSemiring.{u_3} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53) (Semiring.toNonAssocSemiring.{u_7} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50)} {σ₁'₂' : RingHom.{u_8, u_4} R₁' R₂' (Semiring.toNonAssocSemiring.{u_8} R₁' (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59)) (Semiring.toNonAssocSemiring.{u_4} R₂' (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62))} {σ₂'₁' : RingHom.{u_4, u_8} R₂' R₁' (Semiring.toNonAssocSemiring.{u_4} R₂' (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62)) (Semiring.toNonAssocSemiring.{u_8} R₁' (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59))} {σ₁₁' : RingHom.{u_7, u_8} R₁ R₁' (Semiring.toNonAssocSemiring.{u_7} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_8} R₁' (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59))} {σ₂₂' : RingHom.{u_3, u_4} R₂ R₂' (Semiring.toNonAssocSemiring.{u_3} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53) (Semiring.toNonAssocSemiring.{u_4} R₂' (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62))} {σ₂₁' : RingHom.{u_3, u_8} R₂ R₁' (Semiring.toNonAssocSemiring.{u_3} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53) (Semiring.toNonAssocSemiring.{u_8} R₁' (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59))} {σ₁₂' : RingHom.{u_7, u_4} R₁ R₂' (Semiring.toNonAssocSemiring.{u_7} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_4} R₂' (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62))} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.285 : RingHomInvPair.{u_7, u_3} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 σ₁₂ σ₂₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.289 : RingHomInvPair.{u_3, u_7} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 σ₂₁ σ₁₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.293 : RingHomInvPair.{u_8, u_4} R₁' R₂' (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₁'₂' σ₂'₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.297 : RingHomInvPair.{u_4, u_8} R₂' R₁' (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₂'₁' σ₁'₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.351 : RingHomCompTriple.{u_7, u_8, u_4} R₁ R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₁₁' σ₁'₂' σ₁₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.356 : RingHomCompTriple.{u_3, u_7, u_4} R₂ R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₁ σ₁₂' σ₂₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.361 : RingHomCompTriple.{u_3, u_4, u_8} R₂ R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₂₂' σ₂'₁' σ₂₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.366 : RingHomCompTriple.{u_7, u_3, u_8} R₁ R₂ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₂ σ₂₁' σ₁₁'] (e₁ : LinearEquiv.{u_7, u_3, u_6, u_1} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.285 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.289 M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102) (e₂ : LinearEquiv.{u_8, u_4, u_5, u_2} R₁' R₂' (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.297 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (c : R₁') (f : LinearMap.{u_7, u_8, u_6, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110), Eq.{succ (max u_1 u_2)} (LinearMap.{u_3, u_4, u_1, u_2} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (Equiv.toFun.{succ (max u_5 u_6), succ (max u_2 u_1)} (LinearMap.{u_7, u_8, u_6, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (LinearMap.{u_3, u_4, u_1, u_2} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (AddEquiv.toEquiv.{max u_5 u_6, max u_2 u_1} (LinearMap.{u_7, u_8, u_6, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (LinearMap.{u_3, u_4, u_1, u_2} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (LinearMap.instAdd.{u_7, u_8, u_6, u_5} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 σ₁₁') (LinearMap.instAdd.{u_3, u_4, u_1, u_2} R₂ R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 σ₂₂') (LinearEquiv.arrowCongrAddEquiv.{u_7, u_3, u_8, u_4, u_6, u_1, u_5, u_2} R₁ R₂ R₁' R₂' M₁ M₂ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 σ₁₂ σ₂₁ σ₁'₂' σ₂'₁' σ₁₁' σ₂₂' σ₂₁' σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.285 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.289 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.297 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.351 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.356 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.361 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.366 e₁ e₂)) (HSMul.hSMul.{u_8, max u_6 u_5, max u_6 u_5} R₁' (LinearMap.{u_7, u_8, u_6, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (LinearMap.{u_7, u_8, u_6, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (instHSMul.{u_8, max u_6 u_5} R₁' (LinearMap.{u_7, u_8, u_6, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (SMulZeroClass.toSMul.{u_8, max u_6 u_5} R₁' (LinearMap.{u_7, u_8, u_6, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (AddZero.toZero.{max u_6 u_5} (LinearMap.{u_7, u_8, u_6, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (AddZeroClass.toAddZero.{max u_6 u_5} (LinearMap.{u_7, u_8, u_6, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (AddMonoid.toAddZeroClass.{max u_6 u_5} (LinearMap.{u_7, u_8, u_6, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (AddCommMonoid.toAddMonoid.{max u_6 u_5} (LinearMap.{u_7, u_8, u_6, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (LinearMap.addCommMonoid.{u_7, u_8, u_6, u_5} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 σ₁₁'))))) (DistribSMul.toSMulZeroClass.{u_8, max u_6 u_5} R₁' (LinearMap.{u_7, u_8, u_6, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (AddMonoid.toAddZeroClass.{max u_6 u_5} (LinearMap.{u_7, u_8, u_6, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (AddCommMonoid.toAddMonoid.{max u_6 u_5} (LinearMap.{u_7, u_8, u_6, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (LinearMap.addCommMonoid.{u_7, u_8, u_6, u_5} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 σ₁₁'))) (DistribMulAction.toDistribSMul.{u_8, max u_6 u_5} R₁' (LinearMap.{u_7, u_8, u_6, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (MonoidWithZero.toMonoid.{u_8} R₁' (Semiring.toMonoidWithZero.{u_8} R₁' (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59))) (AddCommMonoid.toAddMonoid.{max u_6 u_5} (LinearMap.{u_7, u_8, u_6, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (LinearMap.addCommMonoid.{u_7, u_8, u_6, u_5} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 σ₁₁')) (Module.toDistribMulAction.{u_8, max u_6 u_5} R₁' (LinearMap.{u_7, u_8, u_6, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (LinearMap.addCommMonoid.{u_7, u_8, u_6, u_5} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 σ₁₁') (LinearMap.module.{u_7, u_8, u_8, u_6, u_5} R₁ R₁' R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 σ₁₁' (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 (smulCommClass_self.{u_8, u_5} R₁' M₁' (CommSemiring.toCommMonoid.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_8, u_5} R₁' M₁' (CommMonoid.toMonoid.{u_8} R₁' (CommSemiring.toCommMonoid.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_5} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83) (Module.toDistribMulAction.{u_8, u_5} R₁' M₁' (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110))))))))) c f)) (HSMul.hSMul.{u_4, max u_1 u_2, max u_1 u_2} R₂' (LinearMap.{u_3, u_4, u_1, u_2} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (LinearMap.{u_3, u_4, u_1, u_2} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (instHSMul.{u_4, max u_1 u_2} R₂' (LinearMap.{u_3, u_4, u_1, u_2} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (SMulZeroClass.toSMul.{u_4, max u_1 u_2} R₂' (LinearMap.{u_3, u_4, u_1, u_2} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (AddZero.toZero.{max u_1 u_2} (LinearMap.{u_3, u_4, u_1, u_2} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (AddZeroClass.toAddZero.{max u_1 u_2} (LinearMap.{u_3, u_4, u_1, u_2} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (AddMonoid.toAddZeroClass.{max u_1 u_2} (LinearMap.{u_3, u_4, u_1, u_2} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (LinearMap.{u_3, u_4, u_1, u_2} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (LinearMap.addCommMonoid.{u_3, u_4, u_1, u_2} R₂ R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 σ₂₂'))))) (DistribSMul.toSMulZeroClass.{u_4, max u_1 u_2} R₂' (LinearMap.{u_3, u_4, u_1, u_2} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (AddMonoid.toAddZeroClass.{max u_1 u_2} (LinearMap.{u_3, u_4, u_1, u_2} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (LinearMap.{u_3, u_4, u_1, u_2} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (LinearMap.addCommMonoid.{u_3, u_4, u_1, u_2} R₂ R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 σ₂₂'))) (DistribMulAction.toDistribSMul.{u_4, max u_1 u_2} R₂' (LinearMap.{u_3, u_4, u_1, u_2} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (MonoidWithZero.toMonoid.{u_4} R₂' (Semiring.toMonoidWithZero.{u_4} R₂' (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62))) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (LinearMap.{u_3, u_4, u_1, u_2} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (LinearMap.addCommMonoid.{u_3, u_4, u_1, u_2} R₂ R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 σ₂₂')) (Module.toDistribMulAction.{u_4, max u_1 u_2} R₂' (LinearMap.{u_3, u_4, u_1, u_2} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) (LinearMap.addCommMonoid.{u_3, u_4, u_1, u_2} R₂ R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 σ₂₂') (LinearMap.module.{u_3, u_4, u_4, u_1, u_2} R₂ R₂' R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 σ₂₂' (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 (smulCommClass_self.{u_4, u_2} R₂' M₂' (CommSemiring.toCommMonoid.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_4, u_2} R₂' M₂' (CommMonoid.toMonoid.{u_4} R₂' (CommSemiring.toCommMonoid.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_2} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86) (Module.toDistribMulAction.{u_4, u_2} R₂' M₂' (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114))))))))) (DFunLike.coe.{max (succ u_8) (succ u_4), succ u_8, succ u_4} (RingHom.{u_8, u_4} R₁' R₂' (Semiring.toNonAssocSemiring.{u_8} R₁' (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59)) (Semiring.toNonAssocSemiring.{u_4} R₂' (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62))) R₁' (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : R₁') => R₂') (RingHom.instFunLike.{u_8, u_4} R₁' R₂' (Semiring.toNonAssocSemiring.{u_8} R₁' (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59)) (Semiring.toNonAssocSemiring.{u_4} R₂' (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62))) σ₁'₂' c) (Equiv.toFun.{succ (max u_5 u_6), succ (max u_2 u_1)} (LinearMap.{u_7, u_8, u_6, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (LinearMap.{u_3, u_4, u_1, u_2} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (AddEquiv.toEquiv.{max u_5 u_6, max u_2 u_1} (LinearMap.{u_7, u_8, u_6, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (LinearMap.{u_3, u_4, u_1, u_2} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (LinearMap.instAdd.{u_7, u_8, u_6, u_5} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 σ₁₁') (LinearMap.instAdd.{u_3, u_4, u_1, u_2} R₂ R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 σ₂₂') (LinearEquiv.arrowCongrAddEquiv.{u_7, u_3, u_8, u_4, u_6, u_1, u_5, u_2} R₁ R₂ R₁' R₂' M₁ M₂ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_8} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 σ₁₂ σ₂₁ σ₁'₂' σ₂'₁' σ₁₁' σ₂₂' σ₂₁' σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.285 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.289 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.297 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.351 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.356 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.361 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.366 e₁ e₂)) f))","typeFull":"∀ {R₁ : Type u_7} {R₂ : Type u_3} {R₁' : Type u_8} {R₂' : Type u_4} {M₁ : Type u_6} {M₂ : Type u_1} {M₁' : Type u_5}\n  {M₂' : Type u_2} [inst : Semiring R₁] [inst_1 : Semiring R₂] [inst_2 : CommSemiring R₁'] [inst_3 : CommSemiring R₂']\n  [inst_4 : AddCommMonoid M₁] [inst_5 : AddCommMonoid M₂] [inst_6 : AddCommMonoid M₁'] [inst_7 : AddCommMonoid M₂']\n  [inst_8 : Module R₁ M₁] [inst_9 : Module R₂ M₂] [inst_10 : Module R₁' M₁'] [inst_11 : Module R₂' M₂']\n  {σ₁₂ : R₁ →+* R₂} {σ₂₁ : R₂ →+* R₁} {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} {σ₁₁' : R₁ →+* R₁'}\n  {σ₂₂' : R₂ →+* R₂'} {σ₂₁' : R₂ →+* R₁'} {σ₁₂' : R₁ →+* R₂'} [inst_12 : RingHomInvPair σ₁₂ σ₂₁]\n  [inst_13 : RingHomInvPair σ₂₁ σ₁₂] [inst_14 : RingHomInvPair σ₁'₂' σ₂'₁'] [inst_15 : RingHomInvPair σ₂'₁' σ₁'₂']\n  [inst_16 : RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_17 : RingHomCompTriple σ₂₁ σ₁₂' σ₂₂']\n  [inst_18 : RingHomCompTriple σ₂₂' σ₂'₁' σ₂₁'] [inst_19 : RingHomCompTriple σ₁₂ σ₂₁' σ₁₁'] (e₁ : M₁ ≃ₛₗ[σ₁₂] M₂)\n  (e₂ : M₁' ≃ₛₗ[σ₁'₂'] M₂') (c : R₁') (f : M₁ →ₛₗ[σ₁₁'] M₁'),\n  (e₁.arrowCongrAddEquiv e₂).toFun (c • f) = σ₁'₂' c • (e₁.arrowCongrAddEquiv e₂).toFun f","typeReadable":"∀ {R₁ : Type u_7} {R₂ : Type u_3} {R₁' : Type u_8} {R₂' : Type u_4} {M₁ : Type u_6} {M₂ : Type u_1} {M₁' : Type u_5}\n  {M₂' : Type u_2} [inst : Semiring R₁] [inst_1 : Semiring R₂] [inst_2 : CommSemiring R₁'] [inst_3 : CommSemiring R₂']\n  [inst_4 : AddCommMonoid M₁] [inst_5 : AddCommMonoid M₂] [inst_6 : AddCommMonoid M₁'] [inst_7 : AddCommMonoid M₂']\n  [inst_8 : Module R₁ M₁] [inst_9 : Module R₂ M₂] [inst_10 : Module R₁' M₁'] [inst_11 : Module R₂' M₂']\n  {σ₁₂ : R₁ →+* R₂} {σ₂₁ : R₂ →+* R₁} {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} {σ₁₁' : R₁ →+* R₁'}\n  {σ₂₂' : R₂ →+* R₂'} {σ₂₁' : R₂ →+* R₁'} {σ₁₂' : R₁ →+* R₂'} [inst_12 : RingHomInvPair σ₁₂ σ₂₁]\n  [inst_13 : RingHomInvPair σ₂₁ σ₁₂] [inst_14 : RingHomInvPair σ₁'₂' σ₂'₁'] [inst_15 : RingHomInvPair σ₂'₁' σ₁'₂']\n  [inst_16 : RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_17 : RingHomCompTriple σ₂₁ σ₁₂' σ₂₂']\n  [inst_18 : RingHomCompTriple σ₂₂' σ₂'₁' σ₂₁'] [inst_19 : RingHomCompTriple σ₁₂ σ₂₁' σ₁₁'] (e₁ : M₁ ≃ₛₗ[σ₁₂] M₂)\n  (e₂ : M₁' ≃ₛₗ[σ₁'₂'] M₂') (c : R₁') (f : M₁ →ₛₗ[σ₁₁'] M₁'),\n  (e₁.arrowCongrAddEquiv e₂).toFun (c • f) = σ₁'₂' c • (e₁.arrowCongrAddEquiv e₂).toFun 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Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {m : Type u_9}\n  {n : Type u_10} {p : Type u_11} (e₁ : m ≃ n) (e₂ : n ≃ p),\n  LinearEquiv.funCongrLeft R M (e₁.trans e₂) = LinearEquiv.funCongrLeft R M e₂ ≪≫ₗ LinearEquiv.funCongrLeft R M e₁","typeReferences":[["LinearEquiv","funCongrLeft"],["RingHomCompTriple","ids"],["Module"],["Pi","addCommMonoid"],["LinearEquiv"],["Equiv"],["Pi","Function","module"],["LinearEquiv","trans"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Equiv","trans"],["RingHomInvPair","ids"],["Eq"],["Semiring"]],"valueReferences":[["rfl"],["LinearEquiv","funCongrLeft"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Equiv","trans"],["Pi","addCommMonoid"],["RingHomInvPair","ids"],["LinearEquiv"],["Pi","Function","module"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","symm_conj_apply"],"typeFallback":"forall {R₁' : Type.{u_12}} {R₂' : Type.{u_13}} {M₁' : Type.{u_20}} {M₂' : Type.{u_21}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59 : CommSemiring.{u_12} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62 : CommSemiring.{u_13} R₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83 : AddCommMonoid.{u_20} M₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86 : AddCommMonoid.{u_21} M₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.110 : Module.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114 : Module.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86] {σ₁'₂' : RingHom.{u_12, u_13} R₁' R₂' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59)) (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62))} {σ₂'₁' : RingHom.{u_13, u_12} R₂' R₁' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62)) (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59))} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.293 : RingHomInvPair.{u_12, u_13} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) σ₁'₂' σ₂'₁'] 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114) (f : Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114), Eq.{succ u_20} (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.110) (DFunLike.coe.{max (succ u_20) (succ u_21), succ u_21, succ u_20} (LinearEquiv.{u_13, u_12, u_21, u_20} R₂' R₁' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) σ₂'₁' σ₁'₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.297 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.293 (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114) (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.110) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62)))) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62))) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114)))) (LinearMap.module.{u_12, u_12, u_12, u_20, u_20} R₁' R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.110))))) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114) => Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.110) (EquivLike.toFunLike.{max (succ u_20) (succ u_21), succ u_21, succ u_20} (LinearEquiv.{u_13, u_12, u_21, u_20} R₂' R₁' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) σ₂'₁' σ₁'₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.297 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.293 (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114) (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.110) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62)))) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62))) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114)))) (LinearMap.module.{u_12, u_12, u_12, u_20, u_20} R₁' R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.110))))) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114) (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.110) (LinearEquiv.instEquivLike.{u_13, u_12, u_21, u_20} R₂' R₁' (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114) (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.110) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62)))) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62))) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114)))) (LinearMap.module.{u_12, u_12, u_12, u_20, u_20} R₁' R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.110)))) σ₂'₁' σ₁'₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.297 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.293)) (LinearEquiv.conj.{u_13, u_12, u_21, u_20} R₂' R₁' M₂' M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.110 σ₂'₁' σ₁'₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.297 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.293 (LinearEquiv.symm.{u_12, u_13, u_20, u_21} R₁' R₂' M₁' M₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114 σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.297 e)) f) (LinearMap.comp.{u_12, u_13, u_12, u_20, u_21, u_20} R₁' R₂' R₁' M₁' M₂' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.110 σ₁'₂' σ₂'₁' (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59))) (RingHomInvPair.triples₂.{u_13, u_12} R₂' R₁' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) σ₂'₁' σ₁'₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.297) (LinearMap.comp.{u_13, u_13, u_12, u_21, u_21, u_20} R₂' R₂' R₁' M₂' M₂' M₁' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.110 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62))) σ₂'₁' σ₂'₁' (RingHomCompTriple.ids.{u_13, u_12} R₂' R₁' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) σ₂'₁') (LinearEquiv.toLinearMap.{u_13, u_12, u_21, u_20} R₂' R₁' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) σ₂'₁' σ₁'₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.297 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.293 M₂' M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.110 (LinearEquiv.symm.{u_12, u_13, u_20, u_21} R₁' R₂' M₁' M₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114 σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.297 e)) f) (LinearEquiv.toLinearMap.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.297 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2656983607._hygCtx._hyg.114 e))","typeFull":"∀ {R₁' : Type u_12} {R₂' : Type u_13} {M₁' : Type u_20} {M₂' : Type u_21} [inst : CommSemiring R₁']\n  [inst_1 : CommSemiring R₂'] [inst_2 : AddCommMonoid M₁'] [inst_3 : AddCommMonoid M₂'] [inst_4 : Module R₁' M₁']\n  [inst_5 : Module R₂' M₂'] {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} [inst_6 : RingHomInvPair σ₁'₂' σ₂'₁']\n  [inst_7 : RingHomInvPair σ₂'₁' σ₁'₂'] (e : M₁' ≃ₛₗ[σ₁'₂'] M₂') (f : Module.End R₂' M₂'),\n  e.symm.conj f = (↑e.symm ∘ₛₗ f) ∘ₛₗ ↑e","typeReadable":"∀ {R₁' : Type u_12} {R₂' : Type u_13} {M₁' : Type u_20} {M₂' : Type u_21} [inst : CommSemiring R₁']\n  [inst_1 : CommSemiring R₂'] [inst_2 : AddCommMonoid M₁'] [inst_3 : AddCommMonoid M₂'] [inst_4 : Module R₁' M₁']\n  [inst_5 : Module R₂' M₂'] {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} [inst_6 : RingHomInvPair σ₁'₂' σ₂'₁']\n  [inst_7 : RingHomInvPair σ₂'₁' σ₁'₂'] (e : M₁' ≃ₛₗ[σ₁'₂'] M₂') (f : Module.End R₂' M₂'),\n  e.symm.conj f = (↑e.symm ∘ₛₗ f) ∘ₛₗ ↑e","typeReferences":[["RingHomInvPair","triples₂"],["RingHom"],["smulCommClass_self"],["CommMonoid","toMonoid"],["RingHomCompTriple","ids"],["Module"],["CommSemiring"],["LinearMap","comp"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["DFunLike","coe"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["EquivLike","toFunLike"],["DistribMulAction","toMulAction"],["Eq"],["LinearEquiv","instEquivLike"],["Module","End"],["CommSemiring","toSemiring"],["LinearMap","module"],["LinearEquiv","toLinearMap"],["LinearEquiv","symm"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["LinearEquiv","conj"],["RingHomInvPair"]],"valueReferences":[["rfl"],["smulCommClass_self"],["Module","End"],["CommMonoid","toMonoid"],["CommSemiring","toSemiring"],["LinearMap","module"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["LinearEquiv","symm"],["DFunLike","coe"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["LinearEquiv","conj"],["Module","toDistribMulAction"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["EquivLike","toFunLike"],["DistribMulAction","toMulAction"],["LinearEquiv","instEquivLike"]]},{"isProp":true,"kind":"theorem","name":["Units","symm_mulRightLinearEquiv"],"typeFallback":"forall {R : Type.{u_9}} {A : Type.{u_10}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3826591869._hygCtx._hyg.12 : Semiring.{u_9} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3826591869._hygCtx._hyg.15 : Semiring.{u_10} A] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3826591869._hygCtx._hyg.18 : Module.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3826591869._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3826591869._hygCtx._hyg.15)))] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3826591869._hygCtx._hyg.22 : IsScalarTower.{u_9, u_10, u_10} R A A (SMulZeroClass.toSMul.{u_9, u_10} R A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3826591869._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_9, u_10} R A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3826591869._hygCtx._hyg.15))))) (DistribMulAction.toDistribSMul.{u_9, u_10} R A (MonoidWithZero.toMonoid.{u_9} R (Semiring.toMonoidWithZero.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3826591869._hygCtx._hyg.12)) (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3826591869._hygCtx._hyg.15)))) (Module.toDistribMulAction.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3826591869._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3826591869._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3826591869._hygCtx._hyg.18)))) (SMulZeroClass.toSMul.{u_10, u_10} A A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3826591869._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_10, u_10} A A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3826591869._hygCtx._hyg.15))))) (instDistribSMul.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3826591869._hygCtx._hyg.15))))) (SMulZeroClass.toSMul.{u_9, u_10} R A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3826591869._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_9, u_10} R A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3826591869._hygCtx._hyg.15))))) 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.3826591869._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3826591869._hygCtx._hyg.15 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3826591869._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3826591869._hygCtx._hyg.22 (Inv.inv.{u_10} (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3826591869._hygCtx._hyg.15))) (Units.instInv.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3826591869._hygCtx._hyg.15))) a))","typeFull":"∀ {R : Type u_9} {A : Type u_10} [inst : Semiring R] [inst_1 : Semiring A] [inst_2 : Module R A]\n  [inst_3 : IsScalarTower R A A] (a : Aˣ), (Units.mulRightLinearEquiv R a).symm = Units.mulRightLinearEquiv R a⁻¹","typeReadable":"∀ {R : Type u_9} {A : Type u_10} [inst : Semiring R] [inst_1 : Semiring A] [inst_2 : Module R A]\n  [inst_3 : IsScalarTower R A A] (a : Aˣ), (Units.mulRightLinearEquiv R a).symm = Units.mulRightLinearEquiv R a⁻¹","typeReferences":[["IsScalarTower"],["Module"],["Units","instInv"],["SMulZeroClass","toSMul"],["AddMonoidWithOne","toAddMonoid"],["instDistribSMul"],["LinearEquiv"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Eq"],["NonAssocSemiring","toAddCommMonoidWithOne"],["Units"],["DistribSMul","toSMulZeroClass"],["Inv","inv"],["Units","mulRightLinearEquiv"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["LinearEquiv","symm"],["Module","toDistribMulAction"],["RingHomInvPair","ids"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["rfl"],["Units","mulRightLinearEquiv"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["RingHomInvPair","ids"],["LinearEquiv"],["LinearEquiv","symm"]]},{"isProp":true,"kind":"theorem","name":["addMonoidHomLequivInt","_proof_4"],"typeFallback":"forall 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M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f)) (Inv.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.symm.{u_1, u_1, u_2, u_2} R R M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) f)) (npowRec.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (One.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.refl.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25)) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f))) (Int.negSucc n) a) (LinearEquiv.symm.{u_1, u_1, u_2, u_2} R R M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (zpowRec.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (One.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.refl.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25)) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f)) (Inv.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.symm.{u_1, u_1, u_2, u_2} R R M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) f)) (npowRec.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (One.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.refl.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25)) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f))) (Nat.cast.{0} Int instNatCastInt (Nat.succ n)) a))","typeFull":"∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (n : ℕ)\n  (a : M ≃ₗ[R] M), zpowRec npowRec (Int.negSucc n) a = (zpowRec npowRec (↑n.succ) a).symm","typeReadable":"∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (n : ℕ)\n  (a : M ≃ₗ[R] M), zpowRec npowRec (Int.negSucc n) a = (zpowRec npowRec (↑n.succ) a).symm","typeReferences":[["Mul","mk"],["Nat","cast"],["RingHomCompTriple","ids"],["Module"],["Inv","mk"],["Int","negSucc"],["One","mk"],["LinearEquiv"],["LinearEquiv","symm"],["zpowRec"],["Int"],["LinearEquiv","trans"],["npowRec"],["AddCommMonoid"],["Nat"],["Semiring","toNonAssocSemiring"],["Nat","succ"],["RingHom","id"],["RingHomInvPair","ids"],["Eq"],["instNatCastInt"],["Semiring"],["LinearEquiv","refl"]],"valueReferences":[["Mul","mk"],["RingHomCompTriple","ids"],["Inv","mk"],["Int","negSucc"],["One","mk"],["LinearEquiv"],["zpowRec"],["LinearEquiv","symm"],["LinearEquiv","trans"],["npowRec"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Eq","refl"],["RingHomInvPair","ids"],["LinearEquiv","refl"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","arrowCongr","_proof_3"],"typeFallback":"forall {R₁ : Type.{u_1}} {R₂ : Type.{u_7}} {R₁' : Type.{u_2}} {R₂' : Type.{u_8}} {M₁ : Type.{u_3}} {M₂ : Type.{u_6}} {M₁' : Type.{u_4}} {M₂' : Type.{u_5}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 : Semiring.{u_1} R₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 : Semiring.{u_7} R₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59 : CommSemiring.{u_2} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62 : CommSemiring.{u_8} R₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 : AddCommMonoid.{u_3} M₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 : AddCommMonoid.{u_6} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 : AddCommMonoid.{u_4} M₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 : AddCommMonoid.{u_5} M₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 : Module.{u_1, u_3} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 : Module.{u_7, u_6} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 : Module.{u_2, u_4} R₁' M₁' (CommSemiring.toSemiring.{u_2} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 : Module.{u_8, u_5} R₂' M₂' (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86] {σ₁₂ : RingHom.{u_1, u_7} R₁ R₂ (Semiring.toNonAssocSemiring.{u_1} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_7} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53)} {σ₂₁ : RingHom.{u_7, u_1} R₂ R₁ (Semiring.toNonAssocSemiring.{u_7} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53) (Semiring.toNonAssocSemiring.{u_1} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50)} {σ₁'₂' : RingHom.{u_2, u_8} R₁' R₂' (Semiring.toNonAssocSemiring.{u_2} R₁' (CommSemiring.toSemiring.{u_2} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59)) (Semiring.toNonAssocSemiring.{u_8} R₂' (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62))} {σ₂'₁' : RingHom.{u_8, u_2} R₂' R₁' (Semiring.toNonAssocSemiring.{u_8} R₂' (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62)) (Semiring.toNonAssocSemiring.{u_2} R₁' (CommSemiring.toSemiring.{u_2} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59))} {σ₁₁' : RingHom.{u_1, u_2} R₁ R₁' (Semiring.toNonAssocSemiring.{u_1} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_2} R₁' (CommSemiring.toSemiring.{u_2} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59))} {σ₂₂' : RingHom.{u_7, u_8} R₂ R₂' (Semiring.toNonAssocSemiring.{u_7} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53) (Semiring.toNonAssocSemiring.{u_8} R₂' (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62))} {σ₂₁' : RingHom.{u_7, u_2} R₂ R₁' (Semiring.toNonAssocSemiring.{u_7} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53) (Semiring.toNonAssocSemiring.{u_2} R₁' (CommSemiring.toSemiring.{u_2} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59))} {σ₁₂' : RingHom.{u_1, u_8} R₁ R₂' (Semiring.toNonAssocSemiring.{u_1} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_8} R₂' (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62))} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.285 : RingHomInvPair.{u_1, u_7} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 σ₁₂ σ₂₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.289 : RingHomInvPair.{u_7, u_1} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 σ₂₁ σ₁₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.293 : RingHomInvPair.{u_2, u_8} R₁' R₂' (CommSemiring.toSemiring.{u_2} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₁'₂' σ₂'₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.297 : RingHomInvPair.{u_8, u_2} R₂' R₁' (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_2} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₂'₁' σ₁'₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.351 : RingHomCompTriple.{u_1, u_2, u_8} R₁ R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_2} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₁₁' σ₁'₂' σ₁₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.356 : RingHomCompTriple.{u_7, u_1, u_8} R₂ R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₁ σ₁₂' σ₂₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.361 : RingHomCompTriple.{u_7, u_8, u_2} R₂ R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_2} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₂₂' σ₂'₁' σ₂₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.366 : RingHomCompTriple.{u_1, u_7, u_2} R₁ R₂ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_2} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₂ σ₂₁' σ₁₁'] (e₁ : LinearEquiv.{u_1, u_7, u_3, u_6} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.285 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.289 M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102) (e₂ : LinearEquiv.{u_2, u_8, u_4, u_5} R₁' R₂' (CommSemiring.toSemiring.{u_2} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.297 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (x : LinearMap.{u_1, u_2, u_3, u_4} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_2} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (y : LinearMap.{u_1, u_2, u_3, u_4} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_2} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110), Eq.{succ (max u_5 u_6)} (LinearMap.{u_7, u_8, u_6, u_5} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (Equiv.toFun.{succ (max u_4 u_3), succ (max u_5 u_6)} (LinearMap.{u_1, u_2, u_3, u_4} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_2} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (LinearMap.{u_7, u_8, u_6, u_5} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (AddEquiv.toEquiv.{max u_4 u_3, max u_5 u_6} (LinearMap.{u_1, u_2, u_3, u_4} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_2} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (LinearMap.{u_7, u_8, u_6, u_5} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (LinearMap.instAdd.{u_1, u_2, u_3, u_4} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_2} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 σ₁₁') (LinearMap.instAdd.{u_7, u_8, u_6, u_5} R₂ R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 σ₂₂') (LinearEquiv.arrowCongrAddEquiv.{u_1, u_7, u_2, u_8, u_3, u_6, u_4, u_5} R₁ R₂ R₁' R₂' M₁ M₂ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_2} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 σ₁₂ σ₂₁ σ₁'₂' σ₂'₁' σ₁₁' σ₂₂' σ₂₁' σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.285 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.289 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.297 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.351 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.356 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.361 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.366 e₁ e₂)) (HAdd.hAdd.{max u_4 u_3, max u_4 u_3, max u_4 u_3} (LinearMap.{u_1, u_2, u_3, u_4} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_2} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (LinearMap.{u_1, u_2, u_3, u_4} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_2} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (LinearMap.{u_1, u_2, u_3, u_4} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_2} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (instHAdd.{max u_4 u_3} (LinearMap.{u_1, u_2, u_3, u_4} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_2} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (LinearMap.instAdd.{u_1, u_2, u_3, u_4} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_2} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 σ₁₁')) x y)) (HAdd.hAdd.{max u_5 u_6, max u_5 u_6, max u_5 u_6} (LinearMap.{u_7, u_8, u_6, u_5} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (LinearMap.{u_7, u_8, u_6, u_5} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (LinearMap.{u_7, u_8, u_6, u_5} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (instHAdd.{max u_5 u_6} (LinearMap.{u_7, u_8, u_6, u_5} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (LinearMap.instAdd.{u_7, u_8, u_6, u_5} R₂ R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 σ₂₂')) (Equiv.toFun.{succ (max u_4 u_3), succ (max u_5 u_6)} (LinearMap.{u_1, u_2, u_3, u_4} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_2} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (LinearMap.{u_7, u_8, u_6, u_5} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (AddEquiv.toEquiv.{max u_4 u_3, max u_5 u_6} (LinearMap.{u_1, u_2, u_3, u_4} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_2} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (LinearMap.{u_7, u_8, u_6, u_5} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (LinearMap.instAdd.{u_1, u_2, u_3, u_4} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_2} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 σ₁₁') (LinearMap.instAdd.{u_7, u_8, u_6, u_5} R₂ R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 σ₂₂') (LinearEquiv.arrowCongrAddEquiv.{u_1, u_7, u_2, u_8, u_3, u_6, u_4, u_5} R₁ R₂ R₁' R₂' M₁ M₂ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_2} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_8} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 σ₁₂ σ₂₁ σ₁'₂' σ₂'₁' σ₁₁' σ₂₂' σ₂₁' σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.285 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.289 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.297 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.351 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.356 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.361 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.366 e₁ e₂)) x) (Equiv.toFun.{succ (max u_4 u_3), succ (max u_5 u_6)} (LinearMap.{u_1, u_2, u_3, u_4} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_2} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) 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{R : Type.{u_1}} {R₂ : Type.{u_2}} {M : Type.{u_5}} {M₂ : Type.{u_7}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.13 : Semiring.{u_2} R₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.16 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.19 : AddCommMonoid.{u_7} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.22 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.26 : Module.{u_2, u_7} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.19] {σ₁₂ : RingHom.{u_1, u_2} R R₂ (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.10) (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.13)} {σ₂₁ : RingHom.{u_2, u_1} R₂ R (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.13) (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.10)} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.40 : RingHomInvPair.{u_1, u_2} R R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.13 σ₁₂ σ₂₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.44 : RingHomInvPair.{u_2, u_1} R₂ R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.10 σ₂₁ σ₁₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.48 : Subsingleton.{succ u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.51 : Subsingleton.{succ u_7} M₂] (x : M), Eq.{succ u_7} M₂ (DFunLike.coe.{max (succ u_5) (succ u_7), succ u_5, succ u_7} (LinearEquiv.{u_1, u_2, u_5, u_7} R R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.13 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.40 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.44 M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.26) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M₂) (EquivLike.toFunLike.{max (succ u_5) (succ u_7), succ u_5, succ u_7} (LinearEquiv.{u_1, u_2, u_5, u_7} R R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.13 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.40 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.44 M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.26) M M₂ (LinearEquiv.instEquivLike.{u_1, u_2, u_5, u_7} R R₂ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.26 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.40 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.44)) (OfNat.ofNat.{max u_5 u_7} (LinearEquiv.{u_1, u_2, u_5, u_7} R R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.13 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.40 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.44 M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.26) 0 (Zero.toOfNat0.{max u_5 u_7} (LinearEquiv.{u_1, u_2, u_5, u_7} R R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.13 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.40 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.44 M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.26) (LinearEquiv.instZero.{u_1, u_2, u_5, u_7} R R₂ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.26 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.40 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.44 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.48 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.51))) x) (OfNat.ofNat.{u_7} M₂ 0 (Zero.toOfNat0.{u_7} M₂ (AddZero.toZero.{u_7} M₂ (AddZeroClass.toAddZero.{u_7} M₂ (AddMonoid.toAddZeroClass.{u_7} M₂ (AddCommMonoid.toAddMonoid.{u_7} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2732899462._hygCtx._hyg.19))))))","typeFull":"∀ {R : Type u_1} {R₂ : Type u_2} {M : Type u_5} {M₂ : Type u_7} [inst : Semiring R] [inst_1 : Semiring R₂]\n  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R₂ M₂] {σ₁₂ : R →+* R₂}\n  {σ₂₁ : R₂ →+* R} [inst_6 : RingHomInvPair σ₁₂ σ₂₁] [inst_7 : RingHomInvPair σ₂₁ σ₁₂] [inst_8 : Subsingleton M]\n  [inst_9 : Subsingleton M₂] (x : M), 0 x = 0","typeReadable":"∀ {R : Type u_1} {R₂ : Type u_2} {M : Type u_5} {M₂ : Type u_7} [inst : Semiring R] [inst_1 : Semiring R₂]\n  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R₂ M₂] {σ₁₂ : R →+* R₂}\n  {σ₂₁ : R₂ →+* R} [inst_6 : RingHomInvPair σ₁₂ σ₂₁] [inst_7 : RingHomInvPair σ₂₁ σ₁₂] [inst_8 : Subsingleton M]\n  [inst_9 : Subsingleton M₂] (x : M), 0 x = 0","typeReferences":[["RingHom"],["Module"],["LinearEquiv","instZero"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["LinearEquiv"],["DFunLike","coe"],["OfNat","ofNat"],["AddCommMonoid"],["Subsingleton"],["Semiring","toNonAssocSemiring"],["EquivLike","toFunLike"],["Zero","toOfNat0"],["RingHomInvPair"],["Eq"],["LinearEquiv","instEquivLike"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["rfl"],["LinearEquiv","instZero"],["EquivLike","toFunLike"],["Zero","toOfNat0"],["LinearEquiv","instEquivLike"],["LinearEquiv"],["DFunLike","coe"],["OfNat","ofNat"]]},{"isProp":true,"kind":"theorem","name":["AddEquiv","toLinearEquiv","_proof_1"],"typeFallback":"forall {M : Type.{u_2}} {M₂ : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555652._hygCtx._hyg.13 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555652._hygCtx._hyg.16 : AddCommMonoid.{u_1} M₂] (e : AddEquiv.{u_2, u_1} M M₂ (AddCommMagma.toAdd.{u_2} M 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y","typeReferences":[["HAdd","hAdd"],["AddCommMonoid"],["AddCommMonoid","toAddCommSemigroup"],["instHAdd"],["Equiv","toFun"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["AddEquiv","toEquiv"],["Eq"],["AddEquiv"]],"valueReferences":[["AddCommMonoid","toAddCommSemigroup"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["AddEquiv","map_add'"]]},{"isProp":true,"kind":"theorem","name":["Units","mulLeftLinearEquiv","_proof_3"],"typeFallback":"forall (R : Type.{u_2}) (A : Type.{u_1}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 : Semiring.{u_2} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15 : Semiring.{u_1} A] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 : Module.{u_2, u_1} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A 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R (Semiring.toMonoidWithZero.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (AddMonoidWithOne.toAddMonoid.{u_1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))) (Module.toDistribMulAction.{u_2, u_1} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18)))) (SMulZeroClass.toSMul.{u_1, u_1} A A (AddZero.toZero.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddMonoidWithOne.toAddMonoid.{u_1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_1, u_1} A A (AddMonoid.toAddZeroClass.{u_1} A (AddMonoidWithOne.toAddMonoid.{u_1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))))) (instDistribSMul.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))))] (x._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.73 : Units.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (x._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.75 : Units.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))), Eq.{succ u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18) (let __spread.0._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.55 : Equiv.Perm.{succ u_1} A := Units.mulLeft.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)) (HMul.hMul.{u_1, u_1, u_1} (Units.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (Units.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (Units.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (instHMul.{u_1} (Units.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (MulOne.toMul.{u_1} (Units.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (MulOneClass.toMulOne.{u_1} (Units.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (Units.instMulOneClass.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))))) x._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.73 x._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.75); let __spread.1._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.55 : LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 := LinearMap.mulLeft.{u_2, u_1} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.22 (Units.val.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)) (HMul.hMul.{u_1, u_1, u_1} (Units.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (Units.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (Units.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (instHMul.{u_1} (Units.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (MulOne.toMul.{u_1} (Units.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (MulOneClass.toMulOne.{u_1} (Units.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (Units.instMulOneClass.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))))) x._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.73 x._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.75)); LinearEquiv.mk.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 (LinearMap.mk.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 (AddHom.mk.{u_1, u_1} A A (AddCommMagma.toAdd.{u_1} A (AddCommSemigroup.toAddCommMagma.{u_1} A (AddCommMonoid.toAddCommSemigroup.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))))) (AddCommMagma.toAdd.{u_1} A (AddCommSemigroup.toAddCommMagma.{u_1} A (AddCommMonoid.toAddCommSemigroup.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))))) (Equiv.toFun.{succ u_1, succ u_1} A A __spread.0._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.55) (AddHom.map_add'.{u_1, u_1} A A (AddCommMagma.toAdd.{u_1} A (AddCommSemigroup.toAddCommMagma.{u_1} A (AddCommMonoid.toAddCommSemigroup.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))))) (AddCommMagma.toAdd.{u_1} A (AddCommSemigroup.toAddCommMagma.{u_1} A (AddCommMonoid.toAddCommSemigroup.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))))) (LinearMap.toAddHom.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 __spread.1._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.55))) (LinearMap.map_smul'.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 __spread.1._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.55)) (Equiv.invFun.{succ u_1, succ u_1} A A __spread.0._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.55) (Equiv.left_inv.{succ u_1, succ u_1} A A __spread.0._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.55) (Equiv.right_inv.{succ u_1, succ u_1} A A __spread.0._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.55)) (HMul.hMul.{u_1, u_1, u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18) (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18) (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18) (instHMul.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18) (MulOne.toMul.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18) (MulOneClass.toMulOne.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18) (Monoid.toMulOneClass.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18) (DivInvMonoid.toMonoid.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18) (Group.toDivInvMonoid.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18) (LinearEquiv.automorphismGroup.{u_2, u_1} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18))))))) (let __spread.0._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.55 : Equiv.Perm.{succ u_1} A := Units.mulLeft.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)) x._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.73; let __spread.1._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.55 : LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 := LinearMap.mulLeft.{u_2, u_1} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.22 (Units.val.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)) x._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.73); LinearEquiv.mk.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 (LinearMap.mk.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 (AddHom.mk.{u_1, u_1} A A (AddCommMagma.toAdd.{u_1} A (AddCommSemigroup.toAddCommMagma.{u_1} A (AddCommMonoid.toAddCommSemigroup.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))))) (AddCommMagma.toAdd.{u_1} A (AddCommSemigroup.toAddCommMagma.{u_1} A (AddCommMonoid.toAddCommSemigroup.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))))) (Equiv.toFun.{succ u_1, succ u_1} A A __spread.0._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.55) (AddHom.map_add'.{u_1, u_1} A A (AddCommMagma.toAdd.{u_1} A (AddCommSemigroup.toAddCommMagma.{u_1} A (AddCommMonoid.toAddCommSemigroup.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))))) (AddCommMagma.toAdd.{u_1} A (AddCommSemigroup.toAddCommMagma.{u_1} A (AddCommMonoid.toAddCommSemigroup.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))))) (LinearMap.toAddHom.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 __spread.1._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.55))) (LinearMap.map_smul'.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 __spread.1._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.55)) (Equiv.invFun.{succ u_1, succ u_1} A A __spread.0._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.55) (Equiv.left_inv.{succ u_1, succ u_1} A A __spread.0._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.55) (Equiv.right_inv.{succ u_1, succ u_1} A A __spread.0._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.55)) (let __spread.0._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.55 : Equiv.Perm.{succ u_1} A := Units.mulLeft.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)) x._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.75; let __spread.1._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.55 : LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 := LinearMap.mulLeft.{u_2, u_1} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.22 (Units.val.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)) x._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.75); LinearEquiv.mk.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 (LinearMap.mk.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 (AddHom.mk.{u_1, u_1} A A (AddCommMagma.toAdd.{u_1} A (AddCommSemigroup.toAddCommMagma.{u_1} A (AddCommMonoid.toAddCommSemigroup.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))))) (AddCommMagma.toAdd.{u_1} A (AddCommSemigroup.toAddCommMagma.{u_1} A (AddCommMonoid.toAddCommSemigroup.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))))) (Equiv.toFun.{succ u_1, succ u_1} A A __spread.0._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.55) (AddHom.map_add'.{u_1, u_1} A A (AddCommMagma.toAdd.{u_1} A (AddCommSemigroup.toAddCommMagma.{u_1} A (AddCommMonoid.toAddCommSemigroup.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))))) (AddCommMagma.toAdd.{u_1} A (AddCommSemigroup.toAddCommMagma.{u_1} A (AddCommMonoid.toAddCommSemigroup.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))))) (LinearMap.toAddHom.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 __spread.1._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.55))) (LinearMap.map_smul'.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 __spread.1._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.55)) (Equiv.invFun.{succ u_1, succ u_1} A A __spread.0._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.55) (Equiv.left_inv.{succ u_1, succ u_1} A A __spread.0._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.55) (Equiv.right_inv.{succ u_1, succ u_1} A A __spread.0._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.55)))","typeFull":"∀ (R : Type u_2) (A : Type u_1) [inst : Semiring R] [inst_1 : Semiring A] [inst_2 : Module R A]\n  [inst_3 : SMulCommClass R A A] (x x_1 : Aˣ),\n  (let __spread.0 := (x * x_1).mulLeft;\n    let __spread.1 := LinearMap.mulLeft R ↑(x * x_1);\n    { toFun := __spread.0.toFun, map_add' := ⋯, map_smul' := ⋯, invFun := __spread.0.invFun, left_inv := ⋯,\n      right_inv := ⋯ }) =\n    (let __spread.0 := x.mulLeft;\n      let __spread.1 := LinearMap.mulLeft R ↑x;\n      { toFun := __spread.0.toFun, map_add' := ⋯, map_smul' := ⋯, invFun := __spread.0.invFun, left_inv := ⋯,\n        right_inv := ⋯ }) *\n      let __spread.0 := x_1.mulLeft;\n      let __spread.1 := LinearMap.mulLeft R ↑x_1;\n      { toFun := __spread.0.toFun, map_add' := ⋯, map_smul' := ⋯, invFun := __spread.0.invFun, left_inv := ⋯,\n        right_inv := ⋯ }","typeReadable":"∀ (R : Type u_2) (A : Type u_1) [inst : Semiring R] [inst_1 : Semiring A] [inst_2 : Module R A]\n  [inst_3 : SMulCommClass R A A] (x x_1 : Aˣ),\n  (let __spread.0 := (x * x_1).mulLeft;\n    let __spread.1 := LinearMap.mulLeft R ↑(x * x_1);\n    { toFun := __spread.0.toFun, map_add' := ⋯, map_smul' := ⋯, invFun := __spread.0.invFun, left_inv := ⋯,\n      right_inv := ⋯ }) =\n    (let __spread.0 := x.mulLeft;\n      let __spread.1 := LinearMap.mulLeft R ↑x;\n      { toFun := __spread.0.toFun, map_add' := ⋯, map_smul' := ⋯, invFun := __spread.0.invFun, left_inv := ⋯,\n        right_inv := ⋯ }) *\n      let __spread.0 := x_1.mulLeft;\n      let __spread.1 := LinearMap.mulLeft R ↑x_1;\n      { toFun := __spread.0.toFun, map_add' := ⋯, map_smul' := ⋯, invFun := __spread.0.invFun, left_inv := ⋯,\n        right_inv := ⋯ }","typeReferences":[["Equiv","left_inv"],["AddHom","mk"],["HMul","hMul"],["LinearMap","toAddHom"],["SMulZeroClass","toSMul"],["Units","mulLeft"],["instDistribSMul"],["AddMonoidWithOne","toAddMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Equiv","right_inv"],["LinearEquiv","mk"],["Equiv","toFun"],["LinearMap","map_smul'"],["NonAssocSemiring","toAddCommMonoidWithOne"],["Group","toDivInvMonoid"],["Units"],["DistribSMul","toSMulZeroClass"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["DistribMulAction","toDistribSMul"],["Units","instMulOneClass"],["AddZeroClass","toAddZero"],["DivInvMonoid","toMonoid"],["Units","val"],["RingHomInvPair","ids"],["instHMul"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["MulOneClass","toMulOne"],["Module"],["LinearMap","mk"],["LinearEquiv"],["LinearEquiv","automorphismGroup"],["MulOne","toMul"],["MonoidWithZero","toMonoid"],["Monoid","toMulOneClass"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Eq"],["LinearMap","mulLeft"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["Semiring","toMonoidWithZero"],["SMulCommClass"],["Module","toDistribMulAction"],["AddHom","map_add'"],["AddCommMonoid","toAddCommSemigroup"],["Equiv","invFun"],["Semiring"]],"valueReferences":[["DivInvMonoid","toInv"],["RingHom"],["Equiv","left_inv"],["Eq","trans"],["AddHom","mk"],["HMul","hMul"],["LinearMap","toAddHom"],["NonUnitalSemiring","toSemigroupWithZero"],["SMulZeroClass","toSMul"],["Units","mulLeft"],["Equiv"],["DivisionMonoid","toDivInvMonoid"],["LinearEquiv","ext"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Equiv","right_inv"],["funext"],["LinearEquiv","mk"],["AddHom","toFun"],["Equiv","toFun"],["Eq","ndrec"],["LinearMap","map_smul'"],["Group","toDivInvMonoid"],["Semiring","toNonUnitalSemiring"],["Units"],["DistribSMul","toSMulZeroClass"],["Group","toDivisionMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["DistribMulAction","toDistribSMul"],["Units","instMulOneClass"],["LinearMap"],["AddZeroClass","toAddZero"],["Function","RightInverse"],["LinearEquiv","mk","congr_simp"],["DivInvMonoid","toMonoid"],["Units","val"],["Eq","refl"],["HSMul","hSMul"],["id"],["Function","LeftInverse"],["RingHomInvPair","ids"],["instHMul"],["AddHom"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Units","mulLeft_symm"],["MulOneClass","toMulOne"],["Equiv","instEquivLike"],["Units","instGroup"],["LinearMap","mk"],["Units","instInv"],["RingHom","instFunLike"],["mul_assoc"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["DFunLike","coe"],["Semigroup","toMul"],["congrArg"],["LinearEquiv","automorphismGroup"],["MulOne","toMul"],["congr"],["MonoidWithZero","toMonoid"],["Monoid","toMulOneClass"],["EquivLike","toFunLike"],["Equiv","symm"],["instHSMul"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["congrFun'"],["LinearMap","mulLeft"],["Eq"],["LinearEquiv","instEquivLike"],["mul_inv_rev"],["Inv","inv"],["True"],["instHAdd"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["Semiring","toMonoidWithZero"],["AddHom","mk","congr_simp"],["Equiv","Perm"],["HAdd","hAdd"],["eq_self"],["Module","toDistribMulAction"],["AddHom","map_add'"],["AddCommMonoid","toAddCommSemigroup"],["of_eq_true"],["Equiv","invFun"],["LinearMap","mk","congr_simp"],["SemigroupWithZero","toSemigroup"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","applyDistribMulAction","_proof_4"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 : Module.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19] (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) (x : M) (y : M), Eq.{succ u_2} M (DFunLike.coe.{succ u_2, succ u_2, succ u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (EquivLike.toFunLike.{succ u_2, succ u_2, succ u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10))) f x) (DFunLike.coe.{succ u_2, succ u_2, succ u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10))) f y))","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  (x y : M), f (x + y) = f x + f y","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  (x y : M), f (x + y) = f x + f y","typeReferences":[["Module"],["instHAdd"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["DFunLike","coe"],["HAdd","hAdd"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["AddMonoid","toAddSemigroup"],["EquivLike","toFunLike"],["RingHomInvPair","ids"],["Eq"],["LinearEquiv","instEquivLike"],["AddSemigroup","toAdd"],["Semiring"]],"valueReferences":[["SemilinearMapClass","toAddHomClass"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["map_add"],["SemilinearEquivClass","instSemilinearMapClass"],["LinearEquiv","instSemilinearEquivClass"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["AddMonoid","toAddSemigroup"],["EquivLike","toFunLike"],["RingHomInvPair","ids"],["LinearEquiv","instEquivLike"],["AddSemigroup","toAdd"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","funLeft","_proof_2"],"typeFallback":"forall (R : Type.{u_4}) (M : Type.{u_1}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2931425069._hygCtx._hyg.10 : Semiring.{u_4} R] 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(Pi.addCommMonoid.{u_3, u_1} n (fun (a._@._internal._hyg.0 : n) => M) (fun (i : n) => inst._@.Mathlib.Algebra.Module.Equiv.Basic.2931425069._hygCtx._hyg.13)) (Pi.Function.module.{u_3, u_4, u_1} n R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2931425069._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2931425069._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2931425069._hygCtx._hyg.16)))))) x._@.Mathlib.Algebra.Module.Equiv.Basic.2931425069._hygCtx._hyg.68 x._@.Mathlib.Algebra.Module.Equiv.Basic.2931425069._hygCtx._hyg.70) f)","typeFull":"∀ (R : Type u_4) (M : Type u_1) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {m : Type u_2}\n  {n : Type u_3} (f : m → n) (x : R) (x_1 : n → M), (x • x_1) ∘ f = (x • x_1) ∘ f","typeReadable":"∀ (R : Type u_4) (M : Type u_1) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {m : Type u_2}\n  {n : Type u_3} (f : m → n) (x : R) (x_1 : n → M), (x • x_1) ∘ f = (x • x_1) ∘ f","typeReferences":[["Module"],["Pi","addCommMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["SMulZeroClass","toSMul"],["Function","comp"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["Pi","Function","module"],["Module","toDistribMulAction"],["AddCommMonoid"],["MonoidWithZero","toMonoid"],["HSMul","hSMul"],["instHSMul"],["Eq"],["AddZero","toZero"],["DistribSMul","toSMulZeroClass"],["Semiring"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["rfl"],["Pi","addCommMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["SMulZeroClass","toSMul"],["Function","comp"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["Pi","Function","module"],["Module","toDistribMulAction"],["HSMul","hSMul"],["MonoidWithZero","toMonoid"],["instHSMul"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["DistribSMul","toSMulZeroClass"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","coe_pow"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_5}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.19 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.25 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.19] (e : LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.25) (n : Nat), Eq.{succ u_5} (M -> M) (DFunLike.coe.{succ u_5, succ u_5, succ u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.25) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (EquivLike.toFunLike.{succ u_5, succ u_5, succ u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.25) M M (LinearEquiv.instEquivLike.{u_1, u_1, u_5, u_5} R R M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10))) (HPow.hPow.{u_5, 0, u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.25) Nat (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.25) (instHPow.{u_5, 0} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.25) Nat (Monoid.toPow.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.25) (DivInvMonoid.toMonoid.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.25) (Group.toDivInvMonoid.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.25) (LinearEquiv.automorphismGroup.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.25))))) e n)) (Nat.iterate.{succ u_5} M (DFunLike.coe.{succ u_5, succ u_5, succ u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.25) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (EquivLike.toFunLike.{succ u_5, succ u_5, succ u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.25) M M (LinearEquiv.instEquivLike.{u_1, u_1, u_5, u_5} R R M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1047833717._hygCtx._hyg.10))) e) n)","typeFull":"∀ {R : Type u_1} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (e : M ≃ₗ[R] M)\n  (n : ℕ), ⇑(e ^ n) = (⇑e)^[n]","typeReadable":"∀ {R : Type u_1} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (e : M ≃ₗ[R] M)\n  (n : ℕ), ⇑(e ^ n) = (⇑e)^[n]","typeReferences":[["instHPow"],["Module"],["LinearEquiv"],["HPow","hPow"],["DFunLike","coe"],["LinearEquiv","automorphismGroup"],["AddCommMonoid"],["Nat"],["Nat","iterate"],["Semiring","toNonAssocSemiring"],["DivInvMonoid","toMonoid"],["Monoid","toPow"],["RingHom","id"],["EquivLike","toFunLike"],["RingHomInvPair","ids"],["Eq"],["LinearEquiv","instEquivLike"],["Group","toDivInvMonoid"],["Semiring"]],"valueReferences":[["MulOneClass","toMulOne"],["rfl"],["MulOne","toOne"],["HMul","hMul"],["LinearEquiv"],["DFunLike","coe"],["OfNat","ofNat"],["LinearEquiv","automorphismGroup"],["MulOne","toMul"],["Semiring","toNonAssocSemiring"],["One","toOfNat1"],["DivInvMonoid","toMonoid"],["RingHom","id"],["Monoid","toMulOneClass"],["EquivLike","toFunLike"],["hom_coe_pow"],["RingHomInvPair","ids"],["instHMul"],["LinearEquiv","instEquivLike"],["Group","toDivInvMonoid"]]},{"isProp":true,"kind":"theorem","name":["Units","mulRightLinearEquiv_apply"],"typeFallback":"forall (R : Type.{u_9}) {A : Type.{u_10}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.12 : Semiring.{u_9} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.15 : Semiring.{u_10} A] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.18 : Module.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.15)))] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.22 : IsScalarTower.{u_9, u_10, u_10} R A A (SMulZeroClass.toSMul.{u_9, u_10} R A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_9, u_10} R A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.15))))) (DistribMulAction.toDistribSMul.{u_9, u_10} R A (MonoidWithZero.toMonoid.{u_9} R (Semiring.toMonoidWithZero.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.12)) (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.15)))) (Module.toDistribMulAction.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.18)))) (SMulZeroClass.toSMul.{u_10, u_10} A A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_10, u_10} A A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.15))))) (instDistribSMul.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.15))))) (SMulZeroClass.toSMul.{u_9, u_10} R A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_9, u_10} R A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.15))))) (DistribMulAction.toDistribSMul.{u_9, u_10} R A (MonoidWithZero.toMonoid.{u_9} R (Semiring.toMonoidWithZero.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.12)) (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.15)))) (Module.toDistribMulAction.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.18))))] (a : Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.15))) (x : A), Eq.{succ u_10} A (DFunLike.coe.{succ u_10, succ u_10, succ u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.18) A (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : A) => A) (EquivLike.toFunLike.{succ u_10, succ u_10, succ u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.18) A A (LinearEquiv.instEquivLike.{u_9, u_9, u_10, u_10} R R A A inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.18 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.12))) (Units.mulRightLinearEquiv.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.15 inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.22 a) x) (HMul.hMul.{u_10, u_10, u_10} A A A (instHMul.{u_10} A (Distrib.toMul.{u_10} A (NonUnitalNonAssocSemiring.toDistrib.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.15))))) x (Units.val.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.187611938._hygCtx._hyg.15)) a))","typeFull":"∀ (R : Type u_9) {A : Type u_10} [inst : Semiring R] [inst_1 : Semiring A] [inst_2 : Module R A]\n  [inst_3 : IsScalarTower R A A] (a : Aˣ) (x : A), (Units.mulRightLinearEquiv R a) x = x * ↑a","typeReadable":"∀ (R : Type u_9) {A : Type u_10} [inst : Semiring R] [inst_1 : Semiring A] [inst_2 : Module R A]\n  [inst_3 : IsScalarTower R A A] (a : Aˣ) (x : A), (Units.mulRightLinearEquiv R a) x = x * ↑a","typeReferences":[["IsScalarTower"],["Module"],["HMul","hMul"],["SMulZeroClass","toSMul"],["AddMonoidWithOne","toAddMonoid"],["instDistribSMul"],["LinearEquiv"],["DFunLike","coe"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["EquivLike","toFunLike"],["MonoidWithZero","toMonoid"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["LinearEquiv","instEquivLike"],["Eq"],["NonAssocSemiring","toAddCommMonoidWithOne"],["Units"],["DistribSMul","toSMulZeroClass"],["Units","mulRightLinearEquiv"],["NonUnitalNonAssocSemiring","toDistrib"],["Distrib","toMul"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["Module","toDistribMulAction"],["Units","val"],["RingHomInvPair","ids"],["instHMul"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["rfl"],["Units","mulRightLinearEquiv"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["EquivLike","toFunLike"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["RingHomInvPair","ids"],["LinearEquiv","instEquivLike"],["LinearEquiv"],["DFunLike","coe"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","restrictScalars","_proof_2"],"typeFallback":"forall (R : Type.{u_3}) {S : Type.{u_4}} {M : Type.{u_2}} {M₂ : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10 : Semiring.{u_3} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 : Semiring.{u_4} S] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22 : AddCommMonoid.{u_1} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.25 : Module.{u_3, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.29 : Module.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.33 : Module.{u_4, u_2} S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.37 : Module.{u_4, u_1} S M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.41 : LinearMap.CompatibleSMul.{u_2, u_1, u_3, u_4} M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22 R S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 (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.Equiv.Basic.3287639652._hygCtx._hyg.19)))) (DistribSMul.toSMulZeroClass.{u_3, u_2} R M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19)) (DistribMulAction.toDistribSMul.{u_3, u_2} R M (MonoidWithZero.toMonoid.{u_3} R (Semiring.toMonoidWithZero.{u_3} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19) (Module.toDistribMulAction.{u_3, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.25)))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.33 (SMulZeroClass.toSMul.{u_3, 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.Equiv.Basic.3287639652._hygCtx._hyg.22)))) (DistribSMul.toSMulZeroClass.{u_3, u_1} R M₂ (AddMonoid.toAddZeroClass.{u_1} M₂ (AddCommMonoid.toAddMonoid.{u_1} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22)) (DistribMulAction.toDistribSMul.{u_3, u_1} R M₂ (MonoidWithZero.toMonoid.{u_3} R (Semiring.toMonoidWithZero.{u_3} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22) (Module.toDistribMulAction.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.29)))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.37] (f : LinearEquiv.{u_4, u_4, u_2, u_1} S S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 (RingHom.id.{u_4} S (Semiring.toNonAssocSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13)) (RingHom.id.{u_4} S (Semiring.toNonAssocSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13)) (RingHomInvPair.ids.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13) (RingHomInvPair.ids.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13) M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.37) (m : R) (x : M), Eq.{succ u_1} M₂ (AddHom.toFun.{u_2, u_1} M M₂ (AddCommMagma.toAdd.{u_2} M (AddCommSemigroup.toAddCommMagma.{u_2} M (AddCommMonoid.toAddCommSemigroup.{u_2} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19))) (AddCommMagma.toAdd.{u_1} M₂ (AddCommSemigroup.toAddCommMagma.{u_1} M₂ (AddCommMonoid.toAddCommSemigroup.{u_1} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22))) (LinearMap.toAddHom.{u_3, u_3, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.29 (LinearMap.restrictScalars.{u_3, u_4, u_2, u_1} R S M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10 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: CommSemiring R₁'] [inst_1 : CommSemiring R₂'] {σ₁'₂' : R₁' →+* R₂'},\n  RingHomCompTriple (RingHom.id R₁') σ₁'₂' σ₁'₂'","typeReferences":[["RingHom"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["CommSemiring","toSemiring"],["CommSemiring"],["RingHomCompTriple"]],"valueReferences":[["RingHomCompTriple","ids"],["CommSemiring","toSemiring"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","neg","_proof_1"],"typeFallback":"forall (R : Type.{u_2}) {M : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1717405508._hygCtx._hyg.10 : Semiring.{u_2} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1717405508._hygCtx._hyg.13 : AddCommGroup.{u_1} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1717405508._hygCtx._hyg.16 : Module.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1717405508._hygCtx._hyg.10 (AddCommGroup.toAddCommMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1717405508._hygCtx._hyg.13)] (x : M) (y : M), Eq.{succ u_1} M (AddHom.toFun.{u_1, u_1} 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(inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.25 x) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))) (fun (i : M) => LinearMap.addCommMonoid.{u_1, u_1, u_2, u_1} R R (V i) R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16 i) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.25 i) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R 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(CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.25) (Pi.Function.module.{u_3, u_1, u_1} M R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (LinearMap.{u_1, u_1, max u_3 u_2, max u_1 u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R 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}","typeReferences":[["LinearMap","instFunLike"],["Module"],["LinearMap","mk"],["Pi","addCommMonoid"],["CommSemiring"],["AddHom","mk"],["DFunLike","coe"],["Pi","module"],["Pi","Function","module"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["LinearMap","piApply","_proof_2"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Eq"],["Semiring","toModule"],["instHAdd"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["CommSemiring","toSemiring"],["LinearMap"],["HAdd","hAdd"],["LinearMap","addCommMonoid"],["AddCommMonoid","toAddCommSemigroup"],["LinearMap","piApply","_proof_1"]],"valueReferences":[["LinearMap","instFunLike"],["LinearMap","mk"],["AddHom","mk"],["Pi","addCommMonoid"],["DFunLike","coe"],["Pi","Function","module"],["Pi","module"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["LinearMap","ext"],["funext"],["LinearMap","piApply","_proof_2"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Eq"],["Semiring","toModule"],["instHAdd"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["CommSemiring","toSemiring"],["LinearMap"],["HAdd","hAdd"],["LinearMap","addCommMonoid"],["eq_self"],["AddCommMonoid","toAddCommSemigroup"],["of_eq_true"],["LinearMap","piApply","_proof_1"]]},{"isProp":true,"kind":"theorem","name":["Units","mulRightLinearEquiv","congr_simp"],"typeFallback":"forall (R : Type.{u_9}) {A : Type.{u_10}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12 : Semiring.{u_9} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15 : Semiring.{u_10} A] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.18 : Module.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15)))] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.22 : IsScalarTower.{u_9, u_10, u_10} R A A (SMulZeroClass.toSMul.{u_9, u_10} R A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_9, u_10} R A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))))) (DistribMulAction.toDistribSMul.{u_9, u_10} R A (MonoidWithZero.toMonoid.{u_9} R (Semiring.toMonoidWithZero.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12)) (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15)))) (Module.toDistribMulAction.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.18)))) (SMulZeroClass.toSMul.{u_10, u_10} A A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_10, u_10} A A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))))) (instDistribSMul.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))))) (SMulZeroClass.toSMul.{u_9, u_10} R A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_9, u_10} R A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))))) (DistribMulAction.toDistribSMul.{u_9, u_10} R A (MonoidWithZero.toMonoid.{u_9} R (Semiring.toMonoidWithZero.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12)) (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15)))) (Module.toDistribMulAction.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.18))))] (a : Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))) (a_1 : Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))), (Eq.{succ u_10} (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))) a a_1) -> (Eq.{succ u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.18) (Units.mulRightLinearEquiv.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15 inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.22 a) (Units.mulRightLinearEquiv.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15 inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.22 a_1))","typeFull":"∀ (R : Type u_9) {A : Type u_10} [inst : Semiring R] [inst_1 : Semiring A] [inst_2 : Module R A]\n  [inst_3 : IsScalarTower R A A] (a a_1 : Aˣ), a = a_1 → Units.mulRightLinearEquiv R a = Units.mulRightLinearEquiv R a_1","typeReadable":"∀ (R : Type u_9) {A : Type u_10} [inst : Semiring R] [inst_1 : Semiring A] [inst_2 : Module R A]\n  [inst_3 : IsScalarTower R A A] (a a_1 : Aˣ), a = a_1 → Units.mulRightLinearEquiv R a = Units.mulRightLinearEquiv R a_1","typeReferences":[["IsScalarTower"],["Module"],["SMulZeroClass","toSMul"],["AddMonoidWithOne","toAddMonoid"],["instDistribSMul"],["LinearEquiv"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Eq"],["NonAssocSemiring","toAddCommMonoidWithOne"],["Units"],["DistribSMul","toSMulZeroClass"],["Units","mulRightLinearEquiv"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["Module","toDistribMulAction"],["RingHomInvPair","ids"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["Units","mulRightLinearEquiv"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["Semiring","toMonoidWithZero"],["LinearEquiv"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Eq","refl"],["MonoidWithZero","toMonoid"],["RingHomInvPair","ids"],["Eq","rec"],["Eq"],["Units"]]},{"isProp":true,"kind":"theorem","name":["Units","mulLeftLinearEquiv","_proof_2"],"typeFallback":"forall (R : Type.{u_2}) (A : Type.{u_1}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 : Semiring.{u_2} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15 : Semiring.{u_1} A] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 : Module.{u_2, u_1} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.22 : SMulCommClass.{u_2, u_1, u_1} R A A (SMulZeroClass.toSMul.{u_2, u_1} R A (AddZero.toZero.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddMonoidWithOne.toAddMonoid.{u_1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_2, u_1} R A (AddMonoid.toAddZeroClass.{u_1} A (AddMonoidWithOne.toAddMonoid.{u_1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))))) (DistribMulAction.toDistribSMul.{u_2, u_1} R A (MonoidWithZero.toMonoid.{u_2} R (Semiring.toMonoidWithZero.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (AddMonoidWithOne.toAddMonoid.{u_1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))) (Module.toDistribMulAction.{u_2, u_1} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18)))) (SMulZeroClass.toSMul.{u_1, u_1} A A (AddZero.toZero.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddMonoidWithOne.toAddMonoid.{u_1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_1, u_1} A A (AddMonoid.toAddZeroClass.{u_1} A (AddMonoidWithOne.toAddMonoid.{u_1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))))) (instDistribSMul.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))))], Eq.{succ u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18) (let __spread.0._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.55 : Equiv.Perm.{succ u_1} A := Units.mulLeft.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)) (OfNat.ofNat.{u_1} (Units.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) 1 (One.toOfNat1.{u_1} (Units.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (MulOne.toOne.{u_1} (Units.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (MulOneClass.toMulOne.{u_1} (Units.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (Units.instMulOneClass.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))))))); let __spread.1._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.55 : LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 := LinearMap.mulLeft.{u_2, u_1} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.22 (Units.val.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)) (OfNat.ofNat.{u_1} (Units.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) 1 (One.toOfNat1.{u_1} (Units.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (MulOne.toOne.{u_1} (Units.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (MulOneClass.toMulOne.{u_1} (Units.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (Units.instMulOneClass.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))))))); LinearEquiv.mk.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 (LinearMap.mk.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 (AddHom.mk.{u_1, u_1} A A (AddCommMagma.toAdd.{u_1} A (AddCommSemigroup.toAddCommMagma.{u_1} A (AddCommMonoid.toAddCommSemigroup.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))))) (AddCommMagma.toAdd.{u_1} A (AddCommSemigroup.toAddCommMagma.{u_1} A (AddCommMonoid.toAddCommSemigroup.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))))) (Equiv.toFun.{succ u_1, succ u_1} A A __spread.0._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.55) (AddHom.map_add'.{u_1, u_1} A A (AddCommMagma.toAdd.{u_1} A (AddCommSemigroup.toAddCommMagma.{u_1} A (AddCommMonoid.toAddCommSemigroup.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))))) (AddCommMagma.toAdd.{u_1} A (AddCommSemigroup.toAddCommMagma.{u_1} A (AddCommMonoid.toAddCommSemigroup.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))))) (LinearMap.toAddHom.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 __spread.1._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.55))) (LinearMap.map_smul'.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 __spread.1._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.55)) (Equiv.invFun.{succ u_1, succ u_1} A A __spread.0._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.55) (Equiv.left_inv.{succ u_1, succ u_1} A A __spread.0._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.55) (Equiv.right_inv.{succ u_1, succ u_1} A A __spread.0._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.55)) (OfNat.ofNat.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18) 1 (One.toOfNat1.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18) (MulOne.toOne.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18) (MulOneClass.toMulOne.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18) (Monoid.toMulOneClass.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18) (DivInvMonoid.toMonoid.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18) (Group.toDivInvMonoid.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18) (LinearEquiv.automorphismGroup.{u_2, u_1} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18))))))))","typeFull":"∀ (R : Type u_2) (A : Type u_1) [inst : Semiring R] [inst_1 : Semiring A] [inst_2 : Module R A]\n  [inst_3 : SMulCommClass R A A],\n  (let __spread.0 := Units.mulLeft 1;\n    let __spread.1 := LinearMap.mulLeft R ↑1;\n    { toFun := __spread.0.toFun, map_add' := ⋯, map_smul' := ⋯, invFun := __spread.0.invFun, left_inv := ⋯,\n      right_inv := ⋯ }) =\n    1","typeReadable":"∀ (R : Type u_2) (A : Type u_1) [inst : Semiring R] [inst_1 : Semiring A] [inst_2 : Module R A]\n  [inst_3 : SMulCommClass R A A],\n  (let __spread.0 := Units.mulLeft 1;\n    let __spread.1 := LinearMap.mulLeft R ↑1;\n    { toFun := __spread.0.toFun, map_add' := ⋯, map_smul' := ⋯, invFun := __spread.0.invFun, left_inv := ⋯,\n      right_inv := ⋯ }) =\n    1","typeReferences":[["Equiv","left_inv"],["AddHom","mk"],["LinearMap","toAddHom"],["SMulZeroClass","toSMul"],["Units","mulLeft"],["instDistribSMul"],["AddMonoidWithOne","toAddMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Equiv","right_inv"],["LinearEquiv","mk"],["Equiv","toFun"],["LinearMap","map_smul'"],["NonAssocSemiring","toAddCommMonoidWithOne"],["Group","toDivInvMonoid"],["Units"],["DistribSMul","toSMulZeroClass"],["MulOne","toOne"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["DistribMulAction","toDistribSMul"],["Units","instMulOneClass"],["AddZeroClass","toAddZero"],["DivInvMonoid","toMonoid"],["Units","val"],["RingHomInvPair","ids"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["MulOneClass","toMulOne"],["Module"],["LinearMap","mk"],["LinearEquiv"],["LinearEquiv","automorphismGroup"],["MonoidWithZero","toMonoid"],["Monoid","toMulOneClass"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Eq"],["LinearMap","mulLeft"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["Semiring","toMonoidWithZero"],["OfNat","ofNat"],["SMulCommClass"],["Module","toDistribMulAction"],["AddHom","map_add'"],["One","toOfNat1"],["AddCommMonoid","toAddCommSemigroup"],["Equiv","invFun"],["Semiring"]],"valueReferences":[["RingHom"],["Equiv","left_inv"],["Eq","trans"],["AddHom","mk"],["LinearMap","toAddHom"],["HMul","hMul"],["SMulZeroClass","toSMul"],["Units","mulLeft"],["Equiv"],["LinearEquiv","ext"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Equiv","right_inv"],["funext"],["LinearEquiv","mk"],["AddHom","toFun"],["Equiv","toFun"],["LinearMap","map_smul'"],["Eq","ndrec"],["Group","toDivInvMonoid"],["NonAssocSemiring","toMulZeroOneClass"],["Units"],["DistribSMul","toSMulZeroClass"],["Group","toDivisionMonoid"],["MulOne","toOne"],["InvOneClass","toOne"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["DistribMulAction","toDistribSMul"],["Units","instMulOneClass"],["LinearMap"],["AddZeroClass","toAddZero"],["Function","RightInverse"],["LinearEquiv","mk","congr_simp"],["DivInvMonoid","toMonoid"],["Units","val"],["inv_one"],["HSMul","hSMul"],["Function","LeftInverse"],["RingHomInvPair","ids"],["instHMul"],["AddHom"],["AddZero","toZero"],["one_mul"],["DivisionMonoid","toDivInvOneMonoid"],["AddMonoid","toAddZeroClass"],["Units","mulLeft_symm"],["MulOneClass","toMulOne"],["Units","instGroup"],["Equiv","instEquivLike"],["LinearMap","mk"],["Units","instInv"],["RingHom","instFunLike"],["MulZeroOneClass","toMulOneClass"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["DFunLike","coe"],["congrArg"],["LinearEquiv","automorphismGroup"],["MulOne","toMul"],["MonoidWithZero","toMonoid"],["Monoid","toMulOneClass"],["EquivLike","toFunLike"],["Equiv","symm"],["instHSMul"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["congrFun'"],["LinearMap","mulLeft"],["Eq"],["LinearEquiv","instEquivLike"],["Inv","inv"],["True"],["instHAdd"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["Semiring","toMonoidWithZero"],["AddHom","mk","congr_simp"],["OfNat","ofNat"],["Equiv","Perm"],["HAdd","hAdd"],["eq_self"],["Module","toDistribMulAction"],["AddHom","map_add'"],["DivInvOneMonoid","toInvOneClass"],["AddCommMonoid","toAddCommSemigroup"],["One","toOfNat1"],["of_eq_true"],["Equiv","invFun"],["LinearMap","mk","congr_simp"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","domMulActCongrRight","_proof_5"],"typeFallback":"forall {R₁ : Type.{u_4}} {R₁' : Type.{u_5}} {R₂' : Type.{u_6}} {M₁ : Type.{u_2}} {M₁' : Type.{u_1}} {M₂' : Type.{u_3}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 : Semiring.{u_4} R₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 : Semiring.{u_5} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 : Semiring.{u_6} R₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 : AddCommMonoid.{u_2} M₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 : AddCommMonoid.{u_1} M₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 : AddCommMonoid.{u_3} M₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 : Module.{u_4, u_2} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 : Module.{u_5, u_1} R₁' M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 : Module.{u_6, u_3} R₂' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39] {σ₁'₂' : RingHom.{u_5, u_6} R₁' R₂' (Semiring.toNonAssocSemiring.{u_5} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24) (Semiring.toNonAssocSemiring.{u_6} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27)} {σ₂'₁' : RingHom.{u_6, u_5} R₂' R₁' (Semiring.toNonAssocSemiring.{u_6} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27) (Semiring.toNonAssocSemiring.{u_5} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24)} {σ₁₁' : RingHom.{u_4, u_5} R₁ R₁' (Semiring.toNonAssocSemiring.{u_4} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_5} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24)} {σ₁₂' : RingHom.{u_4, u_6} R₁ R₂' (Semiring.toNonAssocSemiring.{u_4} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_6} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27)} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.106 : RingHomInvPair.{u_5, u_6} R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁'₂' σ₂'₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.110 : RingHomInvPair.{u_6, u_5} R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₂'₁' σ₁'₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.114 : RingHomCompTriple.{u_4, u_5, u_6} R₁ R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₁' σ₁'₂' σ₁₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.146 : RingHomCompTriple.{u_4, u_6, u_5} R₁ R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₂' σ₂'₁' σ₁₁'] (e₂ : LinearEquiv.{u_5, u_6, u_1, u_3} R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.110 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54), Function.LeftInverse.{succ (max u_1 u_2), succ (max u_3 u_2)} (LinearMap.{u_4, u_5, u_2, u_1} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.{u_4, u_6, u_2, u_3} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (Equiv.invFun.{succ (max u_1 u_2), succ (max u_3 u_2)} (LinearMap.{u_4, u_5, u_2, u_1} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.{u_4, u_6, u_2, u_3} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (AddEquiv.toEquiv.{max u_1 u_2, max u_3 u_2} (LinearMap.{u_4, u_5, u_2, u_1} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.{u_4, u_6, u_2, u_3} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (LinearMap.instAdd.{u_4, u_5, u_2, u_1} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁') (LinearMap.instAdd.{u_4, u_6, u_2, u_3} R₁ R₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂') (LinearEquiv.arrowCongrAddEquiv.{u_4, u_4, u_5, u_6, u_2, u_2, u_1, u_3} R₁ R₁ R₁' R₂' M₁ M₁ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 (RingHom.id.{u_4} R₁ (Semiring.toNonAssocSemiring.{u_4} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18)) (RingHom.id.{u_4} R₁ (Semiring.toNonAssocSemiring.{u_4} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18)) σ₁'₂' σ₂'₁' σ₁₁' σ₁₂' σ₁₁' σ₁₂' (RingHomInvPair.ids.{u_4} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) (RingHomInvPair.ids.{u_4} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.114 (RingHomCompTriple.ids.{u_4, u_6} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂') inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.146 (RingHomCompTriple.ids.{u_4, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁') (LinearEquiv.refl.{u_4, u_2} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42) e₂))) (Equiv.toFun.{succ (max u_1 u_2), succ (max u_3 u_2)} (LinearMap.{u_4, u_5, u_2, u_1} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.{u_4, u_6, u_2, u_3} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (AddEquiv.toEquiv.{max u_1 u_2, max u_3 u_2} (LinearMap.{u_4, u_5, u_2, u_1} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.{u_4, u_6, u_2, u_3} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (LinearMap.instAdd.{u_4, u_5, u_2, u_1} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁') (LinearMap.instAdd.{u_4, u_6, u_2, u_3} R₁ R₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂') (LinearEquiv.arrowCongrAddEquiv.{u_4, u_4, u_5, u_6, u_2, u_2, u_1, u_3} R₁ R₁ R₁' R₂' M₁ M₁ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 (RingHom.id.{u_4} R₁ (Semiring.toNonAssocSemiring.{u_4} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18)) (RingHom.id.{u_4} R₁ (Semiring.toNonAssocSemiring.{u_4} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18)) σ₁'₂' σ₂'₁' σ₁₁' σ₁₂' σ₁₁' σ₁₂' (RingHomInvPair.ids.{u_4} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) (RingHomInvPair.ids.{u_4} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.114 (RingHomCompTriple.ids.{u_4, u_6} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂') inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.146 (RingHomCompTriple.ids.{u_4, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁') (LinearEquiv.refl.{u_4, u_2} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42) e₂)))","typeFull":"∀ {R₁ : Type u_4} {R₁' : Type u_5} {R₂' : Type u_6} {M₁ : Type u_2} {M₁' : Type u_1} {M₂' : Type u_3}\n  [inst : Semiring R₁] [inst_1 : Semiring R₁'] [inst_2 : Semiring R₂'] [inst_3 : AddCommMonoid M₁]\n  [inst_4 : AddCommMonoid M₁'] [inst_5 : AddCommMonoid M₂'] [inst_6 : Module R₁ M₁] [inst_7 : Module R₁' M₁']\n  [inst_8 : Module R₂' M₂'] {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} {σ₁₁' : R₁ →+* R₁'} {σ₁₂' : R₁ →+* R₂'}\n  [inst_9 : RingHomInvPair σ₁'₂' σ₂'₁'] [inst_10 : RingHomInvPair σ₂'₁' σ₁'₂']\n  [inst_11 : RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_12 : RingHomCompTriple σ₁₂' σ₂'₁' σ₁₁'] (e₂ : M₁' ≃ₛₗ[σ₁'₂'] M₂'),\n  Function.LeftInverse ((LinearEquiv.refl R₁ M₁).arrowCongrAddEquiv e₂).invFun\n    ((LinearEquiv.refl R₁ M₁).arrowCongrAddEquiv e₂).toFun","typeReadable":"∀ {R₁ : Type u_4} {R₁' : Type u_5} {R₂' : Type u_6} {M₁ : Type u_2} {M₁' : Type u_1} {M₂' : Type u_3}\n  [inst : Semiring R₁] [inst_1 : Semiring R₁'] [inst_2 : Semiring R₂'] [inst_3 : AddCommMonoid M₁]\n  [inst_4 : AddCommMonoid M₁'] [inst_5 : AddCommMonoid M₂'] [inst_6 : Module R₁ M₁] [inst_7 : Module R₁' M₁']\n  [inst_8 : Module R₂' M₂'] {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} {σ₁₁' : R₁ →+* R₁'} {σ₁₂' : R₁ →+* R₂'}\n  [inst_9 : RingHomInvPair σ₁'₂' σ₂'₁'] [inst_10 : RingHomInvPair σ₂'₁' σ₁'₂']\n  [inst_11 : RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_12 : RingHomCompTriple σ₁₂' σ₂'₁' σ₁₁'] (e₂ : M₁' ≃ₛₗ[σ₁'₂'] M₂'),\n  Function.LeftInverse ((LinearEquiv.refl R₁ M₁).arrowCongrAddEquiv e₂).invFun\n    ((LinearEquiv.refl R₁ M₁).arrowCongrAddEquiv e₂).toFun","typeReferences":[["RingHom"],["RingHomCompTriple","ids"],["Module"],["LinearEquiv"],["LinearMap"],["AddEquiv","toEquiv"],["RingHomCompTriple"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["LinearEquiv","arrowCongrAddEquiv"],["RingHom","id"],["Equiv","invFun"],["LinearMap","instAdd"],["RingHomInvPair","ids"],["Function","LeftInverse"],["Equiv","toFun"],["RingHomInvPair"],["LinearEquiv","refl"],["Semiring"]],"valueReferences":[["Equiv","left_inv"],["Semiring","toNonAssocSemiring"],["LinearEquiv","arrowCongrAddEquiv"],["RingHomCompTriple","ids"],["RingHom","id"],["LinearMap","instAdd"],["RingHomInvPair","ids"],["AddEquiv","toEquiv"],["LinearMap"],["LinearEquiv","refl"]]},{"isProp":true,"kind":"theorem","name":["addMonoidEndRingEquivInt_symm_apply"],"typeFallback":"forall (A : Type.{u_9}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11 : AddCommGroup.{u_9} A] (a._@._internal._hyg.0 : LinearMap.{0, 0, u_9, u_9} Int Int Int.instSemiring 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11)))))) (DFunLike.coe.{succ u_9, succ u_9, succ u_9} (RingEquiv.{u_9, u_9} (Module.End.{0, u_9} Int A Int.instSemiring (AddCommGroup.toAddCommMonoid.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (AddCommGroup.toIntModule.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11)) (AddMonoid.End.{u_9} A (AddZeroClass.toAddZero.{u_9} A (AddMonoid.toAddZeroClass.{u_9} A (SubNegMonoid.toAddMonoid.{u_9} A (AddGroup.toSubNegMonoid.{u_9} A (AddCommGroup.toAddGroup.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11)))))) (Module.End.instMul.{0, u_9} Int A Int.instSemiring (AddCommGroup.toAddCommMonoid.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (AddCommGroup.toIntModule.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11)) (AddMonoid.End.instMul.{u_9} A (AddZeroClass.toAddZero.{u_9} A 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(Pi.Function.module.{u_9, u_1, max u_5 u_10} V R (V₂ -> M) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2653326086._hygCtx._hyg.10 (Pi.addCommMonoid.{u_10, u_5} V₂ (fun (a._@._internal._hyg.0 : V₂) => M) (fun (i : V₂) => inst._@.Mathlib.Algebra.Module.Equiv.Basic.2653326086._hygCtx._hyg.13)) (Pi.Function.module.{u_10, u_1, u_5} V₂ R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2653326086._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2653326086._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2653326086._hygCtx._hyg.16))","typeFull":"(R : Type u_1) →\n  (M : Type u_5) →\n    [inst : Semiring R] →\n      [inst_1 : AddCommMonoid M] →\n        [inst_2 : Module R M] → (V : Type u_9) → (V₂ : Type u_10) → (V × V₂ → M) ≃ₗ[R] V → V₂ → M","typeReadable":"(R : Type u_1) →\n  (M : Type u_5) →\n    [inst : Semiring R] →\n      [inst_1 : AddCommMonoid M] →\n        [inst_2 : Module R M] → (V : Type u_9) → (V₂ : Type u_10) → (V × V₂ → M) ≃ₗ[R] V → V₂ → M","typeReferences":[["Prod"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Module"],["Pi","addCommMonoid"],["RingHomInvPair","ids"],["LinearEquiv"],["Pi","Function","module"],["Semiring"]],"valueReferences":[["LinearMap","mk"],["LinearEquiv","curry","_proof_4"],["Pi","addCommMonoid"],["AddHom","mk"],["Pi","Function","module"],["LinearEquiv","curry","_proof_2"],["Prod"],["Semiring","toNonAssocSemiring"],["AddCommMonoid","toAddCommSemigroup"],["Equiv","invFun"],["RingHom","id"],["LinearEquiv","curry","_proof_1"],["Equiv","curry"],["RingHomInvPair","ids"],["LinearEquiv","mk"],["LinearEquiv","curry","_proof_3"],["Equiv","toFun"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","congrLeft_symm_apply"],"typeFallback":"forall (M : Type.{u_5}) {M₂ : Type.{u_7}} {M₃ : Type.{u_8}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 : AddCommMonoid.{u_7} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.19 : AddCommMonoid.{u_8} M₃] {R : Type.{u_9}} (S : Type.{u_10}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 : Semiring.{u_9} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.39 : Semiring.{u_10} S] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 : Module.{u_9, u_7} R M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.46 : Module.{u_9, u_8} R M₃ inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50 : Module.{u_9, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.54 : Module.{u_10, u_5} S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.58 : SMulCommClass.{u_9, u_10, u_5} R S M (SMulZeroClass.toSMul.{u_9, u_5} R M (AddZero.toZero.{u_5} M (AddZeroClass.toAddZero.{u_5} M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_9, u_5} R M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_9, u_5} R M (MonoidWithZero.toMonoid.{u_9} R 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S inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.39)) (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13) (Module.toDistribMulAction.{u_10, u_5} S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.54))))] (e : LinearEquiv.{u_9, u_9, u_7, u_8} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36) (RingHomInvPair.ids.{u_9} R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.54 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.58) (LinearMap.module.{u_9, u_9, u_10, u_7, u_5} R R S M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50) (LinearEquiv.instEquivLike.{u_10, u_10, max u_5 u_8, max u_5 u_7} S S (LinearMap.{u_9, u_9, u_8, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) M₃ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.54 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.58) (RingHom.id.{u_10} S (Semiring.toNonAssocSemiring.{u_10} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.39)) (RingHom.id.{u_10} S (Semiring.toNonAssocSemiring.{u_10} S 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36))) (LinearMap.addCommMonoid.{u_9, u_9, u_8, u_5} R R M₃ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36))) (LinearMap.module.{u_9, u_9, u_10, u_7, u_5} R R S M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.54 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.58) (LinearMap.module.{u_9, u_9, u_10, u_8, u_5} R R S M₃ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 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{R₁ : Type.{u_9}} {R₂ : Type.{u_10}} {R₁' : Type.{u_11}} {R₂' : Type.{u_12}} {M₁ : Type.{u_13}} {M₂ : Type.{u_14}} {M₁' : Type.{u_15}} {M₂' : Type.{u_16}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 : Semiring.{u_9} R₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 : Semiring.{u_10} R₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 : Semiring.{u_11} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 : Semiring.{u_12} R₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 : AddCommMonoid.{u_13} M₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 : AddCommMonoid.{u_14} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 : AddCommMonoid.{u_15} M₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 : AddCommMonoid.{u_16} M₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 : Module.{u_9, u_13} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 : Module.{u_10, u_14} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 : Module.{u_11, u_15} R₁' M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 : Module.{u_12, u_16} R₂' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39] {σ₁₂ : RingHom.{u_9, u_10} R₁ R₂ (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21)} {σ₂₁ : RingHom.{u_10, u_9} R₂ R₁ (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21) (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18)} {σ₁'₂' : RingHom.{u_11, u_12} R₁' R₂' (Semiring.toNonAssocSemiring.{u_11} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24) (Semiring.toNonAssocSemiring.{u_12} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27)} {σ₂'₁' : RingHom.{u_12, u_11} R₂' R₁' (Semiring.toNonAssocSemiring.{u_12} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27) (Semiring.toNonAssocSemiring.{u_11} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24)} {σ₁₁' : RingHom.{u_9, u_11} R₁ R₁' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_11} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24)} {σ₂₂' : RingHom.{u_10, u_12} R₂ R₂' (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21) (Semiring.toNonAssocSemiring.{u_12} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27)} {σ₂₁' : RingHom.{u_10, u_11} R₂ R₁' (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21) (Semiring.toNonAssocSemiring.{u_11} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24)} {σ₁₂' : RingHom.{u_9, u_12} R₁ R₂' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_12} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27)} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 : RingHomInvPair.{u_9, u_10} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 σ₁₂ σ₂₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 : RingHomInvPair.{u_10, u_9} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 σ₂₁ σ₁₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 : RingHomInvPair.{u_11, u_12} R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₁'₂' σ₂'₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 : RingHomInvPair.{u_12, u_11} R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₂'₁' σ₁'₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.114 : RingHomCompTriple.{u_9, u_11, u_12} R₁ R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₁₁' σ₁'₂' σ₁₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.119 : RingHomCompTriple.{u_10, u_9, u_12} R₂ R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₂₁ σ₁₂' σ₂₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.124 : RingHomCompTriple.{u_10, u_12, u_11} R₂ R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₂₂' σ₂'₁' σ₂₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.129 : RingHomCompTriple.{u_9, u_10, u_11} R₁ R₂ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₂ σ₂₁' σ₁₁'] (e₁ : LinearEquiv.{u_9, u_10, u_13, u_14} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54), Eq.{max (succ u_13) (succ u_15)} (LinearMap.{u_9, u_11, u_13, u_15} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50) (DFunLike.coe.{max (succ (max u_16 u_14)) (succ (max u_15 u_13)), succ (max u_16 u_14), succ (max u_15 u_13)} (AddEquiv.{max u_16 u_14, max u_15 u_13} (LinearMap.{u_10, u_12, u_14, u_16} R₂ R₂' 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : LinearMap.{u_10, u_12, u_14, u_16} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54) => LinearMap.{u_9, u_11, u_13, u_15} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50) (EquivLike.toFunLike.{max (succ (max u_16 u_14)) (succ (max u_15 u_13)), succ (max u_16 u_14), succ (max u_15 u_13)} (AddEquiv.{max u_16 u_14, max u_15 u_13} (LinearMap.{u_10, u_12, u_14, u_16} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54) (LinearMap.{u_9, u_11, u_13, u_15} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50) (LinearMap.instAdd.{u_10, u_12, u_14, u_16} R₂ R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 σ₁₂ σ₂₁ σ₁'₂' σ₂'₁' σ₁₁' σ₂₂' σ₂₁' σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.119 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.124 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.129 e₁ e₂)) f) (LinearMap.comp.{u_9, u_10, u_11, u_13, u_14, u_15} R₁ R₂ R₁' M₁ M₂ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 σ₁₂ σ₂₁' σ₁₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.129 (LinearMap.comp.{u_10, u_12, u_11, u_14, u_16, u_15} R₂ R₂' R₁' M₂ M₂' M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 σ₂₂' σ₂'₁' σ₂₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.124 (LinearEquiv.toLinearMap.{u_12, u_11, u_16, u_15} R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₂'₁' σ₁'₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 M₂' M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 (LinearEquiv.symm.{u_11, u_12, u_15, u_16} R₁' R₂' M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 e₁))","typeFull":"∀ {R₁ : Type u_9} {R₂ : Type u_10} {R₁' : Type u_11} {R₂' : Type u_12} {M₁ : Type u_13} {M₂ : Type u_14}\n  {M₁' : Type u_15} {M₂' : Type u_16} [inst : Semiring R₁] [inst_1 : Semiring R₂] [inst_2 : Semiring R₁']\n  [inst_3 : Semiring R₂'] [inst_4 : AddCommMonoid M₁] [inst_5 : AddCommMonoid M₂] [inst_6 : AddCommMonoid M₁']\n  [inst_7 : AddCommMonoid M₂'] [inst_8 : Module R₁ M₁] [inst_9 : Module R₂ M₂] [inst_10 : Module R₁' M₁']\n  [inst_11 : Module R₂' M₂'] {σ₁₂ : R₁ →+* R₂} {σ₂₁ : R₂ →+* R₁} {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'}\n  {σ₁₁' : R₁ →+* R₁'} {σ₂₂' : R₂ →+* R₂'} {σ₂₁' : R₂ →+* R₁'} {σ₁₂' : R₁ →+* R₂'} [inst_12 : RingHomInvPair σ₁₂ σ₂₁]\n  [inst_13 : RingHomInvPair σ₂₁ σ₁₂] [inst_14 : RingHomInvPair σ₁'₂' σ₂'₁'] [inst_15 : RingHomInvPair σ₂'₁' σ₁'₂']\n  [inst_16 : RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_17 : RingHomCompTriple σ₂₁ σ₁₂' σ₂₂']\n  [inst_18 : RingHomCompTriple σ₂₂' σ₂'₁' 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RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_17 : RingHomCompTriple σ₂₁ σ₁₂' σ₂₂']\n  [inst_18 : RingHomCompTriple σ₂₂' σ₂'₁' σ₂₁'] [inst_19 : RingHomCompTriple σ₁₂ σ₂₁' σ₁₁'] (e₁ : M₁ ≃ₛₗ[σ₁₂] M₂)\n  (e₂ : M₁' ≃ₛₗ[σ₁'₂'] M₂') (f : M₂ →ₛₗ[σ₂₂'] M₂'), (e₁.arrowCongrAddEquiv e₂).symm f = (↑e₂.symm ∘ₛₗ f) ∘ₛ��� 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[inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 : Semiring.{u_5} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 : Semiring.{u_6} R₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 : AddCommMonoid.{u_2} M₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 : AddCommMonoid.{u_1} M₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 : AddCommMonoid.{u_3} M₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 : Module.{u_4, u_2} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 : Module.{u_5, u_1} R₁' M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 : Module.{u_6, u_3} R₂' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39] {σ₁'₂' : RingHom.{u_5, u_6} R₁' R₂' (Semiring.toNonAssocSemiring.{u_5} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24) (Semiring.toNonAssocSemiring.{u_6} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27)} {σ₂'₁' : RingHom.{u_6, u_5} R₂' R₁' (Semiring.toNonAssocSemiring.{u_6} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27) (Semiring.toNonAssocSemiring.{u_5} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24)} {σ₁₁' : RingHom.{u_4, u_5} R₁ R₁' (Semiring.toNonAssocSemiring.{u_4} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_5} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24)} {σ₁₂' : RingHom.{u_4, u_6} R₁ R₂' (Semiring.toNonAssocSemiring.{u_4} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_6} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27)} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.106 : RingHomInvPair.{u_5, u_6} R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁'₂' σ₂'₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.110 : RingHomInvPair.{u_6, u_5} R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₂'₁' σ₁'₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.114 : RingHomCompTriple.{u_4, u_5, u_6} R₁ R₁' R₂' 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54), Function.RightInverse.{succ (max u_1 u_2), succ (max u_3 u_2)} (LinearMap.{u_4, u_5, u_2, u_1} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.{u_4, u_6, u_2, u_3} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (AddEquiv.toEquiv.{max u_1 u_2, max u_3 u_2} (LinearMap.{u_4, u_5, u_2, u_1} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.{u_4, u_6, u_2, u_3} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂') (LinearEquiv.arrowCongrAddEquiv.{u_4, u_4, u_5, u_6, u_2, u_2, u_1, u_3} R₁ R₁ R₁' R₂' M₁ M₁ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 (RingHom.id.{u_4} R₁ (Semiring.toNonAssocSemiring.{u_4} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18)) (RingHom.id.{u_4} R₁ (Semiring.toNonAssocSemiring.{u_4} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18)) σ₁'₂' σ₂'₁' σ₁₁' σ₁₂' σ₁₁' σ₁₂' (RingHomInvPair.ids.{u_4} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) (RingHomInvPair.ids.{u_4} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.114 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.{u_4, u_6, u_2, u_3} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (AddEquiv.toEquiv.{max u_1 u_2, max u_3 u_2} (LinearMap.{u_4, u_5, u_2, u_1} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.{u_4, u_6, u_2, u_3} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (LinearMap.instAdd.{u_4, u_5, u_2, u_1} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁') (LinearMap.instAdd.{u_4, u_6, u_2, u_3} R₁ R₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂') (LinearEquiv.arrowCongrAddEquiv.{u_4, u_4, u_5, u_6, u_2, u_2, u_1, u_3} R₁ R₁ R₁' R₂' M₁ M₁ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 (RingHom.id.{u_4} R₁ (Semiring.toNonAssocSemiring.{u_4} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18)) (RingHom.id.{u_4} R₁ (Semiring.toNonAssocSemiring.{u_4} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18)) σ₁'₂' σ₂'₁' σ₁₁' σ₁₂' σ₁₁' σ₁₂' (RingHomInvPair.ids.{u_4} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) (RingHomInvPair.ids.{u_4} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.114 (RingHomCompTriple.ids.{u_4, u_6} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂') inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.146 (RingHomCompTriple.ids.{u_4, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁') (LinearEquiv.refl.{u_4, u_2} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42) e₂)))","typeFull":"∀ {R₁ : Type u_4} {R₁' : Type u_5} {R₂' : Type u_6} {M₁ : Type u_2} {M₁' : Type u_1} {M₂' : Type u_3}\n  [inst : Semiring R₁] [inst_1 : Semiring R₁'] [inst_2 : Semiring R₂'] [inst_3 : AddCommMonoid M₁]\n  [inst_4 : AddCommMonoid M₁'] [inst_5 : AddCommMonoid M₂'] [inst_6 : Module R₁ M₁] [inst_7 : Module R₁' M₁']\n  [inst_8 : Module R₂' M₂'] {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} {σ₁₁' : R₁ →+* R₁'} {σ₁₂' : R₁ →+* R₂'}\n  [inst_9 : RingHomInvPair σ₁'₂' σ₂'₁'] [inst_10 : RingHomInvPair σ₂'₁' σ₁'₂']\n  [inst_11 : RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_12 : RingHomCompTriple σ₁₂' σ₂'₁' σ₁₁'] (e₂ : M₁' ≃ₛₗ[σ₁'₂'] M₂'),\n  Function.RightInverse ((LinearEquiv.refl R₁ M₁).arrowCongrAddEquiv e₂).invFun\n    ((LinearEquiv.refl R₁ M₁).arrowCongrAddEquiv e₂).toFun","typeReadable":"∀ {R₁ : Type u_4} {R₁' : Type u_5} {R₂' : Type u_6} {M₁ : Type u_2} {M₁' : Type u_1} {M₂' : Type u_3}\n  [inst : Semiring R₁] [inst_1 : Semiring R₁'] [inst_2 : Semiring R₂'] [inst_3 : AddCommMonoid M₁]\n  [inst_4 : AddCommMonoid M₁'] [inst_5 : AddCommMonoid M₂'] [inst_6 : Module R₁ M₁] [inst_7 : Module R₁' M₁']\n  [inst_8 : Module R₂' M₂'] {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} {σ₁₁' : R₁ →+* R₁'} {σ₁₂' : R₁ →+* R₂'}\n  [inst_9 : RingHomInvPair σ₁'₂' σ₂'₁'] [inst_10 : RingHomInvPair σ₂'₁' σ₁'₂']\n  [inst_11 : RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_12 : RingHomCompTriple σ₁₂' σ₂'₁' σ₁₁'] (e₂ : M₁' ≃ₛₗ[σ₁'₂'] M₂'),\n  Function.RightInverse ((LinearEquiv.refl R₁ M₁).arrowCongrAddEquiv e₂).invFun\n    ((LinearEquiv.refl R₁ M₁).arrowCongrAddEquiv e₂).toFun","typeReferences":[["RingHom"],["RingHomCompTriple","ids"],["Module"],["LinearEquiv"],["LinearMap"],["AddEquiv","toEquiv"],["RingHomCompTriple"],["Function","RightInverse"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["LinearEquiv","arrowCongrAddEquiv"],["RingHom","id"],["Equiv","invFun"],["LinearMap","instAdd"],["RingHomInvPair","ids"],["Equiv","toFun"],["RingHomInvPair"],["LinearEquiv","refl"],["Semiring"]],"valueReferences":[["Semiring","toNonAssocSemiring"],["LinearEquiv","arrowCongrAddEquiv"],["RingHomCompTriple","ids"],["RingHom","id"],["Equiv","right_inv"],["LinearMap","instAdd"],["RingHomInvPair","ids"],["AddEquiv","toEquiv"],["LinearMap"],["LinearEquiv","refl"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","restrictScalars","_proof_1"],"typeFallback":"forall (R : Type.{u_3}) {S : Type.{u_4}} {M : Type.{u_2}} {M₂ : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10 : Semiring.{u_3} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 : Semiring.{u_4} S] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22 : AddCommMonoid.{u_1} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.25 : Module.{u_3, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.29 : Module.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.33 : Module.{u_4, u_2} S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.37 : Module.{u_4, u_1} S M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.41 : LinearMap.CompatibleSMul.{u_2, u_1, u_3, u_4} M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22 R S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 (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.Equiv.Basic.3287639652._hygCtx._hyg.19)))) (DistribSMul.toSMulZeroClass.{u_3, u_2} R M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19)) (DistribMulAction.toDistribSMul.{u_3, u_2} R M (MonoidWithZero.toMonoid.{u_3} R (Semiring.toMonoidWithZero.{u_3} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19) (Module.toDistribMulAction.{u_3, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.25)))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.33 (SMulZeroClass.toSMul.{u_3, 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.Equiv.Basic.3287639652._hygCtx._hyg.22)))) (DistribSMul.toSMulZeroClass.{u_3, u_1} R M₂ (AddMonoid.toAddZeroClass.{u_1} M₂ (AddCommMonoid.toAddMonoid.{u_1} M₂ 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u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.29 (LinearMap.restrictScalars.{u_3, u_4, u_2, u_1} R S M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.29 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.37 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.41 (LinearEquiv.toLinearMap.{u_4, u_4, u_2, u_1} S S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 (RingHom.id.{u_4} S (Semiring.toNonAssocSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13)) (RingHom.id.{u_4} S (Semiring.toNonAssocSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13)) (RingHomInvPair.ids.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13) (RingHomInvPair.ids.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13) M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.37 f))) y))","typeFull":"∀ (R : Type u_3) {S : Type u_4} {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 M] [inst_7 : Module S M₂] [inst_8 : LinearMap.CompatibleSMul M M₂ R S] (f : M ≃ₗ[S] M₂) (x y : M),\n  (↑R ↑f).toFun (x + y) = (↑R ↑f).toFun x + (↑R ↑f).toFun y","typeReadable":"∀ (R : Type u_3) {S : Type u_4} {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 M] [inst_7 : Module S M₂] [inst_8 : LinearMap.CompatibleSMul M M₂ R S] (f : M ≃ₗ[S] M₂) (x y : M),\n  (↑R ↑f).toFun (x + y) = (↑R ↑f).toFun x + (↑R ↑f).toFun y","typeReferences":[["LinearMap","CompatibleSMul"],["Module"],["LinearMap","toAddHom"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["AddHom","toFun"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Eq"],["LinearMap","restrictScalars"],["DistribSMul","toSMulZeroClass"],["instHAdd"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["LinearEquiv","toLinearMap"],["AddZeroClass","toAddZero"],["HAdd","hAdd"],["Module","toDistribMulAction"],["AddCommMonoid","toAddCommSemigroup"],["RingHomInvPair","ids"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["AddHom","map_add'"],["Semiring","toNonAssocSemiring"],["AddCommMonoid","toAddCommSemigroup"],["RingHom","id"],["RingHomInvPair","ids"],["LinearMap","toAddHom"],["LinearEquiv","toLinearMap"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["LinearMap","restrictScalars"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","piUnique","_proof_1"],"typeFallback":"forall {α : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1979755013._hygCtx._hyg.11 : Unique.{succ u_2} α] (f : α -> Type.{u_1}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1979755013._hygCtx._hyg.21 : forall (x : α), AddCommMonoid.{u_1} (f x)] (x._@.Mathlib.Algebra.Module.Equiv.Basic.1979755013._hygCtx._hyg.75 : forall (t : α), f t) (x._@.Mathlib.Algebra.Module.Equiv.Basic.1979755013._hygCtx._hyg.77 : forall (t : α), f t), Eq.{succ u_1} (f (Inhabited.default.{succ u_2} α (Unique.instInhabited.{succ u_2} α inst._@.Mathlib.Algebra.Module.Equiv.Basic.1979755013._hygCtx._hyg.11))) (Equiv.toFun.{max (succ u_2) (succ u_1), succ u_1} (forall (i : α), f i) (f (Inhabited.default.{succ u_2} α (Unique.instInhabited.{succ u_2} α inst._@.Mathlib.Algebra.Module.Equiv.Basic.1979755013._hygCtx._hyg.11))) (Equiv.piUnique.{succ u_2, succ u_1} α inst._@.Mathlib.Algebra.Module.Equiv.Basic.1979755013._hygCtx._hyg.11 f) (HAdd.hAdd.{max u_1 u_2, max u_1 u_2, max u_1 u_2} (forall (t : α), f t) (forall (t 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(fun (x : M) => LinearMap.{u_1, u_1, u_2, u_1} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))) (V x) R (inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16 x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.25 x) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))) (fun (i : M) => LinearMap.addCommMonoid.{u_1, u_1, u_2, u_1} R R (V i) R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16 i) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.25 i) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))))))) (DistribMulAction.toDistribSMul.{u_1, 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.25 x) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (Pi.addCommMonoid.{u_3, max u_1 u_2} M (fun (x : M) => LinearMap.{u_1, u_1, u_2, u_1} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))) (V x) R (inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16 x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.25 i) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))))) (Pi.module.{u_3, max u_1 u_2, u_1} M (fun (x : M) => LinearMap.{u_1, u_1, u_2, u_1} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))) (V x) R (inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16 x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.25 x) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))) R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (fun (i : M) => LinearMap.addCommMonoid.{u_1, u_1, u_2, u_1} R R (V i) R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16 i) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.25 i) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (fun (i : M) => LinearMap.module.{u_1, u_1, u_1, u_2, u_1} R R R (V i) R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16 i) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R 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(CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)) (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.Equiv.Basic.1550793534._hygCtx._hyg.13))))) (Module.toDistribMulAction.{u_1, u_1} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))))))))))) m x))) (LinearMap.piApply._proof_2.{u_1, 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: M) => R) (fun (i : M) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))))) (Pi.module.{u_3, u_2, u_1} M V R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.25) (Pi.Function.module.{u_3, u_1, u_1} M R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (instHSMul.{u_1, max (max u_1 u_3) u_2} R (LinearMap.{u_1, u_1, max u_3 u_2, max u_1 u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))) (forall (x : M), V x) (M -> R) (Pi.addCommMonoid.{u_3, u_2} M V inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16) (Pi.addCommMonoid.{u_3, u_1} M (fun (a._@._internal._hyg.0 : M) => R) (fun (i : M) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))))) (Pi.module.{u_3, u_2, u_1} M V R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.25) (Pi.Function.module.{u_3, u_1, u_1} M R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (SMulZeroClass.toSMul.{u_1, max (max u_1 u_3) u_2} R (LinearMap.{u_1, u_1, max u_3 u_2, max u_1 u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))) (forall (x : M), V x) (M -> R) (Pi.addCommMonoid.{u_3, u_2} M V inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16) (Pi.addCommMonoid.{u_3, u_1} M (fun (a._@._internal._hyg.0 : M) => R) (fun (i : M) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))))) (Pi.module.{u_3, u_2, u_1} M V R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.25) (Pi.Function.module.{u_3, u_1, u_1} M R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (AddZero.toZero.{max (max u_1 u_3) u_2} (LinearMap.{u_1, u_1, max u_3 u_2, max u_1 u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))) (forall (x : M), V x) (M -> R) (Pi.addCommMonoid.{u_3, u_2} M V inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16) (Pi.addCommMonoid.{u_3, u_1} M (fun (a._@._internal._hyg.0 : M) => R) (fun (i : M) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))))) (Pi.module.{u_3, u_2, u_1} M V R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.25) (Pi.Function.module.{u_3, u_1, u_1} M R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (AddZeroClass.toAddZero.{max (max u_1 u_3) u_2} (LinearMap.{u_1, u_1, max u_3 u_2, max u_1 u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))) (forall (x : M), V x) (M -> R) (Pi.addCommMonoid.{u_3, u_2} M V inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16) (Pi.addCommMonoid.{u_3, u_1} M (fun (a._@._internal._hyg.0 : M) => R) (fun (i : M) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))))) (Pi.module.{u_3, u_2, u_1} M V R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.25) (Pi.Function.module.{u_3, u_1, u_1} M R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (AddMonoid.toAddZeroClass.{max (max u_1 u_3) u_2} (LinearMap.{u_1, u_1, max u_3 u_2, max u_1 u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))) (forall (x : M), V x) (M -> R) (Pi.addCommMonoid.{u_3, u_2} M V inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16) (Pi.addCommMonoid.{u_3, u_1} M (fun (a._@._internal._hyg.0 : M) => R) (fun (i : M) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))))) (Pi.module.{u_3, u_2, u_1} M V R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.25) (Pi.Function.module.{u_3, u_1, u_1} M R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (AddCommMonoid.toAddMonoid.{max (max u_1 u_3) u_2} (LinearMap.{u_1, u_1, max u_3 u_2, max u_1 u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))) (forall (x : M), V x) (M -> R) (Pi.addCommMonoid.{u_3, u_2} M V inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16) (Pi.addCommMonoid.{u_3, u_1} M (fun (a._@._internal._hyg.0 : M) => R) (fun (i : M) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))))) (Pi.module.{u_3, u_2, u_1} M V R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.25) (Pi.Function.module.{u_3, u_1, u_1} M R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (LinearMap.addCommMonoid.{u_1, u_1, max u_3 u_2, max u_1 u_3} R R (forall (x : M), V x) (M -> R) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (Pi.addCommMonoid.{u_3, u_2} M V inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16) (Pi.addCommMonoid.{u_3, u_1} M (fun (a._@._internal._hyg.0 : M) => R) (fun (i : M) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))))) (Pi.module.{u_3, u_2, u_1} M V R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.25) (Pi.Function.module.{u_3, u_1, u_1} M R R (CommSemiring.toSemiring.{u_1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (AddMonoid.toAddZeroClass.{max (max u_1 u_3) u_2} (LinearMap.{u_1, u_1, max u_3 u_2, max u_1 u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))) (forall (x : M), V x) (M -> R) (Pi.addCommMonoid.{u_3, u_2} M V inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16) (Pi.addCommMonoid.{u_3, u_1} M (fun (a._@._internal._hyg.0 : M) => R) (fun (i : M) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))))) (Pi.module.{u_3, u_2, u_1} M V R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.25) (Pi.Function.module.{u_3, u_1, u_1} M R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (AddCommMonoid.toAddMonoid.{max (max u_1 u_3) u_2} (LinearMap.{u_1, u_1, max u_3 u_2, max u_1 u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))) (forall (x : M), V x) (M -> R) (Pi.addCommMonoid.{u_3, u_2} M V inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16) (Pi.addCommMonoid.{u_3, u_1} M (fun (a._@._internal._hyg.0 : M) => R) (fun (i : M) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))))) (Pi.module.{u_3, u_2, u_1} M V R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.25) (Pi.Function.module.{u_3, u_1, u_1} M R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (LinearMap.addCommMonoid.{u_1, u_1, max u_3 u_2, max u_1 u_3} R R (forall (x : M), V x) (M -> R) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (Pi.addCommMonoid.{u_3, u_2} M V inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16) (Pi.addCommMonoid.{u_3, u_1} M (fun (a._@._internal._hyg.0 : M) => R) (fun (i : M) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))))) (Pi.module.{u_3, u_2, u_1} M V R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.25) (Pi.Function.module.{u_3, u_1, u_1} M R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))))) (DistribMulAction.toDistribSMul.{u_1, max (max u_1 u_3) u_2} R (LinearMap.{u_1, u_1, max u_3 u_2, max u_1 u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))) (forall (x : M), V x) (M -> R) (Pi.addCommMonoid.{u_3, u_2} M V inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16) (Pi.addCommMonoid.{u_3, u_1} M (fun (a._@._internal._hyg.0 : M) => R) (fun (i : M) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))))) (Pi.module.{u_3, u_2, u_1} M V R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.25) (Pi.Function.module.{u_3, u_1, u_1} M R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))) (AddCommMonoid.toAddMonoid.{max (max u_1 u_3) u_2} (LinearMap.{u_1, u_1, max u_3 u_2, max u_1 u_3} R R (CommSemiring.toSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.25) (Pi.Function.module.{u_3, u_1, u_1} M R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (LinearMap.addCommMonoid.{u_1, u_1, max u_3 u_2, max u_1 u_3} R R (forall (x : M), V x) (M -> R) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (Pi.addCommMonoid.{u_3, u_2} M V inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16) (Pi.addCommMonoid.{u_3, u_1} M (fun (a._@._internal._hyg.0 : M) => R) (fun (i : M) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))))) (Pi.module.{u_3, u_2, u_1} M V R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.25) (Pi.Function.module.{u_3, u_1, u_1} M R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.25 x)))","typeFull":"∀ {R : Type u_1} {M : Type u_3} {V : M → Type u_2} [inst : CommSemiring R] [inst_1 : (x : M) → AddCommMonoid (V x)]\n  [inst_2 : (x : M) → Module R (V x)] (m : R) (x : (x : M) → V x →ₗ[R] R),\n  { toFun := fun s x_1 => ((m • x) x_1) (s x_1), map_add' := ⋯, map_smul' := ⋯ } =\n    (RingHom.id R) m • { toFun := fun s x_1 => (x x_1) (s x_1), map_add' := ⋯, map_smul' := ⋯ }","typeReadable":"∀ {R : Type u_1} {M : Type u_3} {V : M → Type u_2} [inst : CommSemiring R] [inst_1 : (x : M) → AddCommMonoid (V x)]\n  [inst_2 : (x : M) → Module R (V x)] (m : R) (x : (x : M) → V x →ₗ[R] R),\n  { toFun := fun s x_1 => ((m • x) x_1) (s x_1), map_add' := ⋯, map_smul' := ⋯ } =\n    (RingHom.id R) m • { toFun := fun s x_1 => (x x_1) (s x_1), map_add' := ⋯, map_smul' := ⋯ }","typeReferences":[["RingHom"],["smulCommClass_self"],["CommMonoid","toMonoid"],["LinearMap","instFunLike"],["Module"],["LinearMap","mk"],["Pi","addCommMonoid"],["CommSemiring"],["AddHom","mk"],["RingHom","instFunLike"],["SemigroupAction","toSMul"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["Pi","module"],["Pi","Function","module"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["DistribMulAction","toMulAction"],["LinearMap","piApply","_proof_2"],["instHSMul"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Monoid","toSemigroup"],["Eq"],["Semiring","toModule"],["DistribSMul","toSMulZeroClass"],["LinearMap","module"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["CommSemiring","toSemiring"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["LinearMap"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["Function","smulCommClass"],["Module","toDistribMulAction"],["AddCommMonoid","toAddCommSemigroup"],["LinearMap","piApply","_proof_1"],["HSMul","hSMul"],["MulAction","toSemigroupAction"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["smulCommClass_self"],["RingHom"],["Pi","addCommMonoid"],["AddHom","mk"],["SemigroupAction","toSMul"],["HMul","hMul"],["SMulZeroClass","toSMul"],["Pi","module"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["LinearMap","ext"],["funext"],["DistribMulAction","toMulAction"],["Monoid","toSemigroup"],["Semiring","toModule"],["DistribSMul","toSMulZeroClass"],["NonUnitalNonAssocSemiring","toDistrib"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["LinearMap","module"],["DistribMulAction","toDistribSMul"],["AddZeroClass","toAddZero"],["LinearMap"],["CommSemiring","toCommMonoid"],["Function","smulCommClass"],["HSMul","hSMul"],["LinearMap","piApply","_proof_1"],["instHMul"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["LinearMap","instFunLike"],["CommMonoid","toMonoid"],["LinearMap","mk"],["RingHom","instFunLike"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["Pi","Function","module"],["MonoidWithZero","toMonoid"],["instHSMul"],["LinearMap","piApply","_proof_2"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Eq"],["Distrib","toMul"],["CommSemiring","toSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["Semiring","toMonoidWithZero"],["LinearMap","addCommMonoid"],["eq_self"],["Module","toDistribMulAction"],["AddCommMonoid","toAddCommSemigroup"],["of_eq_true"],["MulAction","toSemigroupAction"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","sumPiEquivProdPi","_proof_2"],"typeFallback":"forall (R : Type.{u_4}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1914868805._hygCtx._hyg.11 : Semiring.{u_4} R] (S : Type.{u_1}) (T : Type.{u_2}) (A : (Sum.{u_1, u_2} S T) -> Type.{u_3}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1914868805._hygCtx._hyg.23 : forall (st : Sum.{u_1, u_2} S T), AddCommMonoid.{u_3} (A st)] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1914868805._hygCtx._hyg.32 : forall (st : Sum.{u_1, u_2} S T), Module.{u_4, u_3} R (A st) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1914868805._hygCtx._hyg.11 (inst._@.Mathlib.Algebra.Module.Equiv.Basic.1914868805._hygCtx._hyg.23 st)] (x._@.Mathlib.Algebra.Module.Equiv.Basic.1914868805._hygCtx._hyg.111 : R) (x._@.Mathlib.Algebra.Module.Equiv.Basic.1914868805._hygCtx._hyg.113 : forall (st : Sum.{u_1, u_2} S T), A st), Eq.{max (max (succ u_1) (succ u_2)) (succ u_3)} (Prod.{max u_1 u_3, max u_2 u_3} (forall (s : S), A (Sum.inl.{u_1, u_2} S T s)) (forall (t : T), A (Sum.inr.{u_1, u_2} S T t))) (Equiv.toFun.{max (max (succ u_3) (succ 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1914868805._hygCtx._hyg.23) (Pi.module.{max u_1 u_2, u_3, u_4} (Sum.{u_1, u_2} S T) A R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1914868805._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1914868805._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1914868805._hygCtx._hyg.32)))))) x._@.Mathlib.Algebra.Module.Equiv.Basic.1914868805._hygCtx._hyg.111 x._@.Mathlib.Algebra.Module.Equiv.Basic.1914868805._hygCtx._hyg.113))","typeFull":"∀ (R : Type u_4) [inst : Semiring R] (S : Type u_1) (T : Type u_2) (A : S ⊕ T → Type u_3)\n  [inst_1 : (st : S ⊕ T) → AddCommMonoid (A st)] [inst_2 : (st : S ⊕ T) → Module R (A st)] (x : R)\n  (x_1 : (st : S ⊕ T) → A st), (Equiv.sumPiEquivProdPi A).toFun (x • x_1) = (Equiv.sumPiEquivProdPi A).toFun (x • x_1)","typeReadable":"∀ (R : Type u_4) [inst : Semiring R] (S : Type u_1) (T : Type u_2) (A : S ⊕ T → Type u_3)\n  [inst_1 : (st : S ⊕ T) → AddCommMonoid (A st)] [inst_2 : (st : S ⊕ T) → Module R (A st)] (x : R)\n  (x_1 : (st : S ⊕ T) → A st), (Equiv.sumPiEquivProdPi A).toFun (x • x_1) = (Equiv.sumPiEquivProdPi A).toFun (x • x_1)","typeReferences":[["Equiv","sumPiEquivProdPi"],["Module"],["Pi","addCommMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["Pi","module"],["Sum"],["Prod"],["Module","toDistribMulAction"],["AddCommMonoid"],["Sum","inl"],["MonoidWithZero","toMonoid"],["HSMul","hSMul"],["instHSMul"],["Equiv","toFun"],["Eq"],["AddZero","toZero"],["Sum","inr"],["DistribSMul","toSMulZeroClass"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["rfl"],["Equiv","sumPiEquivProdPi"],["Pi","addCommMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["Pi","module"],["Sum"],["Prod"],["Module","toDistribMulAction"],["Sum","inl"],["MonoidWithZero","toMonoid"],["HSMul","hSMul"],["instHSMul"],["Equiv","toFun"],["AddZero","toZero"],["Sum","inr"],["DistribSMul","toSMulZeroClass"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","restrictScalars_symm_apply"],"typeFallback":"forall (R : Type.{u_1}) {S : Type.{u_4}} {M : Type.{u_5}} {M₂ : Type.{u_7}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 : Semiring.{u_4} S] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22 : AddCommMonoid.{u_7} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.25 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.29 : Module.{u_1, u_7} R M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.33 : Module.{u_4, u_5} S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.37 : Module.{u_4, u_7} S M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.41 : LinearMap.CompatibleSMul.{u_5, u_7, u_1, u_4} M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22 R S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 (SMulZeroClass.toSMul.{u_1, u_5} R M (AddZero.toZero.{u_5} M (AddZeroClass.toAddZero.{u_5} M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19)))) (DistribSMul.toSMulZeroClass.{u_1, u_5} R M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19)) (DistribMulAction.toDistribSMul.{u_1, u_5} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19) (Module.toDistribMulAction.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.25)))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.33 (SMulZeroClass.toSMul.{u_1, u_7} R M₂ (AddZero.toZero.{u_7} M₂ (AddZeroClass.toAddZero.{u_7} M₂ (AddMonoid.toAddZeroClass.{u_7} M₂ (AddCommMonoid.toAddMonoid.{u_7} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22)))) (DistribSMul.toSMulZeroClass.{u_1, u_7} R M₂ (AddMonoid.toAddZeroClass.{u_7} M₂ (AddCommMonoid.toAddMonoid.{u_7} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22)) (DistribMulAction.toDistribSMul.{u_1, u_7} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_7} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22) (Module.toDistribMulAction.{u_1, u_7} R M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.29)))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.37] (f : LinearEquiv.{u_4, u_4, u_5, u_7} S S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.37 (RingHom.id.{u_4} S (Semiring.toNonAssocSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13)) (RingHom.id.{u_4} S (Semiring.toNonAssocSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13)) (RingHomInvPair.ids.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13) (RingHomInvPair.ids.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13) f) a)","typeFull":"∀ (R : Type u_1) {S : Type u_4} {M : Type u_5} {M₂ : Type u_7} [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 M] [inst_7 : Module S M₂] [inst_8 : LinearMap.CompatibleSMul M M₂ R S] (f : M ≃ₗ[S] M₂) (a : M₂),\n  (LinearEquiv.restrictScalars R f).symm a = f.symm a","typeReadable":"∀ (R : Type u_1) {S : Type u_4} {M : Type u_5} {M₂ : Type u_7} [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 M] [inst_7 : Module S M₂] [inst_8 : LinearMap.CompatibleSMul M M₂ R S] (f : M ≃ₗ[S] M₂) (a : M₂),\n  (LinearEquiv.restrictScalars R f).symm a = f.symm 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Type.{u_1}} {M₂ : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555652._hygCtx._hyg.13 : AddCommMonoid.{u_1} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555652._hygCtx._hyg.16 : AddCommMonoid.{u_2} M₂] (e : AddEquiv.{u_1, u_2} M M₂ (AddCommMagma.toAdd.{u_1} M (AddCommSemigroup.toAddCommMagma.{u_1} M (AddCommMonoid.toAddCommSemigroup.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555652._hygCtx._hyg.13))) (AddCommMagma.toAdd.{u_2} M₂ (AddCommSemigroup.toAddCommMagma.{u_2} M₂ (AddCommMonoid.toAddCommSemigroup.{u_2} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555652._hygCtx._hyg.16)))), Function.RightInverse.{succ u_1, succ u_2} M M₂ (Equiv.invFun.{succ u_1, succ u_2} M M₂ (AddEquiv.toEquiv.{u_1, u_2} M M₂ (AddCommMagma.toAdd.{u_1} M (AddCommSemigroup.toAddCommMagma.{u_1} M (AddCommMonoid.toAddCommSemigroup.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555652._hygCtx._hyg.13))) (AddCommMagma.toAdd.{u_2} M₂ (AddCommSemigroup.toAddCommMagma.{u_2} 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e.toFun","typeReferences":[["Function","RightInverse"],["AddCommMonoid"],["AddCommMonoid","toAddCommSemigroup"],["Equiv","invFun"],["Equiv","toFun"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["AddEquiv","toEquiv"],["AddEquiv"]],"valueReferences":[["AddCommMonoid","toAddCommSemigroup"],["Equiv","right_inv"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["AddEquiv","toEquiv"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","instZero","_proof_1"],"typeFallback":"forall {R : Type.{u_3}} {R₂ : Type.{u_4}} {M : Type.{u_2}} {M₂ : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.10 : Semiring.{u_3} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.13 : Semiring.{u_4} R₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.16 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.19 : AddCommMonoid.{u_1} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.22 : Module.{u_3, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.26 : Module.{u_4, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.19] {σ₁₂ : RingHom.{u_3, u_4} R R₂ (Semiring.toNonAssocSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.10) (Semiring.toNonAssocSemiring.{u_4} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.13)} (x : M) (y : M), Eq.{succ u_1} M₂ (AddHom.toFun.{u_2, u_1} M M₂ (AddCommMagma.toAdd.{u_2} M (AddCommSemigroup.toAddCommMagma.{u_2} M (AddCommMonoid.toAddCommSemigroup.{u_2} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.16))) (AddCommMagma.toAdd.{u_1} M₂ (AddCommSemigroup.toAddCommMagma.{u_1} M₂ (AddCommMonoid.toAddCommSemigroup.{u_1} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.19))) (LinearMap.toAddHom.{u_3, u_4, u_2, u_1} R R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.13 σ₁₂ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.26 (OfNat.ofNat.{max u_2 u_1} (LinearMap.{u_3, u_4, u_2, u_1} R R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.13 σ₁₂ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.26) 0 (Zero.toOfNat0.{max u_2 u_1} (LinearMap.{u_3, u_4, u_2, u_1} R R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.13 σ₁₂ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.26) (LinearMap.instZero.{u_3, u_4, u_2, u_1} R R₂ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.26 σ₁₂)))) (HAdd.hAdd.{u_2, u_2, u_2} M M M (instHAdd.{u_2} M (AddCommMagma.toAdd.{u_2} M (AddCommSemigroup.toAddCommMagma.{u_2} M (AddCommMonoid.toAddCommSemigroup.{u_2} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.16)))) x y)) (HAdd.hAdd.{u_1, u_1, u_1} M₂ M₂ M₂ (instHAdd.{u_1} M₂ (AddCommMagma.toAdd.{u_1} M₂ (AddCommSemigroup.toAddCommMagma.{u_1} M₂ (AddCommMonoid.toAddCommSemigroup.{u_1} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.19)))) (AddHom.toFun.{u_2, u_1} M M₂ (AddCommMagma.toAdd.{u_2} M (AddCommSemigroup.toAddCommMagma.{u_2} M (AddCommMonoid.toAddCommSemigroup.{u_2} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.16))) (AddCommMagma.toAdd.{u_1} M₂ (AddCommSemigroup.toAddCommMagma.{u_1} M₂ (AddCommMonoid.toAddCommSemigroup.{u_1} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.19))) (LinearMap.toAddHom.{u_3, u_4, u_2, u_1} R R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.13 σ₁₂ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.26 (OfNat.ofNat.{max u_2 u_1} (LinearMap.{u_3, u_4, u_2, u_1} R R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.13 σ₁₂ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.26) 0 (Zero.toOfNat0.{max u_2 u_1} (LinearMap.{u_3, u_4, u_2, u_1} R R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.13 σ₁₂ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.26) (LinearMap.instZero.{u_3, u_4, u_2, u_1} R R₂ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.26 σ₁₂)))) x) (AddHom.toFun.{u_2, u_1} M M₂ (AddCommMagma.toAdd.{u_2} M (AddCommSemigroup.toAddCommMagma.{u_2} M (AddCommMonoid.toAddCommSemigroup.{u_2} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.16))) (AddCommMagma.toAdd.{u_1} M₂ (AddCommSemigroup.toAddCommMagma.{u_1} M₂ (AddCommMonoid.toAddCommSemigroup.{u_1} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.19))) (LinearMap.toAddHom.{u_3, u_4, u_2, u_1} R R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.13 σ₁₂ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.26 (OfNat.ofNat.{max u_2 u_1} (LinearMap.{u_3, u_4, u_2, u_1} R R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.13 σ₁₂ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.26) 0 (Zero.toOfNat0.{max u_2 u_1} (LinearMap.{u_3, u_4, u_2, u_1} R R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.13 σ₁₂ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.26) (LinearMap.instZero.{u_3, u_4, u_2, u_1} R R₂ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.26 σ₁₂)))) y))","typeFull":"∀ {R : Type u_3} {R₂ : Type u_4} {M : Type u_2} {M₂ : Type u_1} [inst : Semiring R] [inst_1 : Semiring R₂]\n  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R₂ M₂] {σ₁₂ : R →+* R₂}\n  (x y : M), (LinearMap.toAddHom 0).toFun (x + y) = (LinearMap.toAddHom 0).toFun x + (LinearMap.toAddHom 0).toFun y","typeReadable":"∀ {R : Type u_3} {R₂ : Type u_4} {M : Type u_2} {M₂ : Type u_1} [inst : Semiring R] [inst_1 : Semiring R₂]\n  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R₂ M₂] {σ₁₂ : R →+* R₂}\n  (x y : M), (LinearMap.toAddHom 0).toFun (x + y) = (LinearMap.toAddHom 0).toFun x + (LinearMap.toAddHom 0).toFun y","typeReferences":[["LinearMap","instZero"],["RingHom"],["instHAdd"],["Module"],["LinearMap","toAddHom"],["LinearMap"],["OfNat","ofNat"],["HAdd","hAdd"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["AddCommMonoid","toAddCommSemigroup"],["Zero","toOfNat0"],["AddHom","toFun"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Eq"],["Semiring"]],"valueReferences":[["LinearMap","instZero"],["AddHom","map_add'"],["AddCommMonoid","toAddCommSemigroup"],["LinearMap","toAddHom"],["Zero","toOfNat0"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["LinearMap"],["OfNat","ofNat"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","piApply","_proof_1"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_2}} {V : M -> Type.{u_3}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13 : CommSemiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16 : forall (x : M), AddCommMonoid.{u_3} (V x)] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.25 : forall (x : M), Module.{u_1, u_3} R (V x) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16 x)] (e : forall (x : M), LinearMap.{u_1, u_1, u_3, u_1} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))) (V x) R (inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16 x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.25 x) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))) (x : forall (x : M), V x) (y : forall (x : M), V x), Eq.{succ (max u_1 u_2)} (M -> R) (fun (x_1 : M) => DFunLike.coe.{max (succ u_1) (succ u_3), succ u_3, succ u_1} (LinearMap.{u_1, u_1, u_3, u_1} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))) (V x_1) R (inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16 x_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.25 x_1) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))) (V x_1) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : V x_1) => R) (LinearMap.instFunLike.{u_1, u_1, u_3, u_1} R R (V x_1) R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.16 x_1) 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{M : Type u_2} {V : M → Type u_3} [inst : CommSemiring R] [inst_1 : (x : M) → AddCommMonoid (V x)]\n  [inst_2 : (x : M) → Module R (V x)] (e : (x : M) → V x →ₗ[R] R) (x y : (x : M) → V x),\n  (fun x_1 => (e x_1) ((x + y) x_1)) = (fun x_1 => (e x_1) (x x_1)) + fun x => (e x) (y x)","typeReadable":"∀ {R : Type u_1} {M : Type u_2} {V : M → Type u_3} [inst : CommSemiring R] [inst_1 : (x : M) → AddCommMonoid (V x)]\n  [inst_2 : (x : M) → Module R (V x)] (e : (x : M) → V x →ₗ[R] R) (x y : (x : M) → V x),\n  (fun x_1 => (e x_1) ((x + y) x_1)) = (fun x_1 => (e x_1) (x x_1)) + fun x => (e x) (y x)","typeReferences":[["LinearMap","instFunLike"],["instHAdd"],["Module"],["Pi","addCommMonoid"],["CommSemiring"],["CommSemiring","toSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["LinearMap"],["DFunLike","coe"],["HAdd","hAdd"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["AddCommMonoid","toAddCommSemigroup"],["RingHom","id"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Semiring","toModule"],["Eq"]],"valueReferences":[["LinearMap","instFunLike"],["Eq","trans"],["Pi","addCommMonoid"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["congrArg"],["LinearMap","semilinearMapClass"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["funext"],["congrFun'"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Semiring","toModule"],["Eq"],["AddSemigroup","toAdd"],["Distrib","toAdd"],["NonUnitalNonAssocSemiring","toDistrib"],["True"],["instHAdd"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["CommSemiring","toSemiring"],["SemilinearMapClass","toAddHomClass"],["LinearMap"],["map_add"],["HAdd","hAdd"],["eq_self"],["AddCommMonoid","toAddCommSemigroup"],["of_eq_true"],["AddMonoid","toAddSemigroup"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","restrictScalars_injective"],"typeFallback":"forall (R : Type.{u_1}) {S : Type.{u_4}} {M : Type.{u_5}} {M₂ : Type.{u_7}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.13 : Semiring.{u_4} S] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.19 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.22 : AddCommMonoid.{u_7} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.25 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.29 : Module.{u_1, u_7} R M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.33 : Module.{u_4, u_5} S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.37 : Module.{u_4, u_7} S M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.41 : LinearMap.CompatibleSMul.{u_5, u_7, u_1, u_4} M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.22 R S inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.13 (SMulZeroClass.toSMul.{u_1, u_5} R M (AddZero.toZero.{u_5} M (AddZeroClass.toAddZero.{u_5} M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.19)))) 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.22)))) (DistribSMul.toSMulZeroClass.{u_1, u_7} R M₂ (AddMonoid.toAddZeroClass.{u_7} M₂ (AddCommMonoid.toAddMonoid.{u_7} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.22)) (DistribMulAction.toDistribSMul.{u_1, u_7} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_7} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.22) (Module.toDistribMulAction.{u_1, u_7} R M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.29)))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.37], Function.Injective.{max (succ u_5) (succ u_7), max (succ u_5) (succ u_7)} (LinearEquiv.{u_4, u_4, u_5, u_7} S S 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.10) M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.29) (LinearEquiv.restrictScalars.{u_1, u_4, u_5, u_7} R S M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4146065061._hygCtx._hyg.10 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Type u_7} [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 M] [inst_7 : Module S M₂] [inst_8 : LinearMap.CompatibleSMul M M₂ R S],\n  Function.Injective (LinearEquiv.restrictScalars 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13)))) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13))) (Function.smulCommClass.{u_5, u_1, u_1, u_1} M R R R (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.Equiv.Basic.874467674._hygCtx._hyg.13)))) (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.Equiv.Basic.874467674._hygCtx._hyg.13))) (DistribMulAction.toMulAction.{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.Equiv.Basic.874467674._hygCtx._hyg.13))) (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.Equiv.Basic.874467674._hygCtx._hyg.13))))) (Module.toDistribMulAction.{u_1, u_1} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13)))) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13)))))) (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.Equiv.Basic.874467674._hygCtx._hyg.13)))) (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.Equiv.Basic.874467674._hygCtx._hyg.13))) (DistribMulAction.toMulAction.{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.Equiv.Basic.874467674._hygCtx._hyg.13))) (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.Equiv.Basic.874467674._hygCtx._hyg.13))))) (Module.toDistribMulAction.{u_1, u_1} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13)))) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13)))))) (smulCommClass_self.{u_1, u_1} R R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13) (DistribMulAction.toMulAction.{u_1, u_1} R R (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13)) (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.Equiv.Basic.874467674._hygCtx._hyg.13))))) (Module.toDistribMulAction.{u_1, u_1} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13)))) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13)))))))) (forall (x : M), LinearMap.{u_1, u_1, u_9, u_1} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13))) (V x) R (inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.16 x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13)))) (inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.25 x) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13))) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : forall (x : M), LinearMap.{u_1, u_1, u_9, u_1} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13))) (V x) R (inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.16 x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13)))) (inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.25 x) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13))) => LinearMap.{u_1, u_1, max u_5 u_9, max u_1 u_5} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13))) (forall (x : M), V x) (M -> R) 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(CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13)))) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13)))) (LinearMap.instFunLike.{u_1, u_1, max (max u_9 u_5) u_1, max (max u_9 u_5) u_1} R R (forall (x : M), LinearMap.{u_1, u_1, u_9, u_1} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13))) (V x) R (inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.16 x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13)))) (inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.25 x) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13))) (LinearMap.{u_1, u_1, max u_5 u_9, max u_1 u_5} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.13))) (forall (x : M), V x) (M -> R) (Pi.addCommMonoid.{u_5, u_9} M V inst._@.Mathlib.Algebra.Module.Equiv.Basic.874467674._hygCtx._hyg.16) (Pi.addCommMonoid.{u_5, u_1} M (fun (a._@._internal._hyg.0 : M) => R) (fun (i : M) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.16 (Semiring.toModule.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.19) M (LinearMap.addCommMonoid.{u_1, u_1, u_1, u_2} R R R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.16 (Semiring.toModule.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10) 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.27) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.23) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (LinearMap.{u_3, u_3, max u_2 u_1, u_2} S S inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.13)) (LinearMap.{u_1, u_1, u_1, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.16 (Semiring.toModule.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.19) M (LinearMap.addCommMonoid.{u_1, u_1, u_1, u_2} R R R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.16 (Semiring.toModule.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_3, u_1, u_2} R R S R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.16 (Semiring.toModule.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.27) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.23) (LinearMap.addCommMonoid.{u_3, u_3, max u_1 u_2, u_2} S S (LinearMap.{u_1, u_1, u_1, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.16 (Semiring.toModule.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.19) M inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.13 (LinearMap.addCommMonoid.{u_1, u_1, u_1, u_2} R R R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.16 (Semiring.toModule.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.16 (LinearMap.module.{u_1, u_1, u_3, u_1, u_2} R R S R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.16 (Semiring.toModule.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.19 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.27) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.23 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.13))))))) (LinearMap.applyₗ'.{u_1, u_3, u_1, u_2} R S R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.13 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.16 (Semiring.toModule.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.27) (OfNat.ofNat.{u_1} R 1 (One.toOfNat1.{u_1} R (AddMonoidWithOne.toOne.{u_1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10)))))))) y))","typeFull":"∀ (R : Type u_1) (S : Type u_3) (M : Type u_2) [inst : Semiring R] [inst_1 : Semiring S] [inst_2 : AddCommMonoid M]\n  [inst_3 : Module R M] [inst_4 : Module S M] [inst_5 : SMulCommClass R S M] (x y : R →ₗ[R] M),\n  ((LinearMap.applyₗ' S) 1).toFun (x + y) = ((LinearMap.applyₗ' S) 1).toFun x + ((LinearMap.applyₗ' S) 1).toFun y","typeReadable":"∀ (R : Type u_1) (S : Type u_3) (M : Type u_2) [inst : Semiring R] [inst_1 : Semiring S] [inst_2 : AddCommMonoid M]\n  [inst_3 : Module R M] [inst_4 : Module S M] [inst_5 : SMulCommClass R S M] (x y : R →ₗ[R] M),\n  ((LinearMap.applyₗ' S) 1).toFun (x + y) = ((LinearMap.applyₗ' S) 1).toFun x + ((LinearMap.applyₗ' S) 1).toFun 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(R : Type.{u_1}) {S : Type.{u_4}} {M : Type.{u_5}} {M₂ : Type.{u_7}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13 : Semiring.{u_4} S] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.19 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.22 : AddCommMonoid.{u_7} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.25 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.29 : Module.{u_1, u_7} R M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.33 : Module.{u_4, u_5} S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.37 : Module.{u_4, u_7} S M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.41 : LinearMap.CompatibleSMul.{u_5, u_7, u_1, u_4} M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.22 R S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13 (SMulZeroClass.toSMul.{u_1, u_5} R M (AddZero.toZero.{u_5} M (AddZeroClass.toAddZero.{u_5} M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.19)))) 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.22)))) (DistribSMul.toSMulZeroClass.{u_1, u_7} R M₂ (AddMonoid.toAddZeroClass.{u_7} M₂ (AddCommMonoid.toAddMonoid.{u_7} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.22)) (DistribMulAction.toDistribSMul.{u_1, u_7} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_7} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.22) (Module.toDistribMulAction.{u_1, u_7} R M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.29)))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.37] (f : LinearEquiv.{u_4, u_4, u_5, u_7} S S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13 (RingHom.id.{u_4} S (Semiring.toNonAssocSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13)) (RingHom.id.{u_4} S (Semiring.toNonAssocSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13)) (RingHomInvPair.ids.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13) (RingHomInvPair.ids.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13) M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.37) (g : LinearEquiv.{u_4, u_4, u_5, u_7} S S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13 (RingHom.id.{u_4} S (Semiring.toNonAssocSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13)) (RingHom.id.{u_4} S (Semiring.toNonAssocSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13)) (RingHomInvPair.ids.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13) (RingHomInvPair.ids.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13) M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.37), Eq.{1} Prop (Eq.{max (succ u_5) (succ u_7)} (LinearEquiv.{u_1, u_1, u_5, u_7} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.10 (RingHom.id.{u_1} R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.29 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.37 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.41 f) (LinearEquiv.restrictScalars.{u_1, u_4, u_5, u_7} R S M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.29 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.37 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.41 g)) (Eq.{max (succ u_5) (succ u_7)} (LinearEquiv.{u_4, u_4, u_5, u_7} S S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13 (RingHom.id.{u_4} S (Semiring.toNonAssocSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13)) (RingHom.id.{u_4} S (Semiring.toNonAssocSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13)) (RingHomInvPair.ids.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13) (RingHomInvPair.ids.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13) M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.37) f g)","typeFull":"∀ (R : Type u_1) {S : Type u_4} {M : Type u_5} {M₂ : Type u_7} [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 M] [inst_7 : Module S M₂] [inst_8 : LinearMap.CompatibleSMul M M₂ R S] (f g : M ≃ₗ[S] M₂),\n  (LinearEquiv.restrictScalars R f = LinearEquiv.restrictScalars R g) = (f = g)","typeReadable":"∀ (R : Type u_1) {S : Type u_4} {M : Type u_5} {M₂ : Type u_7} [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 M] [inst_7 : Module S M₂] [inst_8 : LinearMap.CompatibleSMul M M₂ R S] (f g : M ≃ₗ[S] M₂),\n  (LinearEquiv.restrictScalars R f = LinearEquiv.restrictScalars R g) = (f = g)","typeReferences":[["LinearMap","CompatibleSMul"],["Module"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["AddZeroClass","toAddZero"],["LinearEquiv","restrictScalars"],["Module","toDistribMulAction"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["RingHomInvPair","ids"],["Eq"],["AddZero","toZero"],["Semiring"],["AddMonoid","toAddZeroClass"],["DistribSMul","toSMulZeroClass"]],"valueReferences":[["LinearEquiv","restrictScalars"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["RingHomInvPair","ids"],["LinearEquiv","restrictScalars_inj"],["LinearEquiv"],["Eq"],["propext"]]},{"isProp":true,"kind":"theorem","name":["AddEquiv","toNatLinearEquiv","_proof_1"],"typeFallback":"forall {M : Type.{u_2}} {M₂ : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3107006938._hygCtx._hyg.13 : AddCommMonoid.{u_2} M] 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AddCommMonoid M] [inst_2 : Module R M] (V : Type u_9)\n  (V₂ : Type u_10), ⇑(LinearEquiv.curry R M V V₂).symm = Function.uncurry","typeReferences":[["Module"],["Pi","addCommMonoid"],["LinearEquiv"],["LinearEquiv","symm"],["DFunLike","coe"],["Pi","Function","module"],["Prod"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["EquivLike","toFunLike"],["RingHomInvPair","ids"],["LinearEquiv","curry"],["LinearEquiv","instEquivLike"],["Eq"],["Function","uncurry"],["Semiring"]],"valueReferences":[["rfl"],["Pi","addCommMonoid"],["LinearEquiv"],["DFunLike","coe"],["LinearEquiv","symm"],["Pi","Function","module"],["Prod"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["EquivLike","toFunLike"],["RingHomInvPair","ids"],["LinearEquiv","curry"],["LinearEquiv","instEquivLike"]]},{"isProp":false,"kind":"definition","name":["LinearEquiv","uniqueOfSubsingleton"],"typeFallback":"forall {R : Type.{u_1}} {R₂ : Type.{u_2}} {M : Type.{u_5}} {M₂ : Type.{u_7}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2730942766._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2730942766._hygCtx._hyg.13 : Semiring.{u_2} R₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2730942766._hygCtx._hyg.16 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2730942766._hygCtx._hyg.19 : AddCommMonoid.{u_7} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2730942766._hygCtx._hyg.22 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2730942766._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2730942766._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2730942766._hygCtx._hyg.26 : Module.{u_2, u_7} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2730942766._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2730942766._hygCtx._hyg.19] {σ₁₂ : RingHom.{u_1, u_2} R R₂ (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2730942766._hygCtx._hyg.10) (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2730942766._hygCtx._hyg.13)} {σ₂₁ : RingHom.{u_2, u_1} R₂ R (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2730942766._hygCtx._hyg.13) (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2730942766._hygCtx._hyg.10)} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2730942766._hygCtx._hyg.40 : RingHomInvPair.{u_1, u_2} R R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2730942766._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2730942766._hygCtx._hyg.13 σ₁₂ σ₂₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2730942766._hygCtx._hyg.44 : RingHomInvPair.{u_2, u_1} R₂ R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2730942766._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2730942766._hygCtx._hyg.10 σ₂₁ σ₁₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2730942766._hygCtx._hyg.48 : Subsingleton.{succ u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2730942766._hygCtx._hyg.51 : Subsingleton.{succ u_2} R₂], Unique.{max (succ u_7) (succ u_5)} (LinearEquiv.{u_1, u_2, u_5, u_7} R R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2730942766._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2730942766._hygCtx._hyg.13 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2730942766._hygCtx._hyg.40 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2730942766._hygCtx._hyg.44 M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2730942766._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2730942766._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2730942766._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2730942766._hygCtx._hyg.26)","typeFull":"{R : Type u_1} →\n  {R₂ : Type u_2} →\n    {M : Type u_5} →\n      {M₂ : Type u_7} →\n        [inst : Semiring R] →\n          [inst_1 : Semiring R₂] →\n            [inst_2 : AddCommMonoid M] →\n              [inst_3 : AddCommMonoid M₂] →\n                [inst_4 : Module R M] →\n                  [inst_5 : Module R₂ M₂] →\n                    {σ₁₂ : R →+* R₂} →\n                      {σ₂₁ : R₂ →+* R} →\n                        [inst_6 : RingHomInvPair σ₁₂ σ₂₁] →\n                          [inst_7 : RingHomInvPair σ₂₁ σ₁₂] →\n                            [Subsingleton R] → [Subsingleton R₂] → Unique (M ≃ₛₗ[σ₁₂] M₂)","typeReadable":"{R : Type u_1} →\n  {R₂ : Type u_2} →\n    {M : Type u_5} →\n      {M₂ : Type u_7} →\n        [inst : Semiring R] →\n          [inst_1 : Semiring R₂] →\n            [inst_2 : AddCommMonoid M] →\n              [inst_3 : AddCommMonoid M₂] →\n                [inst_4 : Module R M] →\n                  [inst_5 : Module R₂ M₂] →\n                    {σ₁₂ : R →+* R₂} →\n                      {σ₂₁ : R₂ →+* R} →\n                        [inst_6 : RingHomInvPair σ₁₂ σ₂₁] →\n                          [inst_7 : RingHomInvPair σ₂₁ σ₁₂] →\n                            [Subsingleton R] → [Subsingleton R₂] → Unique (M ≃ₛₗ[σ₁₂] M₂)","typeReferences":[["Unique"],["RingHom"],["Subsingleton"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["Module"],["LinearEquiv"],["RingHomInvPair"],["Semiring"]],"valueReferences":[["Unique"],["LinearEquiv","uniqueOfSubsingleton","_proof_1"],["LinearEquiv","instUnique"],["inferInstance"],["LinearEquiv"]]},{"isProp":true,"kind":"theorem","name":["Units","toEquiv_mulLeftLinearEquiv"],"typeFallback":"forall {R : Type.{u_9}} {A : Type.{u_10}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12 : Semiring.{u_9} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15 : Semiring.{u_10} A] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.18 : Module.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15)))] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.22 : SMulCommClass.{u_9, u_10, u_10} R A A (SMulZeroClass.toSMul.{u_9, u_10} R A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_9, u_10} R A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15))))) (DistribMulAction.toDistribSMul.{u_9, u_10} R A (MonoidWithZero.toMonoid.{u_9} R (Semiring.toMonoidWithZero.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12)) (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15)))) (Module.toDistribMulAction.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.18)))) (SMulZeroClass.toSMul.{u_10, u_10} A A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_10, u_10} A A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15))))) (instDistribSMul.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15)))))] (u : Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15))), Eq.{succ u_10} (Equiv.{succ u_10, succ u_10} A A) (LinearEquiv.toEquiv.{u_9, u_9, u_10, u_10} R R A A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.18 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12) (DFunLike.coe.{succ u_10, succ u_10, succ u_10} (MonoidHom.{u_10, u_10} (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15))) (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.18) (MulOneClass.toMulOne.{u_10} (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15))) (Units.instMulOneClass.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15)))) (MulOneClass.toMulOne.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.18) (Monoid.toMulOneClass.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.18) (DivInvMonoid.toMonoid.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.18) (Group.toDivInvMonoid.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.18) (LinearEquiv.automorphismGroup.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.18)))))) (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15))) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.18) (MonoidHom.instFunLike.{u_10, u_10} (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15))) (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R 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(MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15)))) (MulOneClass.toMulOne.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A 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(RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.18) (DivInvMonoid.toMonoid.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R 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(Group.toDivInvMonoid.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.18) (LinearEquiv.automorphismGroup.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.18)))))) (Units.mulLeftLinearEquiv.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.15 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1301413755._hygCtx._hyg.22) u)) 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.40 M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.22) (LinearEquiv.symm.{u_1, u_2, u_5, u_7} R R₂ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.26 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.40 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.44 (OfNat.ofNat.{max u_5 u_7} (LinearEquiv.{u_1, u_2, u_5, u_7} R R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.13 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.40 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.44 M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.26) 0 (Zero.toOfNat0.{max u_5 u_7} (LinearEquiv.{u_1, u_2, u_5, u_7} R R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.13 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.40 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.44 M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.26) (LinearEquiv.instZero.{u_1, u_2, u_5, u_7} R R₂ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.26 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.40 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.44 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.48 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.51)))) (OfNat.ofNat.{max u_5 u_7} (LinearEquiv.{u_2, u_1, u_7, u_5} R₂ R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.10 σ₂₁ σ₁₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.44 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.40 M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.22) 0 (Zero.toOfNat0.{max u_5 u_7} (LinearEquiv.{u_2, u_1, u_7, u_5} R₂ R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.10 σ₂₁ σ₁₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.44 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.40 M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.22) (LinearEquiv.instZero.{u_2, u_1, u_7, u_5} R₂ R M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.22 σ₂₁ σ₁₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.44 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.40 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.51 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4279025264._hygCtx._hyg.48)))","typeFull":"∀ {R : Type u_1} {R₂ : Type u_2} {M : Type u_5} {M₂ : Type u_7} [inst : Semiring R] [inst_1 : Semiring R₂]\n  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R₂ M₂] {σ₁₂ : R →+* R₂}\n  {σ₂₁ : R₂ →+* R} [inst_6 : RingHomInvPair σ₁₂ σ₂₁] [inst_7 : RingHomInvPair σ₂₁ σ₁₂] [inst_8 : Subsingleton M]\n  [inst_9 : Subsingleton M₂], LinearEquiv.symm 0 = 0","typeReadable":"∀ {R : Type u_1} {R₂ : Type u_2} {M : Type u_5} {M₂ : Type u_7} [inst : Semiring R] [inst_1 : Semiring R₂]\n  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R₂ M₂] {σ₁₂ : R →+* R₂}\n  {σ₂₁ : R₂ →+* R} [inst_6 : RingHomInvPair σ₁₂ σ₂₁] [inst_7 : RingHomInvPair σ₂₁ σ₁₂] [inst_8 : Subsingleton M]\n  [inst_9 : Subsingleton M₂], LinearEquiv.symm 0 = 0","typeReferences":[["RingHom"],["Module"],["LinearEquiv","instZero"],["LinearEquiv"],["LinearEquiv","symm"],["OfNat","ofNat"],["AddCommMonoid"],["Subsingleton"],["Semiring","toNonAssocSemiring"],["Zero","toOfNat0"],["RingHomInvPair"],["Eq"],["Semiring"]],"valueReferences":[["rfl"],["LinearEquiv","instZero"],["Zero","toOfNat0"],["LinearEquiv"],["LinearEquiv","symm"],["OfNat","ofNat"]]},{"isProp":true,"kind":"theorem","name":["Units","toLinearMap_mulRightLinearEquiv"],"typeFallback":"forall {R : Type.{u_9}} {A : Type.{u_10}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.12 : Semiring.{u_9} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.15 : Semiring.{u_10} A] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.18 : Module.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.15)))] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.22 : IsScalarTower.{u_9, u_10, u_10} R A A (SMulZeroClass.toSMul.{u_9, u_10} R A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_9, u_10} R A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.15))))) (DistribMulAction.toDistribSMul.{u_9, u_10} R A (MonoidWithZero.toMonoid.{u_9} R (Semiring.toMonoidWithZero.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.12)) (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.15)))) (Module.toDistribMulAction.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.18)))) (SMulZeroClass.toSMul.{u_10, u_10} A A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_10, u_10} A A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.15))))) (instDistribSMul.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.15))))) (SMulZeroClass.toSMul.{u_9, u_10} R A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_9, u_10} R A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.15))))) (DistribMulAction.toDistribSMul.{u_9, u_10} R A (MonoidWithZero.toMonoid.{u_9} R (Semiring.toMonoidWithZero.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.12)) (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.15)))) (Module.toDistribMulAction.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.18))))] (u : Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.15))), Eq.{succ u_10} (LinearMap.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.12)) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.18) (LinearEquiv.toLinearMap.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.18 (Units.mulRightLinearEquiv.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.15 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.22 u)) (LinearMap.mulRight.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.12 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.15)) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.22 (Units.val.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2682677825._hygCtx._hyg.15)) u))","typeFull":"∀ {R : Type u_9} {A : Type u_10} [inst : Semiring R] [inst_1 : Semiring A] [inst_2 : Module R A]\n  [inst_3 : IsScalarTower R A A] (u : Aˣ), ↑(Units.mulRightLinearEquiv R u) = LinearMap.mulRight R ↑u","typeReadable":"∀ {R : Type u_9} {A : Type u_10} [inst : Semiring R] [inst_1 : Semiring A] [inst_2 : Module R A]\n  [inst_3 : IsScalarTower R A A] (u : Aˣ), ↑(Units.mulRightLinearEquiv R u) = LinearMap.mulRight R ↑u","typeReferences":[["IsScalarTower"],["Module"],["SMulZeroClass","toSMul"],["AddMonoidWithOne","toAddMonoid"],["instDistribSMul"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Eq"],["NonAssocSemiring","toAddCommMonoidWithOne"],["Units"],["DistribSMul","toSMulZeroClass"],["Units","mulRightLinearEquiv"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["LinearEquiv","toLinearMap"],["AddZeroClass","toAddZero"],["LinearMap"],["Module","toDistribMulAction"],["Units","val"],["RingHomInvPair","ids"],["LinearMap","mulRight"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["rfl"],["Units","mulRightLinearEquiv"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["RingHomInvPair","ids"],["LinearEquiv","toLinearMap"],["LinearMap"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","domMulActCongrRight","_proof_2"],"typeFallback":"forall {S : Type.{u_7}} {R₁ : Type.{u_3}} {R₁' : Type.{u_6}} {R₂' : Type.{u_4}} {M₁ : Type.{u_1}} {M₁' : Type.{u_5}} {M₂' : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 : Semiring.{u_3} R₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 : Semiring.{u_6} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 : Semiring.{u_4} R₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 : AddCommMonoid.{u_1} M₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 : AddCommMonoid.{u_5} M₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 : AddCommMonoid.{u_2} M₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 : Module.{u_3, u_1} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 : Module.{u_6, u_5} R₁' M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 : Module.{u_4, u_2} R₂' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39] {σ₁'₂' : RingHom.{u_6, u_4} R₁' R₂' (Semiring.toNonAssocSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24) (Semiring.toNonAssocSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27)} {σ₂'₁' : RingHom.{u_4, u_6} R₂' R₁' (Semiring.toNonAssocSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27) (Semiring.toNonAssocSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24)} {σ₁₁' : RingHom.{u_3, u_6} R₁ R₁' (Semiring.toNonAssocSemiring.{u_3} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24)} {σ₁₂' : RingHom.{u_3, u_4} R₁ R₂' (Semiring.toNonAssocSemiring.{u_3} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27)} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.106 : RingHomInvPair.{u_6, u_4} R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁'₂' σ₂'₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.110 : RingHomInvPair.{u_4, u_6} R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₂'₁' σ₁'₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.114 : RingHomCompTriple.{u_3, u_6, u_4} R₁ R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₁' σ₁'₂' σ₁₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134 : Semiring.{u_7} S] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.137 : Module.{u_7, u_1} S M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.141 : SMulCommClass.{u_3, u_7, u_1} R₁ S M₁ (SMulZeroClass.toSMul.{u_3, u_1} R₁ M₁ (AddZero.toZero.{u_1} M₁ (AddZeroClass.toAddZero.{u_1} M₁ (AddMonoid.toAddZeroClass.{u_1} M₁ (AddCommMonoid.toAddMonoid.{u_1} M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30)))) (DistribSMul.toSMulZeroClass.{u_3, u_1} R₁ M₁ (AddMonoid.toAddZeroClass.{u_1} M₁ (AddCommMonoid.toAddMonoid.{u_1} M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30)) (DistribMulAction.toDistribSMul.{u_3, u_1} R₁ M₁ (MonoidWithZero.toMonoid.{u_3} R₁ (Semiring.toMonoidWithZero.{u_3} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18)) (AddCommMonoid.toAddMonoid.{u_1} M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30) (Module.toDistribMulAction.{u_3, u_1} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42)))) (SMulZeroClass.toSMul.{u_7, u_1} S M₁ (AddZero.toZero.{u_1} M₁ (AddZeroClass.toAddZero.{u_1} M₁ (AddMonoid.toAddZeroClass.{u_1} M₁ (AddCommMonoid.toAddMonoid.{u_1} M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30)))) (DistribSMul.toSMulZeroClass.{u_7, u_1} S M₁ (AddMonoid.toAddZeroClass.{u_1} M₁ (AddCommMonoid.toAddMonoid.{u_1} M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30)) (DistribMulAction.toDistribSMul.{u_7, u_1} S M₁ (MonoidWithZero.toMonoid.{u_7} S (Semiring.toMonoidWithZero.{u_7} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)) (AddCommMonoid.toAddMonoid.{u_1} M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30) (Module.toDistribMulAction.{u_7, u_1} S M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.137))))] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.146 : RingHomCompTriple.{u_3, u_4, u_6} R₁ R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₂' σ₂'₁' σ₁₁'] (e₂ : LinearEquiv.{u_6, u_4, u_5, u_2} R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.110 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (x._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.199 : S) (x._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.201 : LinearMap.{u_3, u_6, u_1, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50), Eq.{succ (max u_1 u_2)} (LinearMap.{u_3, u_4, u_1, u_2} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (Equiv.toFun.{succ (max u_5 u_1), succ (max u_2 u_1)} (LinearMap.{u_3, u_6, u_1, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.{u_3, u_4, u_1, u_2} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (AddEquiv.toEquiv.{max u_5 u_1, max u_2 u_1} (LinearMap.{u_3, u_6, u_1, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.{u_3, u_4, u_1, u_2} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (LinearMap.instAdd.{u_3, u_6, u_1, u_5} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁') (LinearMap.instAdd.{u_3, u_4, u_1, u_2} R₁ R₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂') (LinearEquiv.arrowCongrAddEquiv.{u_3, u_3, u_6, u_4, u_1, u_1, u_5, u_2} R₁ R₁ R₁' R₂' M₁ M₁ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 (RingHom.id.{u_3} R₁ (Semiring.toNonAssocSemiring.{u_3} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18)) (RingHom.id.{u_3} R₁ (Semiring.toNonAssocSemiring.{u_3} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18)) σ₁'₂' σ₂'₁' σ₁₁' σ₁₂' σ₁₁' σ₁₂' (RingHomInvPair.ids.{u_3} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) (RingHomInvPair.ids.{u_3} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.114 (RingHomCompTriple.ids.{u_3, u_4} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂') inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.146 (RingHomCompTriple.ids.{u_3, u_6} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁') (LinearEquiv.refl.{u_3, u_1} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42) e₂)) (HSMul.hSMul.{u_7, max u_1 u_5, max u_1 u_5} (DomMulAct.{u_7} S) (LinearMap.{u_3, u_6, u_1, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.{u_3, u_6, u_1, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (instHSMul.{u_7, max u_1 u_5} (DomMulAct.{u_7} S) (LinearMap.{u_3, u_6, u_1, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (SMulZeroClass.toSMul.{u_7, max u_1 u_5} (DomMulAct.{u_7} S) (LinearMap.{u_3, u_6, u_1, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (AddZero.toZero.{max u_1 u_5} (LinearMap.{u_3, u_6, u_1, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (AddZeroClass.toAddZero.{max u_1 u_5} (LinearMap.{u_3, u_6, u_1, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (AddMonoid.toAddZeroClass.{max u_1 u_5} (LinearMap.{u_3, u_6, u_1, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (AddCommMonoid.toAddMonoid.{max u_1 u_5} (LinearMap.{u_3, u_6, u_1, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.addCommMonoid.{u_3, u_6, u_1, u_5} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁'))))) (DistribSMul.toSMulZeroClass.{u_7, max u_1 u_5} (DomMulAct.{u_7} S) (LinearMap.{u_3, u_6, u_1, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (AddMonoid.toAddZeroClass.{max u_1 u_5} (LinearMap.{u_3, u_6, u_1, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (AddCommMonoid.toAddMonoid.{max u_1 u_5} (LinearMap.{u_3, u_6, u_1, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.addCommMonoid.{u_3, u_6, u_1, u_5} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁'))) (DistribMulAction.toDistribSMul.{u_7, max u_1 u_5} (DomMulAct.{u_7} S) (LinearMap.{u_3, u_6, u_1, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (MonoidWithZero.toMonoid.{u_7} (DomMulAct.{u_7} S) (Semiring.toMonoidWithZero.{u_7} (DomMulAct.{u_7} S) (DomMulAct.instSemiringOfMulOpposite.{u_7} S (MulOpposite.instSemiring.{u_7} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)))) (AddCommMonoid.toAddMonoid.{max u_1 u_5} (LinearMap.{u_3, u_6, u_1, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.addCommMonoid.{u_3, u_6, u_1, u_5} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁')) (Module.toDistribMulAction.{u_7, max u_1 u_5} (DomMulAct.{u_7} S) (LinearMap.{u_3, u_6, u_1, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (DomMulAct.instSemiringOfMulOpposite.{u_7} S (MulOpposite.instSemiring.{u_7} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)) (LinearMap.addCommMonoid.{u_3, u_6, u_1, u_5} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁') (LinearMap.instModuleDomMulActOfSMulCommClass.{u_3, u_6, u_7, u_1, u_5} R₁ R₁' S M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.137 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.141)))))) (DFunLike.coe.{succ u_7, succ u_7, succ u_7} (Equiv.{succ u_7, succ u_7} S (DomMulAct.{u_7} S)) S (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : S) => DomMulAct.{u_7} S) (EquivLike.toFunLike.{succ u_7, succ u_7, succ u_7} (Equiv.{succ u_7, succ u_7} S (DomMulAct.{u_7} S)) S (DomMulAct.{u_7} S) (Equiv.instEquivLike.{succ u_7, succ u_7} S (DomMulAct.{u_7} S))) (DomMulAct.mk.{u_7} S) x._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.199) x._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.201)) (HSMul.hSMul.{u_7, max u_1 u_2, max u_1 u_2} (DomMulAct.{u_7} S) (LinearMap.{u_3, u_4, u_1, u_2} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (LinearMap.{u_3, u_4, u_1, u_2} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (instHSMul.{u_7, max u_1 u_2} (DomMulAct.{u_7} S) (LinearMap.{u_3, u_4, u_1, u_2} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (SMulZeroClass.toSMul.{u_7, max u_1 u_2} (DomMulAct.{u_7} S) (LinearMap.{u_3, u_4, u_1, u_2} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (AddZero.toZero.{max u_1 u_2} (LinearMap.{u_3, u_4, u_1, u_2} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (AddZeroClass.toAddZero.{max u_1 u_2} (LinearMap.{u_3, u_4, u_1, u_2} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (AddMonoid.toAddZeroClass.{max u_1 u_2} (LinearMap.{u_3, u_4, u_1, u_2} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (LinearMap.{u_3, u_4, u_1, u_2} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (LinearMap.addCommMonoid.{u_3, u_4, u_1, u_2} R₁ R₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂'))))) (DistribSMul.toSMulZeroClass.{u_7, max u_1 u_2} (DomMulAct.{u_7} S) (LinearMap.{u_3, u_4, u_1, u_2} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (AddMonoid.toAddZeroClass.{max u_1 u_2} (LinearMap.{u_3, u_4, u_1, u_2} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (LinearMap.{u_3, u_4, u_1, u_2} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (LinearMap.addCommMonoid.{u_3, u_4, u_1, u_2} R₁ R₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂'))) (DistribMulAction.toDistribSMul.{u_7, max u_1 u_2} (DomMulAct.{u_7} S) (LinearMap.{u_3, u_4, u_1, u_2} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (MonoidWithZero.toMonoid.{u_7} (DomMulAct.{u_7} S) (Semiring.toMonoidWithZero.{u_7} (DomMulAct.{u_7} S) (DomMulAct.instSemiringOfMulOpposite.{u_7} S (MulOpposite.instSemiring.{u_7} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)))) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (LinearMap.{u_3, u_4, u_1, u_2} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (LinearMap.addCommMonoid.{u_3, u_4, u_1, u_2} R₁ R₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂')) (Module.toDistribMulAction.{u_7, max u_1 u_2} (DomMulAct.{u_7} S) (LinearMap.{u_3, u_4, u_1, u_2} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (DomMulAct.instSemiringOfMulOpposite.{u_7} S (MulOpposite.instSemiring.{u_7} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)) (LinearMap.addCommMonoid.{u_3, u_4, u_1, u_2} R₁ R₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂') (LinearMap.instModuleDomMulActOfSMulCommClass.{u_3, u_4, u_7, u_1, u_2} R₁ R₂' S M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.137 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.141)))))) (DFunLike.coe.{succ u_7, succ u_7, succ u_7} (RingHom.{u_7, u_7} (DomMulAct.{u_7} S) (DomMulAct.{u_7} S) (Semiring.toNonAssocSemiring.{u_7} (DomMulAct.{u_7} S) (DomMulAct.instSemiringOfMulOpposite.{u_7} S (MulOpposite.instSemiring.{u_7} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134))) (Semiring.toNonAssocSemiring.{u_7} (DomMulAct.{u_7} S) (DomMulAct.instSemiringOfMulOpposite.{u_7} S (MulOpposite.instSemiring.{u_7} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)))) (DomMulAct.{u_7} S) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : DomMulAct.{u_7} S) => DomMulAct.{u_7} S) (RingHom.instFunLike.{u_7, u_7} (DomMulAct.{u_7} S) (DomMulAct.{u_7} S) (Semiring.toNonAssocSemiring.{u_7} (DomMulAct.{u_7} S) (DomMulAct.instSemiringOfMulOpposite.{u_7} S (MulOpposite.instSemiring.{u_7} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134))) (Semiring.toNonAssocSemiring.{u_7} (DomMulAct.{u_7} S) (DomMulAct.instSemiringOfMulOpposite.{u_7} S (MulOpposite.instSemiring.{u_7} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)))) (RingHom.id.{u_7} (DomMulAct.{u_7} S) (DomMulAct.instNonAssocSemiringOfMulOpposite.{u_7} S (MulOpposite.instNonAssocSemiring.{u_7} S (Semiring.toNonAssocSemiring.{u_7} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)))) (DFunLike.coe.{succ u_7, succ u_7, succ u_7} (Equiv.{succ u_7, succ u_7} S (DomMulAct.{u_7} S)) S (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : S) => DomMulAct.{u_7} S) (EquivLike.toFunLike.{succ u_7, succ u_7, succ u_7} (Equiv.{succ u_7, succ u_7} S (DomMulAct.{u_7} S)) S (DomMulAct.{u_7} S) (Equiv.instEquivLike.{succ u_7, succ u_7} S (DomMulAct.{u_7} S))) (DomMulAct.mk.{u_7} S) x._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.199)) (Equiv.toFun.{succ (max u_5 u_1), succ (max u_2 u_1)} (LinearMap.{u_3, u_6, u_1, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.{u_3, u_4, u_1, u_2} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (AddEquiv.toEquiv.{max u_5 u_1, max u_2 u_1} (LinearMap.{u_3, u_6, u_1, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.{u_3, u_4, u_1, u_2} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (LinearMap.instAdd.{u_3, u_6, u_1, u_5} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁') (LinearMap.instAdd.{u_3, u_4, u_1, u_2} R₁ R₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂') (LinearEquiv.arrowCongrAddEquiv.{u_3, u_3, u_6, u_4, u_1, u_1, u_5, u_2} R₁ R₁ R₁' R₂' M₁ M₁ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 (RingHom.id.{u_3} R₁ (Semiring.toNonAssocSemiring.{u_3} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18)) (RingHom.id.{u_3} R₁ (Semiring.toNonAssocSemiring.{u_3} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18)) σ₁'₂' σ₂'₁' σ₁₁' σ₁₂' σ₁₁' σ₁₂' (RingHomInvPair.ids.{u_3} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) (RingHomInvPair.ids.{u_3} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.114 (RingHomCompTriple.ids.{u_3, u_4} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂') inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.146 (RingHomCompTriple.ids.{u_3, u_6} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁') (LinearEquiv.refl.{u_3, u_1} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42) e₂)) x._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.201))","typeFull":"∀ {S : Type u_7} {R₁ : Type u_3} {R₁' : Type u_6} {R₂' : Type u_4} {M₁ : Type u_1} {M₁' : Type u_5} {M₂' : Type u_2}\n  [inst : Semiring R₁] [inst_1 : Semiring R₁'] [inst_2 : Semiring R₂'] [inst_3 : AddCommMonoid M₁]\n  [inst_4 : AddCommMonoid M₁'] [inst_5 : AddCommMonoid M₂'] [inst_6 : Module R₁ M₁] [inst_7 : Module R₁' M₁']\n  [inst_8 : Module R₂' M₂'] {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} {σ₁₁' : R₁ →+* R₁'} {σ₁₂' : R₁ →+* R₂'}\n  [inst_9 : RingHomInvPair σ₁'₂' σ₂'₁'] [inst_10 : RingHomInvPair σ₂'₁' σ₁'₂']\n  [inst_11 : RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_12 : Semiring S] [inst_13 : Module S M₁]\n  [inst_14 : SMulCommClass R₁ S M₁] [inst_15 : RingHomCompTriple σ₁₂' σ₂'₁' σ₁₁'] (e₂ : M₁' ≃ₛₗ[σ₁'₂'] M₂') (x : S)\n  (x_1 : M₁ →ₛₗ[σ₁₁'] M₁'),\n  ((LinearEquiv.refl R₁ M₁).arrowCongrAddEquiv e₂).toFun (DomMulAct.mk x • x_1) =\n    (RingHom.id Sᵈᵐᵃ) (DomMulAct.mk x) • ((LinearEquiv.refl R₁ M₁).arrowCongrAddEquiv e₂).toFun x_1","typeReadable":"∀ {S : Type u_7} {R₁ : Type u_3} {R₁' : Type u_6} {R₂' : Type u_4} {M₁ : Type u_1} {M₁' : Type u_5} {M₂' : Type u_2}\n  [inst : Semiring R₁] [inst_1 : Semiring R₁'] [inst_2 : Semiring R₂'] [inst_3 : AddCommMonoid M₁]\n  [inst_4 : AddCommMonoid M₁'] [inst_5 : AddCommMonoid M₂'] [inst_6 : Module R₁ M₁] [inst_7 : Module R₁' M₁']\n  [inst_8 : Module R₂' M₂'] {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} {σ₁₁' : R₁ →+* R₁'} {σ₁₂' : R₁ →+* R₂'}\n  [inst_9 : RingHomInvPair σ₁'₂' σ₂'₁'] [inst_10 : RingHomInvPair σ₂'₁' σ₁'₂']\n  [inst_11 : RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_12 : Semiring S] [inst_13 : Module S M₁]\n  [inst_14 : SMulCommClass R₁ S M₁] [inst_15 : RingHomCompTriple σ₁₂' σ₂'₁' σ₁₁'] (e₂ : M₁' ≃ₛₗ[σ₁'₂'] M₂') (x : S)\n  (x_1 : M₁ →ₛₗ[σ₁₁'] M₁'),\n  ((LinearEquiv.refl R₁ M₁).arrowCongrAddEquiv e₂).toFun (DomMulAct.mk x • x_1) =\n    (RingHom.id Sᵈᵐᵃ) (DomMulAct.mk x) • ((LinearEquiv.refl R₁ M₁).arrowCongrAddEquiv e₂).toFun x_1","typeReferences":[["RingHom"],["Equiv","instEquivLike"],["RingHomCompTriple","ids"],["Module"],["DomMulAct","instNonAssocSemiringOfMulOpposite"],["RingHom","instFunLike"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["DFunLike","coe"],["Equiv"],["RingHomCompTriple"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["EquivLike","toFunLike"],["MonoidWithZero","toMonoid"],["LinearMap","instAdd"],["instHSMul"],["Equiv","toFun"],["Eq"],["MulOpposite","instSemiring"],["DistribSMul","toSMulZeroClass"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["DomMulAct"],["AddZeroClass","toAddZero"],["LinearMap"],["AddEquiv","toEquiv"],["LinearMap","instModuleDomMulActOfSMulCommClass"],["DomMulAct","mk"],["LinearMap","addCommMonoid"],["SMulCommClass"],["Module","toDistribMulAction"],["LinearEquiv","arrowCongrAddEquiv"],["HSMul","hSMul"],["MulOpposite","instNonAssocSemiring"],["RingHomInvPair","ids"],["RingHomInvPair"],["AddZero","toZero"],["DomMulAct","instSemiringOfMulOpposite"],["LinearEquiv","refl"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["RingHom"],["Equiv","instEquivLike"],["LinearMap","instFunLike"],["RingHomCompTriple","ids"],["DomMulAct","instNonAssocSemiringOfMulOpposite"],["RingHom","instFunLike"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["DFunLike","coe"],["Equiv"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["LinearMap","ext"],["EquivLike","toFunLike"],["LinearMap","instAdd"],["MonoidWithZero","toMonoid"],["instHSMul"],["Equiv","toFun"],["LinearEquiv","instEquivLike"],["Eq"],["MulOpposite","instSemiring"],["DistribSMul","toSMulZeroClass"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["DomMulAct"],["AddEquiv","toEquiv"],["LinearMap"],["AddZeroClass","toAddZero"],["LinearMap","instModuleDomMulActOfSMulCommClass"],["DomMulAct","mk"],["LinearMap","addCommMonoid"],["eq_self"],["Module","toDistribMulAction"],["of_eq_true"],["LinearEquiv","arrowCongrAddEquiv"],["HSMul","hSMul"],["MulOpposite","instNonAssocSemiring"],["RingHomInvPair","ids"],["AddZero","toZero"],["DomMulAct","instSemiringOfMulOpposite"],["LinearEquiv","refl"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","arrowCongrAddEquiv","_proof_2"],"typeFallback":"forall {R₁ : Type.{u_5}} {R₂ : Type.{u_3}} {R₁' : Type.{u_6}} {R₂' : Type.{u_4}} {M₁ : Type.{u_7}} {M₂ : Type.{u_1}} {M₁' : Type.{u_8}} {M₂' : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 : Semiring.{u_5} R₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 : Semiring.{u_3} R₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 : Semiring.{u_6} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 : Semiring.{u_4} R₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 : AddCommMonoid.{u_7} M₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 : AddCommMonoid.{u_1} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 : AddCommMonoid.{u_8} M₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 : AddCommMonoid.{u_2} M₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 : Module.{u_5, u_7} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 : Module.{u_3, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 : Module.{u_6, u_8} R₁' M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 : Module.{u_4, u_2} R₂' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39] {σ₁₂ : RingHom.{u_5, u_3} R₁ R₂ (Semiring.toNonAssocSemiring.{u_5} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_3} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21)} {σ₂₁ : RingHom.{u_3, u_5} R₂ R₁ (Semiring.toNonAssocSemiring.{u_3} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21) (Semiring.toNonAssocSemiring.{u_5} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18)} {σ₁'₂' : RingHom.{u_6, u_4} R₁' R₂' (Semiring.toNonAssocSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24) (Semiring.toNonAssocSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27)} {σ₂'₁' : RingHom.{u_4, u_6} R₂' R₁' (Semiring.toNonAssocSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27) (Semiring.toNonAssocSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24)} {σ₁₁' : RingHom.{u_5, u_6} R₁ R₁' (Semiring.toNonAssocSemiring.{u_5} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24)} {σ₂₂' : RingHom.{u_3, u_4} R₂ R₂' (Semiring.toNonAssocSemiring.{u_3} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21) (Semiring.toNonAssocSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27)} {σ₂₁' : RingHom.{u_3, u_6} R₂ R₁' (Semiring.toNonAssocSemiring.{u_3} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21) (Semiring.toNonAssocSemiring.{u_6} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24)} {σ₁₂' : RingHom.{u_5, u_4} R₁ R₂' (Semiring.toNonAssocSemiring.{u_5} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27)} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 : RingHomInvPair.{u_5, u_3} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 σ₁₂ σ₂₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 : RingHomInvPair.{u_3, u_5} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 σ₂₁ σ₁₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 : RingHomInvPair.{u_6, u_4} R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₁'₂' σ₂'₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 : RingHomInvPair.{u_4, u_6} R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₂'₁' σ₁'₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.114 : RingHomCompTriple.{u_5, u_6, u_4} R₁ R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₁₁' σ₁'₂' σ₁₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.119 : RingHomCompTriple.{u_3, u_5, u_4} R₂ R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₂₁ σ₁₂' σ₂₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.124 : RingHomCompTriple.{u_3, u_4, u_6} R₂ R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₂₂' σ₂'₁' σ₂₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.129 : RingHomCompTriple.{u_5, u_3, u_6} R₁ R₂ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₂ σ₂₁' σ₁₁'] (e₁ : LinearEquiv.{u_5, u_3, u_7, u_1} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46) (e₂ : LinearEquiv.{u_6, u_4, u_8, u_2} R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54) (f : LinearMap.{u_3, u_4, u_1, u_2} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54), Eq.{succ (max u_1 u_2)} (LinearMap.{u_3, u_4, u_1, u_2} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54) ((fun (f : LinearMap.{u_5, u_6, u_7, u_8} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50) => LinearMap.comp.{u_3, u_5, u_4, u_1, u_7, u_2} R₂ R₁ R₂' M₂ M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 σ₂₁ σ₁₂' σ₂₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.119 (LinearMap.comp.{u_5, u_6, u_4, u_7, u_8, u_2} R₁ R₁' R₂' M₁ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 σ₁₁' σ₁'₂' σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.114 (LinearEquiv.toLinearMap.{u_6, u_4, u_8, u_2} R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 e₂) f) (LinearEquiv.toLinearMap.{u_3, u_5, u_1, u_7} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 σ₂₁ σ₁₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 M₂ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 (LinearEquiv.symm.{u_5, u_3, u_7, u_1} R₁ R₂ M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 e₁))) ((fun (f : LinearMap.{u_3, u_4, u_1, u_2} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 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(e₂ : M₁' ≃ₛₗ[σ₁'₂'] M₂') (f : M₂ →ₛₗ[σ₂₂'] M₂'),\n  (fun f => (↑e₂ ∘ₛₗ f) ∘ₛₗ ↑e₁.symm) ((fun f => (↑e₂.symm ∘ₛₗ f) ∘ₛₗ ↑e₁) f) = f","typeReferences":[["RingHom"],["Module"],["LinearMap","comp"],["LinearEquiv","toLinearMap"],["LinearEquiv"],["LinearMap"],["LinearEquiv","symm"],["RingHomCompTriple"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHomInvPair"],["Eq"],["Semiring"]],"valueReferences":[["LinearMap","instFunLike"],["Eq","trans"],["True"],["LinearMap","comp"],["LinearEquiv","toLinearMap"],["Function","comp"],["LinearEquiv"],["LinearMap"],["LinearEquiv","symm"],["DFunLike","coe"],["congrArg"],["eq_self"],["of_eq_true"],["LinearEquiv","apply_symm_apply"],["LinearMap","ext"],["EquivLike","toFunLike"],["congrFun'"],["LinearEquiv","instEquivLike"],["Eq"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","ringLmapEquivSelf","_proof_2"],"typeFallback":"forall (R : Type.{u_2}) (M : Type.{u_1}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 : 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10)))) x)) x","typeFull":"∀ (R : Type u_2) (M : Type u_1) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (x : M),\n  (fun f => f 1) (LinearMap.smulRight 1 x) = 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  (fun f => f 1) (LinearMap.smulRight 1 x) = x","typeReferences":[["LinearMap","instFunLike"],["Module"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["DistribMulAction","toMulAction"],["Module","End","instOne"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Semiring","toModule"],["Eq"],["NonAssocSemiring","toAddCommMonoidWithOne"],["LinearMap","smulRight"],["IsScalarTower","left"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["Semiring","toMonoidWithZero"],["LinearMap"],["OfNat","ofNat"],["Module","toDistribMulAction"],["One","toOfNat1"],["AddMonoidWithOne","toOne"],["Semiring"]],"valueReferences":[["LinearMap","instFunLike"],["Eq","trans"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["congrArg"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["DistribMulAction","toMulAction"],["congrFun'"],["Module","End","instOne"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Semiring","toModule"],["Eq"],["NonAssocSemiring","toAddCommMonoidWithOne"],["LinearMap","smulRight"],["IsScalarTower","left"],["True"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["Semiring","toMonoidWithZero"],["LinearMap"],["OfNat","ofNat"],["eq_self"],["Module","toDistribMulAction"],["One","toOfNat1"],["of_eq_true"],["one_smul"],["AddMonoidWithOne","toOne"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","conj_refl"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_5}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10 : CommSemiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.13 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.22 : Module.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.13] (f : Module.End.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.22), Eq.{succ u_5} (Module.End.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.22) (DFunLike.coe.{succ u_5, succ u_5, succ u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10))) (RingHomInvPair.ids.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10)) (Module.End.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.22) (Module.End.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.22) (LinearMap.addCommMonoid.{u_1, u_1, u_5, u_5} R R M M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.22 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10)))) (LinearMap.addCommMonoid.{u_1, u_1, u_5, u_5} R R M M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.22 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10)))) (LinearMap.module.{u_1, u_1, u_1, u_5, u_5} R R R M M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.22 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.22 (smulCommClass_self.{u_1, u_5} R M (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_5} R M (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.22)))) (LinearMap.module.{u_1, u_1, u_1, u_5, u_5} R R R M M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.22 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.22 (smulCommClass_self.{u_1, u_5} R M (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_5} R M (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.22))))) (Module.End.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.22) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : Module.End.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.22) => Module.End.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.22) (EquivLike.toFunLike.{succ u_5, succ u_5, succ u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10))) (RingHomInvPair.ids.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10)) (Module.End.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.22) (Module.End.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.22) (LinearMap.addCommMonoid.{u_1, u_1, u_5, u_5} R R M M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.22 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10)))) (LinearMap.addCommMonoid.{u_1, u_1, u_5, u_5} R R M M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.22 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10)))) (LinearMap.module.{u_1, u_1, u_1, u_5, u_5} R R R M M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.22 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.22 (smulCommClass_self.{u_1, u_5} R M (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_5} R M (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.22)))) (LinearMap.module.{u_1, u_1, u_1, u_5, u_5} R R R M M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1423612827._hygCtx._hyg.10) 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(RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHomInvPair.ids.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36) (RingHomInvPair.ids.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36) (RingHomInvPair.ids.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36) (RingHomInvPair.ids.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36) (LinearEquiv.automorphismGroup._proof_7.{u_4} R 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(LinearEquiv.refl R M)).invFun\n    (e.arrowCongrAddEquiv (LinearEquiv.refl R M)).toFun","typeReadable":"∀ (M : Type u_1) {M₂ : Type u_2} {M₃ : Type u_3} [inst : AddCommMonoid M] [inst_1 : AddCommMonoid M₂]\n  [inst_2 : AddCommMonoid M₃] {R : Type u_4} [inst_3 : Semiring R] [inst_4 : Module R M₂] [inst_5 : Module R M₃]\n  [inst_6 : Module R M] (e : M₂ ≃ₗ[R] M₃),\n  Function.RightInverse (e.arrowCongrAddEquiv (LinearEquiv.refl R M)).invFun\n    (e.arrowCongrAddEquiv (LinearEquiv.refl R 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LinearEquiv.funCongrLeft R M (Equiv.refl n) = LinearEquiv.refl R (n → M)","typeReferences":[["LinearEquiv","funCongrLeft"],["Module"],["Pi","addCommMonoid"],["LinearEquiv"],["Pi","Function","module"],["Equiv","refl"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["RingHomInvPair","ids"],["Eq"],["Semiring"],["LinearEquiv","refl"]],"valueReferences":[["rfl"],["Equiv","refl"],["LinearEquiv","funCongrLeft"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Pi","addCommMonoid"],["RingHomInvPair","ids"],["LinearEquiv"],["Pi","Function","module"]]},{"isProp":true,"kind":"theorem","name":["Units","symm_mulRightLinearEquiv_apply"],"typeFallback":"forall (R : Type.{u_9}) {A : Type.{u_10}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.472063986._hygCtx._hyg.12 : Semiring.{u_9} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.472063986._hygCtx._hyg.15 : Semiring.{u_10} A] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.472063986._hygCtx._hyg.18 : Module.{u_9, u_10} R A 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[inst_1 : (x : M) → AddCommMonoid (V x)] →\n          [inst_2 : (x : M) → Module R (V x)] → ((x : M) → V x →ₗ[R] R) →ₗ[R] ((x : M) → V x) →ₗ[R] M → 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{R₁ : Type.{u_9}} {R₂ : Type.{u_10}} {R₁' : Type.{u_12}} {R₂' : Type.{u_13}} {M₁ : Type.{u_17}} {M₂ : Type.{u_18}} {M₁' : Type.{u_20}} {M₂' : Type.{u_21}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.50 : Semiring.{u_9} R₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.53 : Semiring.{u_10} R₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.59 : CommSemiring.{u_12} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.62 : CommSemiring.{u_13} R₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.74 : AddCommMonoid.{u_17} M₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.77 : AddCommMonoid.{u_18} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.83 : AddCommMonoid.{u_20} M₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.86 : AddCommMonoid.{u_21} M₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.98 : Module.{u_9, u_17} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.74] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.102 : Module.{u_10, u_18} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.77] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.110 : Module.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.83] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.114 : Module.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.86] {σ₁₂ : RingHom.{u_9, u_10} R₁ R₂ (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.53)} {σ₂₁ : RingHom.{u_10, u_9} R₂ R₁ (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.53) (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.50)} {σ₁'₂' : RingHom.{u_12, u_13} R₁' R₂' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.59)) (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.62))} {σ₂'₁' : RingHom.{u_13, u_12} R₂' R₁' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.62)) 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.59))} {σ₁₂' : RingHom.{u_9, u_13} R₁ R₂' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.62))} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.285 : RingHomInvPair.{u_9, u_10} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.53 σ₁₂ σ₂₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.289 : RingHomInvPair.{u_10, u_9} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.50 σ₂₁ σ₁₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.293 : RingHomInvPair.{u_12, u_13} R₁' R₂' 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.110) (x : M₂), Eq.{succ u_21} M₂' (DFunLike.coe.{max (succ u_18) (succ u_21), succ u_18, succ u_21} (LinearMap.{u_10, u_13, u_18, u_21} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.114) M₂ (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M₂) => M₂') (LinearMap.instFunLike.{u_10, u_13, u_18, u_21} R₂ R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.114 σ₂₂') (DFunLike.coe.{max (max (max (succ u_17) (succ u_18)) (succ u_20)) (succ u_21), max (succ u_17) (succ u_20), max (succ u_18) (succ u_21)} (LinearEquiv.{u_12, u_13, max u_20 u_17, max u_21 u_18} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.297 (LinearMap.{u_9, u_12, u_17, u_20} R₁ R₁' 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.114))))) (LinearMap.{u_9, u_12, u_17, u_20} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.110) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : LinearMap.{u_9, u_12, u_17, u_20} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.110) => LinearMap.{u_10, u_13, u_18, u_21} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.114) (EquivLike.toFunLike.{max (max (max (succ u_17) (succ u_18)) (succ u_20)) (succ u_21), max (succ u_17) (succ u_20), max (succ u_18) (succ u_21)} (LinearEquiv.{u_12, u_13, max u_20 u_17, max u_21 u_18} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.297 (LinearMap.{u_9, u_12, u_17, u_20} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.110) (LinearMap.{u_10, u_13, u_18, u_21} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.114) (LinearMap.addCommMonoid.{u_9, u_12, u_17, u_20} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.110 σ₁₁') (LinearMap.addCommMonoid.{u_10, u_13, u_18, u_21} R₂ R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.114 σ₂₂') (LinearMap.module.{u_9, u_12, u_12, u_17, u_20} R₁ R₁' R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.110 σ₁₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.110)))) (LinearMap.module.{u_10, u_13, u_13, u_18, u_21} R₂ R₂' R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.114 σ₂₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.114))))) (LinearMap.{u_9, u_12, u_17, u_20} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.110) (LinearMap.{u_10, u_13, u_18, u_21} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.114) (LinearEquiv.instEquivLike.{u_12, u_13, max u_17 u_20, max u_18 u_21} R₁' R₂' (LinearMap.{u_9, u_12, u_17, u_20} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.110) (LinearMap.{u_10, u_13, u_18, u_21} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.114) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.62) (LinearMap.addCommMonoid.{u_9, u_12, u_17, u_20} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.110 σ₁₁') (LinearMap.addCommMonoid.{u_10, u_13, u_18, u_21} R₂ R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.114 σ₂₂') (LinearMap.module.{u_9, u_12, u_12, u_17, u_20} R₁ R₁' R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.110 σ₁₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.110)))) (LinearMap.module.{u_10, u_13, u_13, u_18, u_21} R₂ R₂' R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.114 σ₂₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.114)))) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.297)) (LinearEquiv.arrowCongr.{u_9, u_10, u_12, u_13, u_17, u_18, u_20, u_21} R₁ R₂ R₁' R₂' M₁ M₂ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.59 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.62 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.114 σ₁₂ σ₂₁ σ₁'₂' σ₂'₁' σ₁₁' σ₂₂' σ₂₁' σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.285 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.289 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.297 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.351 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.356 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.361 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.366 e₁ e₂) f) x) (DFunLike.coe.{max (succ u_20) (succ u_21), succ u_20, succ u_21} (LinearEquiv.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.297 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.114) M₁' (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M₁') => M₂') (EquivLike.toFunLike.{max (succ u_20) (succ u_21), succ u_20, succ u_21} (LinearEquiv.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.297 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.114) M₁' M₂' (LinearEquiv.instEquivLike.{u_12, u_13, u_20, u_21} R₁' R₂' M₁' M₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.114 σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.297)) e₂ (DFunLike.coe.{max (succ u_17) (succ u_20), succ u_17, succ u_20} (LinearMap.{u_9, u_12, u_17, u_20} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.110) M₁ (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M₁) => M₁') (LinearMap.instFunLike.{u_9, u_12, 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.98) M₂ (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M₂) => M₁) (EquivLike.toFunLike.{max (succ u_17) (succ u_18), succ u_18, succ u_17} (LinearEquiv.{u_10, u_9, u_18, u_17} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.50 σ₂₁ σ₁₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.289 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.285 M₂ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.98) M₂ M₁ (LinearEquiv.instEquivLike.{u_10, u_9, u_18, u_17} R₂ R₁ M₂ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.98 σ₂₁ σ₁₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.289 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.285)) (LinearEquiv.symm.{u_9, u_10, u_17, u_18} R₁ R₂ M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.102 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.285 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3038038552._hygCtx._hyg.289 e₁) x)))","typeFull":"∀ {R₁ : Type u_9} {R₂ : Type u_10} {R₁' : Type u_12} {R₂' : Type u_13} {M₁ : Type u_17} {M₂ : Type u_18}\n  {M₁' : Type u_20} {M₂' : Type u_21} [inst : Semiring R₁] [inst_1 : Semiring R₂] [inst_2 : CommSemiring R₁']\n  [inst_3 : CommSemiring R₂'] [inst_4 : AddCommMonoid M₁] [inst_5 : AddCommMonoid M₂] [inst_6 : AddCommMonoid M₁']\n  [inst_7 : AddCommMonoid M₂'] [inst_8 : Module R₁ M₁] [inst_9 : Module R₂ M₂] [inst_10 : Module R₁' M₁']\n  [inst_11 : Module R₂' M₂'] {σ₁₂ : R₁ →+* R₂} {σ₂₁ : R₂ →+* R₁} {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'}\n  {σ₁₁' : R₁ →+* R₁'} {σ₂₂' : R₂ →+* R₂'} {σ₂₁' : R₂ →+* R₁'} {σ₁₂' : R₁ →+* R₂'} [inst_12 : RingHomInvPair σ₁₂ σ₂₁]\n  [inst_13 : RingHomInvPair σ₂₁ σ₁₂] [inst_14 : RingHomInvPair σ₁'₂' σ₂'₁'] [inst_15 : RingHomInvPair σ₂'₁' σ₁'₂']\n  [inst_16 : RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_17 : RingHomCompTriple σ₂₁ σ₁₂' σ₂₂']\n  [inst_18 : RingHomCompTriple σ₂₂' σ₂'₁' σ₂₁'] [inst_19 : RingHomCompTriple σ₁₂ σ₂₁' σ₁₁'] (e₁ : M₁ ≃ₛₗ[σ₁₂] M₂)\n  (e₂ : M₁' ≃ₛₗ[σ₁'₂'] M₂') (f : M₁ →ₛₗ[σ₁₁'] M₁') (x : M₂), ((e₁.arrowCongr e₂) f) x = e₂ (f (e₁.symm x))","typeReadable":"∀ {R₁ : Type u_9} {R₂ : Type u_10} {R₁' : Type u_12} {R₂' : Type u_13} {M₁ : Type u_17} {M₂ : Type u_18}\n  {M₁' : Type u_20} {M₂' : Type u_21} [inst : Semiring R₁] [inst_1 : Semiring R₂] [inst_2 : CommSemiring R₁']\n  [inst_3 : CommSemiring R₂'] [inst_4 : AddCommMonoid M₁] [inst_5 : AddCommMonoid M₂] [inst_6 : AddCommMonoid M₁']\n  [inst_7 : AddCommMonoid M₂'] [inst_8 : Module R₁ M₁] [inst_9 : Module R₂ M₂] [inst_10 : Module R₁' M₁']\n  [inst_11 : Module R₂' M₂'] {σ₁₂ : R₁ →+* R₂} {σ₂₁ : R₂ →+* R₁} {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'}\n  {σ₁₁' : R₁ →+* R₁'} {σ₂₂' : R₂ →+* R₂'} {σ₂₁' : R₂ →+* R₁'} {σ₁₂' : R₁ →+* R₂'} [inst_12 : RingHomInvPair σ₁₂ σ₂₁]\n  [inst_13 : RingHomInvPair σ₂₁ σ₁₂] [inst_14 : RingHomInvPair σ₁'₂' σ₂'₁'] [inst_15 : RingHomInvPair σ₂'₁' σ₁'₂']\n  [inst_16 : RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_17 : RingHomCompTriple σ₂₁ σ₁₂' σ₂₂']\n  [inst_18 : RingHomCompTriple σ₂₂' σ₂'₁' σ₂��'] [inst_19 : RingHomCompTriple σ₁₂ σ₂₁' σ₁₁'] (e₁ : M₁ ≃ₛₗ[σ₁₂] M₂)\n  (e₂ : M₁' ≃ₛₗ[σ₁'₂'] M₂') (f : M₁ →ₛₗ[σ₁₁'] M₁') (x : M₂), ((e₁.arrowCongr e₂) f) x = e₂ (f (e₁.symm x))","typeReferences":[["RingHom"],["smulCommClass_self"],["LinearMap","instFunLike"],["CommMonoid","toMonoid"],["Module"],["CommSemiring"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["DFunLike","coe"],["RingHomCompTriple"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["EquivLike","toFunLike"],["DistribMulAction","toMulAction"],["Eq"],["LinearEquiv","instEquivLike"],["CommSemiring","toSemiring"],["LinearMap","module"],["LinearMap"],["LinearEquiv","symm"],["CommSemiring","toCommMonoid"],["LinearEquiv","arrowCongr"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["RingHomInvPair"],["Semiring"]],"valueReferences":[["rfl"],["smulCommClass_self"],["LinearMap","instFunLike"],["CommMonoid","toMonoid"],["CommSemiring","toSemiring"],["LinearMap","module"],["AddCommMonoid","toAddMonoid"],["LinearMap"],["LinearEquiv"],["DFunLike","coe"],["LinearEquiv","arrowCongr"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["EquivLike","toFunLike"],["DistribMulAction","toMulAction"],["LinearEquiv","instEquivLike"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","restrictScalars_inj"],"typeFallback":"forall (R : Type.{u_1}) {S : Type.{u_4}} {M : Type.{u_5}} {M₂ : Type.{u_7}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13 : Semiring.{u_4} S] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.19 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.22 : AddCommMonoid.{u_7} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.25 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.29 : Module.{u_1, u_7} R M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.33 : Module.{u_4, u_5} S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.37 : Module.{u_4, u_7} S M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.41 : LinearMap.CompatibleSMul.{u_5, u_7, u_1, u_4} M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.22 R S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13 (SMulZeroClass.toSMul.{u_1, u_5} R M (AddZero.toZero.{u_5} M (AddZeroClass.toAddZero.{u_5} M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.19)))) (DistribSMul.toSMulZeroClass.{u_1, u_5} R M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.19)) (DistribMulAction.toDistribSMul.{u_1, u_5} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.19) (Module.toDistribMulAction.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.25)))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.33 (SMulZeroClass.toSMul.{u_1, u_7} R M₂ (AddZero.toZero.{u_7} M₂ (AddZeroClass.toAddZero.{u_7} M₂ (AddMonoid.toAddZeroClass.{u_7} M₂ (AddCommMonoid.toAddMonoid.{u_7} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.22)))) (DistribSMul.toSMulZeroClass.{u_1, u_7} R M₂ (AddMonoid.toAddZeroClass.{u_7} M₂ (AddCommMonoid.toAddMonoid.{u_7} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.22)) (DistribMulAction.toDistribSMul.{u_1, u_7} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_7} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.22) (Module.toDistribMulAction.{u_1, u_7} R M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.29)))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.37] (f : LinearEquiv.{u_4, u_4, u_5, u_7} S S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13 (RingHom.id.{u_4} S (Semiring.toNonAssocSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13)) (RingHom.id.{u_4} S (Semiring.toNonAssocSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13)) (RingHomInvPair.ids.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13) (RingHomInvPair.ids.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13) M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.37) (g : LinearEquiv.{u_4, u_4, u_5, u_7} S S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13 (RingHom.id.{u_4} S (Semiring.toNonAssocSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13)) (RingHom.id.{u_4} S (Semiring.toNonAssocSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13)) (RingHomInvPair.ids.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13) (RingHomInvPair.ids.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.13) M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.37), Iff (Eq.{max (succ u_5) (succ u_7)} (LinearEquiv.{u_1, u_1, u_5, u_7} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2573026654._hygCtx._hyg.10 (RingHom.id.{u_1} R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.13)} {σ₂₁ : RingHom.{u_2, u_1} R₂ R (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.13) (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.10)} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.40 : RingHomInvPair.{u_1, u_2} R R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.13 σ₁₂ σ₂₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.44 : RingHomInvPair.{u_2, u_1} R₂ R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.10 σ₂₁ σ₁₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.48 : Subsingleton.{succ u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.51 : 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i)","typeReferences":[["LinearMap","funLeft"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["LinearMap","instFunLike"],["RingHom","id"],["Module"],["Pi","addCommMonoid"],["LinearMap"],["Eq"],["DFunLike","coe"],["Pi","Function","module"],["Semiring"]],"valueReferences":[["rfl"],["LinearMap","funLeft"],["Semiring","toNonAssocSemiring"],["LinearMap","instFunLike"],["RingHom","id"],["Pi","addCommMonoid"],["LinearMap"],["DFunLike","coe"],["Pi","Function","module"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","applyDistribMulAction","_proof_1"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 : Module.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) M (fun (x1._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.51 : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) (x2._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.51 : M) => DFunLike.coe.{succ u_2, succ u_2, succ u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (EquivLike.toFunLike.{succ u_2, succ u_2, succ u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) M M (LinearEquiv.instEquivLike.{u_1, u_1, u_2, u_2} R R M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) (instHMul.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) (Semigroup.toMul.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) (Monoid.toSemigroup.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) (DivInvMonoid.toMonoid.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) (Group.toDivInvMonoid.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) (LinearEquiv.automorphismGroup.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25)))))) x._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.63 x._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.65) x._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.67) (HSMul.hSMul.{u_2, u_2, u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) M M (instHSMul.{u_2, u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) M (SMul.mk.{u_2, u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) M (fun (x1._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.51 : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) (x2._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.51 : M) => DFunLike.coe.{succ u_2, succ u_2, succ u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (EquivLike.toFunLike.{succ u_2, succ u_2, succ u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) M M (LinearEquiv.instEquivLike.{u_1, u_1, u_2, u_2} R R M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10))) x1._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.51 x2._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.51))) (HMul.hMul.{u_2, u_2, u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) (instHMul.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) (Semigroup.toMul.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) (Monoid.toSemigroup.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) (DivInvMonoid.toMonoid.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) (Group.toDivInvMonoid.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) (LinearEquiv.automorphismGroup.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25)))))) x._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.63 x._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.65) x._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.67)","typeFull":"∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (x x_1 : M ≃ₗ[R] M)\n  (x_2 : 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] (x x_1 : M ≃ₗ[R] M)\n  (x_2 : M), (x * x_1) • x_2 = (x * x_1) • x_2","typeReferences":[["SMul","mk"],["Module"],["HMul","hMul"],["LinearEquiv"],["DFunLike","coe"],["Semigroup","toMul"],["LinearEquiv","automorphismGroup"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["DivInvMonoid","toMonoid"],["RingHom","id"],["HSMul","hSMul"],["EquivLike","toFunLike"],["RingHomInvPair","ids"],["instHMul"],["instHSMul"],["Monoid","toSemigroup"],["LinearEquiv","instEquivLike"],["Eq"],["Group","toDivInvMonoid"],["Semiring"]],"valueReferences":[["rfl"],["SMul","mk"],["HMul","hMul"],["LinearEquiv"],["DFunLike","coe"],["Semigroup","toMul"],["LinearEquiv","automorphismGroup"],["Semiring","toNonAssocSemiring"],["DivInvMonoid","toMonoid"],["RingHom","id"],["HSMul","hSMul"],["EquivLike","toFunLike"],["RingHomInvPair","ids"],["instHSMul"],["instHMul"],["Monoid","toSemigroup"],["LinearEquiv","instEquivLike"],["Group","toDivInvMonoid"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","conjRingEquiv","_proof_1"],"typeFallback":"forall {R₁ : Type.{u_1}} {R₂ : Type.{u_4}} {M₁ : Type.{u_2}} {M₂ : Type.{u_3}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 : Semiring.{u_1} R₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 : Semiring.{u_4} R₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 : AddCommMonoid.{u_2} M₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 : AddCommMonoid.{u_3} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 : Module.{u_1, u_2} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 : Module.{u_4, u_3} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33] {σ₁₂ : RingHom.{u_1, u_4} R₁ R₂ (Semiring.toNonAssocSemiring.{u_1} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_4} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21)} {σ₂₁ : RingHom.{u_4, u_1} R₂ R₁ (Semiring.toNonAssocSemiring.{u_4} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21) (Semiring.toNonAssocSemiring.{u_1} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18)} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.98 : RingHomInvPair.{u_1, u_4} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 σ₁₂ σ₂₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.102 : RingHomInvPair.{u_4, u_1} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 σ₂₁ σ₁₂] (e : LinearEquiv.{u_1, u_4, u_2, u_3} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.102 M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46) (x : LinearMap.{u_1, u_1, u_2, u_2} R₁ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 (RingHom.id.{u_1} R₁ (Semiring.toNonAssocSemiring.{u_1} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18)) M₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42) (y : LinearMap.{u_1, u_1, u_2, u_2} R₁ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 (RingHom.id.{u_1} R₁ (Semiring.toNonAssocSemiring.{u_1} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18)) M₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42), Eq.{succ u_3} (LinearMap.{u_4, u_4, u_3, u_3} R₂ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 (RingHom.id.{u_4} R₂ (Semiring.toNonAssocSemiring.{u_4} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21)) M₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46) (Equiv.toFun.{succ u_2, succ u_3} (LinearMap.{u_1, u_1, u_2, u_2} R₁ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 (RingHom.id.{u_1} R₁ (Semiring.toNonAssocSemiring.{u_1} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18)) M₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42) (LinearMap.{u_4, u_4, u_3, u_3} R₂ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 (RingHom.id.{u_4} R₂ (Semiring.toNonAssocSemiring.{u_4} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21)) M₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46) (AddEquiv.toEquiv.{u_2, u_3} (LinearMap.{u_1, u_1, u_2, u_2} R₁ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 (RingHom.id.{u_1} R₁ (Semiring.toNonAssocSemiring.{u_1} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18)) M₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42) (LinearMap.{u_4, u_4, u_3, u_3} R₂ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 (RingHom.id.{u_4} R₂ (Semiring.toNonAssocSemiring.{u_4} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21)) M₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46) (LinearMap.instAdd.{u_1, u_1, u_2, u_2} R₁ R₁ M₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 (RingHom.id.{u_1} R₁ (Semiring.toNonAssocSemiring.{u_1} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18))) (LinearMap.instAdd.{u_4, u_4, u_3, u_3} R₂ R₂ M₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 (RingHom.id.{u_4} R₂ (Semiring.toNonAssocSemiring.{u_4} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21))) (LinearEquiv.arrowCongrAddEquiv.{u_1, u_4, u_1, u_4, u_2, u_3, u_2, u_3} R₁ R₂ R₁ R₂ M₁ M₂ M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 σ₁₂ σ₂₁ σ₁₂ σ₂₁ (RingHom.id.{u_1} R₁ (Semiring.toNonAssocSemiring.{u_1} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18)) (RingHom.id.{u_4} R₂ (Semiring.toNonAssocSemiring.{u_4} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21)) σ₂₁ σ₁₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.102 (RingHomCompTriple.ids.{u_1, u_4} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 σ₁₂) (RingHomInvPair.triples₂.{u_1, u_4} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.98) (RingHomCompTriple.ids.{u_4, u_1} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 σ₂₁) (RingHomInvPair.triples₂.{u_4, u_1} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 σ₂₁ σ₁₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.102) e e)) (HAdd.hAdd.{u_2, u_2, u_2} (LinearMap.{u_1, u_1, u_2, u_2} R₁ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 (RingHom.id.{u_1} R₁ (Semiring.toNonAssocSemiring.{u_1} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18)) M₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42) (LinearMap.{u_1, u_1, u_2, u_2} R₁ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 (RingHom.id.{u_1} R₁ (Semiring.toNonAssocSemiring.{u_1} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18)) M₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42) (LinearMap.{u_1, u_1, u_2, u_2} R₁ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 (RingHom.id.{u_1} R₁ (Semiring.toNonAssocSemiring.{u_1} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18)) M₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42) (instHAdd.{u_2} (LinearMap.{u_1, u_1, u_2, u_2} R₁ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 (RingHom.id.{u_1} R₁ (Semiring.toNonAssocSemiring.{u_1} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18)) M₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42) (LinearMap.instAdd.{u_1, u_1, u_2, u_2} R₁ R₁ M₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 (RingHom.id.{u_1} R₁ (Semiring.toNonAssocSemiring.{u_1} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18)))) x y)) (HAdd.hAdd.{u_3, u_3, u_3} (LinearMap.{u_4, u_4, u_3, u_3} R₂ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 (RingHom.id.{u_4} R₂ (Semiring.toNonAssocSemiring.{u_4} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21)) M₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46) (LinearMap.{u_4, u_4, u_3, u_3} R₂ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 (RingHom.id.{u_4} R₂ (Semiring.toNonAssocSemiring.{u_4} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21)) M₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46) (LinearMap.{u_4, u_4, u_3, u_3} R₂ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 (RingHom.id.{u_4} R₂ (Semiring.toNonAssocSemiring.{u_4} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21)) M₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46) (instHAdd.{u_3} (LinearMap.{u_4, u_4, u_3, u_3} R₂ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 (RingHom.id.{u_4} R₂ (Semiring.toNonAssocSemiring.{u_4} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21)) M₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46) (LinearMap.instAdd.{u_4, u_4, u_3, u_3} R₂ R₂ M₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 (RingHom.id.{u_4} R₂ (Semiring.toNonAssocSemiring.{u_4} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21)))) (Equiv.toFun.{succ u_2, succ u_3} (LinearMap.{u_1, u_1, u_2, u_2} R₁ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 (RingHom.id.{u_1} R₁ (Semiring.toNonAssocSemiring.{u_1} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18)) M₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42) (LinearMap.{u_4, u_4, u_3, u_3} R₂ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 (RingHom.id.{u_4} R₂ (Semiring.toNonAssocSemiring.{u_4} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21)) M₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46) (AddEquiv.toEquiv.{u_2, u_3} (LinearMap.{u_1, u_1, u_2, u_2} R₁ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 (RingHom.id.{u_1} R₁ (Semiring.toNonAssocSemiring.{u_1} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18)) M₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42) (LinearMap.{u_4, u_4, u_3, u_3} R₂ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 (RingHom.id.{u_4} R₂ (Semiring.toNonAssocSemiring.{u_4} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21)) M₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46) (LinearMap.instAdd.{u_1, u_1, u_2, u_2} R₁ R₁ M₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 (RingHom.id.{u_1} R₁ (Semiring.toNonAssocSemiring.{u_1} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18))) (LinearMap.instAdd.{u_4, u_4, u_3, u_3} R₂ R₂ M₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 (RingHom.id.{u_4} R₂ (Semiring.toNonAssocSemiring.{u_4} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21))) (LinearEquiv.arrowCongrAddEquiv.{u_1, u_4, u_1, u_4, u_2, u_3, u_2, u_3} R₁ R₂ R₁ R₂ M₁ M₂ M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 σ₁₂ σ₂₁ σ₁₂ σ₂₁ (RingHom.id.{u_1} R₁ (Semiring.toNonAssocSemiring.{u_1} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18)) (RingHom.id.{u_4} R₂ (Semiring.toNonAssocSemiring.{u_4} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21)) σ₂₁ σ₁₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.102 (RingHomCompTriple.ids.{u_1, u_4} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 σ₁₂) (RingHomInvPair.triples₂.{u_1, u_4} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.98) (RingHomCompTriple.ids.{u_4, u_1} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 σ₂₁) (RingHomInvPair.triples₂.{u_4, u_1} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 σ₂₁ σ₁₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.102) e e)) x) (Equiv.toFun.{succ u_2, succ u_3} (LinearMap.{u_1, u_1, u_2, u_2} R₁ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 (RingHom.id.{u_1} R₁ (Semiring.toNonAssocSemiring.{u_1} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18)) M₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42) (LinearMap.{u_4, u_4, u_3, u_3} R₂ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 (RingHom.id.{u_4} R₂ (Semiring.toNonAssocSemiring.{u_4} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21)) M₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46) (AddEquiv.toEquiv.{u_2, u_3} (LinearMap.{u_1, u_1, u_2, u_2} R₁ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 (RingHom.id.{u_1} R₁ (Semiring.toNonAssocSemiring.{u_1} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18)) M₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42) (LinearMap.{u_4, u_4, u_3, u_3} R₂ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 (RingHom.id.{u_4} R₂ (Semiring.toNonAssocSemiring.{u_4} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21)) M₂ M₂ 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 σ₁₂ σ₂₁ σ₁₂ σ₂₁ (RingHom.id.{u_1} R₁ (Semiring.toNonAssocSemiring.{u_1} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18)) (RingHom.id.{u_4} R₂ (Semiring.toNonAssocSemiring.{u_4} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21)) σ₂₁ σ₁₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.102 (RingHomCompTriple.ids.{u_1, u_4} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 σ₁₂) (RingHomInvPair.triples₂.{u_1, u_4} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.98) (RingHomCompTriple.ids.{u_4, u_1} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 σ₂₁) (RingHomInvPair.triples₂.{u_4, u_1} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 σ₂₁ σ₁₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.102) e e)) y))","typeFull":"∀ {R₁ : Type u_1} {R₂ : Type u_4} {M₁ : Type u_2} {M₂ : Type u_3} [inst : Semiring R₁] [inst_1 : Semiring R₂]\n  [inst_2 : AddCommMonoid M₁] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R₁ M₁] [inst_5 : Module R₂ M₂]\n  {σ₁₂ : R₁ →+* R₂} {σ₂₁ : R₂ →+* R₁} [inst_6 : RingHomInvPair σ₁₂ σ₂₁] [inst_7 : RingHomInvPair σ₂₁ σ₁₂]\n  (e : M₁ ≃ₛₗ[σ₁₂] M₂) (x y : M₁ →ₗ[R₁] M₁),\n  (e.arrowCongrAddEquiv e).toFun (x + y) = (e.arrowCongrAddEquiv e).toFun x + (e.arrowCongrAddEquiv e).toFun y","typeReadable":"∀ {R₁ : Type u_1} {R₂ : Type u_4} {M₁ : Type u_2} {M₂ : Type u_3} [inst : Semiring R₁] [inst_1 : Semiring R₂]\n  [inst_2 : AddCommMonoid M₁] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R₁ M₁] [inst_5 : Module R₂ M₂]\n  {σ₁₂ : R₁ →+* R₂} {σ₂₁ : R₂ →+* R₁} [inst_6 : RingHomInvPair σ₁₂ σ₂₁] [inst_7 : RingHomInvPair σ₂₁ σ₁₂]\n  (e : M₁ ≃ₛₗ[σ₁₂] M₂) (x y : M₁ →ₗ[R₁] M₁),\n  (e.arrowCongrAddEquiv e).toFun (x + y) = (e.arrowCongrAddEquiv e).toFun x + (e.arrowCongrAddEquiv e).toFun y","typeReferences":[["RingHomInvPair","triples₂"],["RingHom"],["instHAdd"],["RingHomCompTriple","ids"],["Module"],["LinearEquiv"],["LinearMap"],["AddEquiv","toEquiv"],["HAdd","hAdd"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["LinearEquiv","arrowCongrAddEquiv"],["RingHom","id"],["LinearMap","instAdd"],["Equiv","toFun"],["RingHomInvPair"],["Eq"],["Semiring"]],"valueReferences":[["RingHomInvPair","triples₂"],["Semiring","toNonAssocSemiring"],["LinearEquiv","arrowCongrAddEquiv"],["RingHomCompTriple","ids"],["RingHom","id"],["LinearMap","instAdd"],["AddEquiv","map_add'"],["LinearMap"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","ofSubsingleton_self"],"typeFallback":"forall {R : Type.{u_1}} (M : Type.{u_5}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1494211772._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1494211772._hygCtx._hyg.19 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1494211772._hygCtx._hyg.25 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1494211772._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1494211772._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1494211772._hygCtx._hyg.33 : Subsingleton.{succ u_5} M], Eq.{succ u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1494211772._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1494211772._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1494211772._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1494211772._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1494211772._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1494211772._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1494211772._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1494211772._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1494211772._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1494211772._hygCtx._hyg.25) (LinearEquiv.ofSubsingleton.{u_1, u_5, u_5} R M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1494211772._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1494211772._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1494211772._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1494211772._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1494211772._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1494211772._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1494211772._hygCtx._hyg.33) (LinearEquiv.refl.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1494211772._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1494211772._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1494211772._hygCtx._hyg.25)","typeFull":"∀ {R : Type u_1} (M : Type u_5) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  [inst_3 : Subsingleton M], LinearEquiv.ofSubsingleton M M = LinearEquiv.refl R M","typeReadable":"∀ {R : Type u_1} (M : Type u_5) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  [inst_3 : Subsingleton M], LinearEquiv.ofSubsingleton M M = LinearEquiv.refl R M","typeReferences":[["Subsingleton"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["LinearEquiv","ofSubsingleton"],["RingHom","id"],["Module"],["RingHomInvPair","ids"],["LinearEquiv"],["Eq"],["LinearEquiv","refl"],["Semiring"]],"valueReferences":[["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["LinearEquiv","ext"],["Semiring","toNonAssocSemiring"],["of_eq_true"],["_private","Mathlib","Algebra","Module","Equiv","Basic",0,"LinearEquiv","ofSubsingleton_self","_simp_1_1"],["RingHom","id"],["LinearEquiv","ofSubsingleton"],["RingHomInvPair","ids"],["Zero","toOfNat0"],["Eq"],["AddZero","toZero"],["LinearEquiv","refl"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["Units","mulLeftLinearEquiv","congr_simp"],"typeFallback":"forall (R : Type.{u_9}) (A : Type.{u_10}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 : Semiring.{u_9} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15 : Semiring.{u_10} A] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 : Module.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.22 : SMulCommClass.{u_9, u_10, u_10} R A A (SMulZeroClass.toSMul.{u_9, u_10} R A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_9, u_10} R A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))))) (DistribMulAction.toDistribSMul.{u_9, u_10} R A (MonoidWithZero.toMonoid.{u_9} R (Semiring.toMonoidWithZero.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))) (Module.toDistribMulAction.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18)))) (SMulZeroClass.toSMul.{u_10, u_10} A A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_10, u_10} A A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))))) (instDistribSMul.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))))], Eq.{succ u_10} (MonoidHom.{u_10, u_10} (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18) (MulOneClass.toMulOne.{u_10} (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (Units.instMulOneClass.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))) (MulOneClass.toMulOne.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18) (Monoid.toMulOneClass.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18) (DivInvMonoid.toMonoid.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18) (Group.toDivInvMonoid.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18) (LinearEquiv.automorphismGroup.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18)))))) (Units.mulLeftLinearEquiv.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.22) (Units.mulLeftLinearEquiv.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.22)","typeFull":"∀ (R : Type u_9) (A : Type u_10) [inst : Semiring R] [inst_1 : Semiring A] [inst_2 : Module R A]\n  [inst_3 : SMulCommClass R A A], Units.mulLeftLinearEquiv R A = Units.mulLeftLinearEquiv R A","typeReadable":"∀ (R : Type u_9) (A : Type u_10) [inst : Semiring R] [inst_1 : Semiring A] [inst_2 : Module R A]\n  [inst_3 : SMulCommClass R A A], Units.mulLeftLinearEquiv R A = Units.mulLeftLinearEquiv R A","typeReferences":[["MulOneClass","toMulOne"],["Module"],["MonoidHom"],["SMulZeroClass","toSMul"],["AddMonoidWithOne","toAddMonoid"],["instDistribSMul"],["LinearEquiv"],["LinearEquiv","automorphismGroup"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Monoid","toMulOneClass"],["MonoidWithZero","toMonoid"],["Units","mulLeftLinearEquiv"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Eq"],["Group","toDivInvMonoid"],["NonAssocSemiring","toAddCommMonoidWithOne"],["Units"],["DistribSMul","toSMulZeroClass"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["Units","instMulOneClass"],["AddZeroClass","toAddZero"],["SMulCommClass"],["Module","toDistribMulAction"],["DivInvMonoid","toMonoid"],["RingHomInvPair","ids"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["MulOneClass","toMulOne"],["MonoidHom"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["Semiring","toMonoidWithZero"],["Units","instMulOneClass"],["LinearEquiv"],["LinearEquiv","automorphismGroup"],["Semiring","toNonAssocSemiring"],["DivInvMonoid","toMonoid"],["RingHom","id"],["Eq","refl"],["Monoid","toMulOneClass"],["MonoidWithZero","toMonoid"],["RingHomInvPair","ids"],["Units","mulLeftLinearEquiv"],["Group","toDivInvMonoid"],["Units"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","conj_id"],"typeFallback":"forall {R₁' : Type.{u_12}} {R₂' : Type.{u_13}} {M₁' : Type.{u_20}} {M₂' : Type.{u_21}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59 : CommSemiring.{u_12} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62 : CommSemiring.{u_13} R₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.83 : AddCommMonoid.{u_20} M₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.86 : AddCommMonoid.{u_21} M₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.110 : Module.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.83] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.114 : Module.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.86] {σ₁'₂' : RingHom.{u_12, u_13} R₁' R₂' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59)) (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62))} {σ₂'₁' : RingHom.{u_13, u_12} R₂' R₁' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62)) (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59))} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.293 : RingHomInvPair.{u_12, u_13} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) σ₁'₂' σ₂'₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.297 : RingHomInvPair.{u_13, u_12} R₂' R₁' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59) σ₂'₁' σ₁'₂'] (e : LinearEquiv.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.297 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.114), Eq.{succ u_21} (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.114) (DFunLike.coe.{max (succ u_20) (succ u_21), succ u_20, succ u_21} (LinearEquiv.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.297 (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.114) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59)))) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62)))) 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.110)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62))) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.114))))) (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.110) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.110) => Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.114) (EquivLike.toFunLike.{max (succ u_20) (succ u_21), succ u_20, succ u_21} (LinearEquiv.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.297 (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.114) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59)))) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62)))) (LinearMap.module.{u_12, u_12, u_12, u_20, u_20} R₁' R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.110)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62))) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.114))))) (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.114) (LinearEquiv.instEquivLike.{u_12, u_13, u_20, u_21} R₁' R₂' (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.114) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59)))) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62)))) (LinearMap.module.{u_12, u_12, u_12, u_20, u_20} R₁' R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.110)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62))) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.114)))) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.297)) (LinearEquiv.conj.{u_12, u_13, u_20, u_21} R₁' R₂' M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.114 σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.297 e) (LinearMap.id.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.110)) (LinearMap.id.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3355961124._hygCtx._hyg.114)","typeFull":"∀ {R₁' : Type u_12} {R₂' : Type u_13} {M₁' : Type u_20} {M₂' : Type u_21} [inst : CommSemiring R₁']\n  [inst_1 : CommSemiring R₂'] [inst_2 : AddCommMonoid M₁'] [inst_3 : AddCommMonoid M₂'] [inst_4 : Module R₁' M₁']\n  [inst_5 : Module R₂' M₂'] {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} [inst_6 : RingHomInvPair σ₁'₂' σ₂'₁']\n  [inst_7 : RingHomInvPair σ₂'₁' σ₁'₂'] (e : M₁' ≃ₛₗ[σ₁'₂'] M₂'), e.conj LinearMap.id = LinearMap.id","typeReadable":"∀ {R₁' : Type u_12} {R₂' : Type u_13} {M₁' : Type u_20} {M₂' : Type u_21} [inst : CommSemiring R₁']\n  [inst_1 : CommSemiring R₂'] [inst_2 : AddCommMonoid M₁'] [inst_3 : AddCommMonoid M₂'] [inst_4 : Module R₁' M₁']\n  [inst_5 : Module R₂' M₂'] {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} [inst_6 : RingHomInvPair σ₁'₂' σ₂'₁']\n  [inst_7 : RingHomInvPair σ₂'₁' σ₁'₂'] (e : M₁' ≃ₛₗ[σ₁'₂'] M₂'), e.conj LinearMap.id = LinearMap.id","typeReferences":[["smulCommClass_self"],["RingHom"],["Module","End"],["CommMonoid","toMonoid"],["Module"],["LinearMap","module"],["CommSemiring"],["CommSemiring","toSemiring"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["LinearMap","id"],["DFunLike","coe"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["LinearEquiv","conj"],["Module","toDistribMulAction"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["EquivLike","toFunLike"],["DistribMulAction","toMulAction"],["LinearEquiv","instEquivLike"],["RingHomInvPair"],["Eq"]],"valueReferences":[["smulCommClass_self"],["CommMonoid","toMonoid"],["LinearMap","instFunLike"],["Eq","trans"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["DFunLike","coe"],["LinearMap","id"],["congrArg"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["LinearMap","ext"],["EquivLike","toFunLike"],["DistribMulAction","toMulAction"],["congrFun'"],["LinearEquiv","instEquivLike"],["Eq"],["Module","End"],["True"],["LinearMap","module"],["CommSemiring","toSemiring"],["LinearMap"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["eq_self"],["Module","toDistribMulAction"],["LinearEquiv","conj"],["of_eq_true"],["LinearEquiv","apply_symm_apply"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","piApply_apply_apply"],"typeFallback":"forall 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13) (Pi.addCommMonoid.{u_5, u_9} M V inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.16) (Pi.addCommMonoid.{u_5, u_1} M (fun (a._@._internal._hyg.0 : M) => R) (fun (i : M) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13))))) (Pi.module.{u_5, u_9, u_1} M V R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.25) (Pi.Function.module.{u_5, u_1, u_1} M R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13)))) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13) (Pi.Function.module.{u_5, u_1, u_1} M R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13)))) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13))) (Function.smulCommClass.{u_5, u_1, u_1, u_1} M R R R (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.Equiv.Basic.419635005._hygCtx._hyg.13)))) (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.Equiv.Basic.419635005._hygCtx._hyg.13))) (DistribMulAction.toMulAction.{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.Equiv.Basic.419635005._hygCtx._hyg.13))) 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13)))) (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.Equiv.Basic.419635005._hygCtx._hyg.13))) (DistribMulAction.toMulAction.{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.Equiv.Basic.419635005._hygCtx._hyg.13))) (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.Equiv.Basic.419635005._hygCtx._hyg.13))))) (Module.toDistribMulAction.{u_1, u_1} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13)))) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13)))))) (smulCommClass_self.{u_1, u_1} R R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13) (DistribMulAction.toMulAction.{u_1, u_1} R R (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13)) (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.Equiv.Basic.419635005._hygCtx._hyg.13))))) (Module.toDistribMulAction.{u_1, u_1} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13)))) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13)))))))) (forall (x : M), LinearMap.{u_1, u_1, u_9, u_1} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13))) (V x) R (inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.16 x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13)))) (inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.25 x) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13))) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : forall (x : M), LinearMap.{u_1, u_1, u_9, u_1} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13))) (V x) R 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u_1} M V R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.25) (Pi.Function.module.{u_5, u_1, u_1} M R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13)))) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13)))) (Pi.module.{u_5, max u_1 u_9, u_1} M (fun (x : M) => LinearMap.{u_1, u_1, u_9, u_1} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13))) (V x) R (inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.16 x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13)))) (inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.25 x) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13))) R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13) (fun (i : M) => LinearMap.addCommMonoid.{u_1, u_1, u_9, u_1} R R (V i) R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13) (inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.16 i) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13)))) (inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.25 i) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13))))))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13)))) (LinearMap.piApply.{u_1, u_5, u_9} R M V inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.25) e) s x) (DFunLike.coe.{max (succ u_1) (succ u_9), succ u_9, succ u_1} (LinearMap.{u_1, u_1, u_9, u_1} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13))) (V x) R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13)))) (inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.25 x) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.419635005._hygCtx._hyg.13)))) (e x) (s x))","typeFull":"∀ {R : Type u_1} {M : Type u_5} {V : M → Type u_9} [inst : CommSemiring R] [inst_1 : (x : M) → AddCommMonoid (V x)]\n  [inst_2 : (x : M) → Module R (V x)] (e : (x : M) → V x →ₗ[R] R) (s : (x : M) → V x) (x : M),\n  (LinearMap.piApply e) s x = (e x) (s x)","typeReadable":"∀ {R : Type u_1} {M : Type u_5} {V : M → Type u_9} [inst : CommSemiring R] [inst_1 : (x : M) → AddCommMonoid (V x)]\n  [inst_2 : (x : M) → Module R (V x)] (e : (x : M) → V x →ₗ[R] R) (s : (x : M) → V x) (x : M),\n  (LinearMap.piApply e) s x = (e x) (s x)","typeReferences":[["smulCommClass_self"],["LinearMap","instFunLike"],["CommMonoid","toMonoid"],["Module"],["Pi","addCommMonoid"],["CommSemiring"],["SemigroupAction","toSMul"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["Pi","module"],["Pi","Function","module"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["DistribMulAction","toMulAction"],["Monoid","toSemigroup"],["Eq"],["Semiring","toModule"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["CommSemiring","toSemiring"],["LinearMap","module"],["Semiring","toMonoidWithZero"],["LinearMap"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["LinearMap","piApply"],["Module","toDistribMulAction"],["Function","smulCommClass"],["MulAction","toSemigroupAction"]],"valueReferences":[["smulCommClass_self"],["LinearMap","instFunLike"],["CommMonoid","toMonoid"],["Pi","addCommMonoid"],["SemigroupAction","toSMul"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["Pi","Function","module"],["Pi","module"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["DistribMulAction","toMulAction"],["Monoid","toSemigroup"],["Semiring","toModule"],["rfl"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["CommSemiring","toSemiring"],["LinearMap","module"],["Semiring","toMonoidWithZero"],["LinearMap"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["LinearMap","piApply"],["Module","toDistribMulAction"],["Function","smulCommClass"],["MulAction","toSemigroupAction"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","coe_inv"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_5}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.19 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.25 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.19] (f : LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.25), Eq.{succ u_5} (M -> M) (DFunLike.coe.{succ u_5, succ u_5, succ u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.25) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (EquivLike.toFunLike.{succ u_5, succ u_5, succ u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.25) M M (LinearEquiv.instEquivLike.{u_1, u_1, u_5, u_5} R R M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10))) (Inv.inv.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.25) (InvOneClass.toInv.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.25) (DivInvOneMonoid.toInvOneClass.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.25) (DivisionMonoid.toDivInvOneMonoid.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.25) (Group.toDivisionMonoid.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.25) (LinearEquiv.automorphismGroup.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.25))))) f)) (DFunLike.coe.{succ u_5, succ u_5, succ u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.25) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (EquivLike.toFunLike.{succ u_5, succ u_5, succ u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.25) M M (LinearEquiv.instEquivLike.{u_1, u_1, u_5, u_5} R R M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10))) (LinearEquiv.symm.{u_1, u_1, u_5, u_5} R R M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1996732810._hygCtx._hyg.10) f))","typeFull":"∀ {R : Type u_1} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (f : M ≃ₗ[R] M),\n  ⇑f⁻¹ = ⇑f.symm","typeReadable":"∀ {R : Type u_1} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (f : M ≃ₗ[R] M),\n  ⇑f⁻¹ = ⇑f.symm","typeReferences":[["Group","toDivisionMonoid"],["Inv","inv"],["InvOneClass","toInv"],["Module"],["LinearEquiv"],["LinearEquiv","symm"],["DFunLike","coe"],["LinearEquiv","automorphismGroup"],["AddCommMonoid"],["DivInvOneMonoid","toInvOneClass"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["EquivLike","toFunLike"],["RingHomInvPair","ids"],["Eq"],["LinearEquiv","instEquivLike"],["DivisionMonoid","toDivInvOneMonoid"],["Semiring"]],"valueReferences":[["rfl"],["Inv","inv"],["Group","toDivisionMonoid"],["InvOneClass","toInv"],["LinearEquiv"],["DFunLike","coe"],["LinearEquiv","automorphismGroup"],["Semiring","toNonAssocSemiring"],["DivInvOneMonoid","toInvOneClass"],["RingHom","id"],["EquivLike","toFunLike"],["RingHomInvPair","ids"],["LinearEquiv","instEquivLike"],["DivisionMonoid","toDivInvOneMonoid"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","conj","_proof_3"],"typeFallback":"forall {R₁' : Type.{u_2}} {R₂' : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.59 : CommSemiring.{u_2} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.62 : CommSemiring.{u_1} R₂'] {σ₂'₁' : RingHom.{u_1, u_2} R₂' R₁' (Semiring.toNonAssocSemiring.{u_1} R₂' (CommSemiring.toSemiring.{u_1} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.62)) (Semiring.toNonAssocSemiring.{u_2} R₁' (CommSemiring.toSemiring.{u_2} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.59))}, RingHomCompTriple.{u_1, u_1, u_2} R₂' R₂' R₁' (CommSemiring.toSemiring.{u_1} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_1} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_2} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.59) (RingHom.id.{u_1} R₂' (Semiring.toNonAssocSemiring.{u_1} R₂' (CommSemiring.toSemiring.{u_1} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.62))) σ₂'₁' σ₂'₁'","typeFull":"∀ {R₁' : Type u_2} {R₂' : Type u_1} [inst : CommSemiring R₁'] [inst_1 : CommSemiring R₂'] {σ₂'₁' : R₂' →+* R₁'},\n  RingHomCompTriple (RingHom.id R₂') σ₂'₁' σ₂'₁'","typeReadable":"∀ {R₁' : Type u_2} {R₂' : Type u_1} [inst : CommSemiring R₁'] [inst_1 : CommSemiring R₂'] {σ₂'₁' : R₂' →+* R₁'},\n  RingHomCompTriple (RingHom.id R₂') σ₂'₁' σ₂'₁'","typeReferences":[["RingHom"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["CommSemiring","toSemiring"],["CommSemiring"],["RingHomCompTriple"]],"valueReferences":[["RingHomCompTriple","ids"],["CommSemiring","toSemiring"]]},{"isProp":true,"kind":"theorem","name":["addMonoidEndRingEquivInt_apply"],"typeFallback":"forall (A : Type.{u_9}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11 : AddCommGroup.{u_9} A] (a._@._internal._hyg.0 : AddMonoidHom.{u_9, u_9} A A (AddZeroClass.toAddZero.{u_9} A (AddMonoid.toAddZeroClass.{u_9} A (SubNegMonoid.toAddMonoid.{u_9} A (AddGroup.toSubNegMonoid.{u_9} A (AddCommGroup.toAddGroup.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11))))) (AddZeroClass.toAddZero.{u_9} A (AddMonoid.toAddZeroClass.{u_9} A (SubNegMonoid.toAddMonoid.{u_9} A (AddGroup.toSubNegMonoid.{u_9} A (AddCommGroup.toAddGroup.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11)))))), Eq.{succ u_9} (LinearMap.{0, 0, u_9, u_9} Int Int Int.instSemiring Int.instSemiring (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int Int.instSemiring)) A A (AddCommGroup.toAddCommMonoid.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (AddCommGroup.toAddCommMonoid.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (AddCommGroup.toIntModule.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (AddCommGroup.toIntModule.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11)) (DFunLike.coe.{succ u_9, succ u_9, succ u_9} (RingEquiv.{u_9, u_9} (AddMonoid.End.{u_9} A (AddZeroClass.toAddZero.{u_9} A (AddMonoid.toAddZeroClass.{u_9} A (SubNegMonoid.toAddMonoid.{u_9} A (AddGroup.toSubNegMonoid.{u_9} A (AddCommGroup.toAddGroup.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11)))))) (Module.End.{0, u_9} Int A Int.instSemiring (AddCommGroup.toAddCommMonoid.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (AddCommGroup.toIntModule.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11)) (AddMonoid.End.instMul.{u_9} A (AddZeroClass.toAddZero.{u_9} A (AddMonoid.toAddZeroClass.{u_9} A (SubNegMonoid.toAddMonoid.{u_9} A (AddGroup.toSubNegMonoid.{u_9} A (AddCommGroup.toAddGroup.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11)))))) (Module.End.instMul.{0, u_9} Int A Int.instSemiring (AddCommGroup.toAddCommMonoid.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (AddCommGroup.toIntModule.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11)) (Distrib.toAdd.{u_9} (AddMonoid.End.{u_9} A (AddZeroClass.toAddZero.{u_9} A (AddMonoid.toAddZeroClass.{u_9} A (SubNegMonoid.toAddMonoid.{u_9} A (AddGroup.toSubNegMonoid.{u_9} A (AddCommGroup.toAddGroup.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11)))))) (NonUnitalNonAssocSemiring.toDistrib.{u_9} (AddMonoid.End.{u_9} A (AddZeroClass.toAddZero.{u_9} A (AddMonoid.toAddZeroClass.{u_9} A (SubNegMonoid.toAddMonoid.{u_9} A (AddGroup.toSubNegMonoid.{u_9} A (AddCommGroup.toAddGroup.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11)))))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_9} (AddMonoid.End.{u_9} A (AddZeroClass.toAddZero.{u_9} A (AddMonoid.toAddZeroClass.{u_9} A (SubNegMonoid.toAddMonoid.{u_9} A 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (AddCommGroup.toAddCommMonoid.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (AddCommGroup.toIntModule.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (AddCommGroup.toIntModule.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int Int.instSemiring)))) (AddMonoid.End.{u_9} A (AddZeroClass.toAddZero.{u_9} A (AddMonoid.toAddZeroClass.{u_9} A (SubNegMonoid.toAddMonoid.{u_9} A (AddGroup.toSubNegMonoid.{u_9} A (AddCommGroup.toAddGroup.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11)))))) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : AddMonoid.End.{u_9} A (AddZeroClass.toAddZero.{u_9} A (AddMonoid.toAddZeroClass.{u_9} A (SubNegMonoid.toAddMonoid.{u_9} A (AddGroup.toSubNegMonoid.{u_9} A (AddCommGroup.toAddGroup.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11)))))) => Module.End.{0, u_9} Int A Int.instSemiring (AddCommGroup.toAddCommMonoid.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (AddCommGroup.toIntModule.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11)) (EquivLike.toFunLike.{succ u_9, succ u_9, succ u_9} (RingEquiv.{u_9, u_9} (AddMonoid.End.{u_9} A (AddZeroClass.toAddZero.{u_9} A (AddMonoid.toAddZeroClass.{u_9} A (SubNegMonoid.toAddMonoid.{u_9} A (AddGroup.toSubNegMonoid.{u_9} A (AddCommGroup.toAddGroup.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11)))))) (Module.End.{0, u_9} Int A Int.instSemiring (AddCommGroup.toAddCommMonoid.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (AddCommGroup.toIntModule.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11)) (AddMonoid.End.instMul.{u_9} A (AddZeroClass.toAddZero.{u_9} A 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.22)))))) x._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.68 x._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.70))","typeFull":"∀ {A : Type u_1} {B : Type u_2} (R : Type u_3) [inst : Semiring R] [inst_1 : AddCommMonoid A] [inst_2 : AddCommMonoid B]\n  [inst_3 : Module R B] (x : R) (x_1 : A →+ B), (x • x_1).toNatLinearMap = (x • x_1).toNatLinearMap","typeReadable":"∀ {A : Type u_1} {B : Type u_2} (R : Type u_3) [inst : Semiring R] [inst_1 : AddCommMonoid A] [inst_2 : AddCommMonoid B]\n  [inst_3 : Module R B] (x : R) (x_1 : A →+ B), (x • x_1).toNatLinearMap = (x • 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{R : Type.{u_1}} {R₂ : Type.{u_2}} {M : Type.{u_5}} {M₂ : Type.{u_7}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.669047338._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.669047338._hygCtx._hyg.13 : Semiring.{u_2} R₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.669047338._hygCtx._hyg.16 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.669047338._hygCtx._hyg.19 : AddCommMonoid.{u_7} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.669047338._hygCtx._hyg.22 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.669047338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.669047338._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.669047338._hygCtx._hyg.26 : Module.{u_2, u_7} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.669047338._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.669047338._hygCtx._hyg.19] {σ₁₂ : RingHom.{u_1, u_2} R R₂ (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.669047338._hygCtx._hyg.10) (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.669047338._hygCtx._hyg.13)} {σ₂₁ : RingHom.{u_2, u_1} R₂ R (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.669047338._hygCtx._hyg.13) (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.669047338._hygCtx._hyg.10)} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.669047338._hygCtx._hyg.40 : RingHomInvPair.{u_1, u_2} R R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.669047338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.669047338._hygCtx._hyg.13 σ₁₂ σ₂₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.669047338._hygCtx._hyg.44 : RingHomInvPair.{u_2, u_1} R₂ R inst._@.Mathlib.Algebra.Module.Equiv.Basic.669047338._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.669047338._hygCtx._hyg.10 σ₂₁ σ₁₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.669047338._hygCtx._hyg.48 : Subsingleton.{succ u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.669047338._hygCtx._hyg.51 : Subsingleton.{succ u_7} M₂], Unique.{max (succ u_7) (succ u_5)} (LinearEquiv.{u_1, u_2, u_5, u_7} R R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.669047338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.669047338._hygCtx._hyg.13 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.669047338._hygCtx._hyg.40 inst._@.Mathlib.Algebra.Module.Equiv.Basic.669047338._hygCtx._hyg.44 M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.669047338._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.669047338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.669047338._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.669047338._hygCtx._hyg.26)","typeFull":"{R : Type u_1} →\n  {R₂ : Type u_2} →\n    {M : Type u_5} →\n      {M₂ : Type u_7} →\n        [inst : Semiring R] →\n          [inst_1 : Semiring R₂] →\n            [inst_2 : AddCommMonoid M] →\n              [inst_3 : AddCommMonoid M₂] →\n                [inst_4 : Module R M] →\n                  [inst_5 : Module R₂ M₂] →\n                    {σ₁₂ : R →+* R₂} →\n                      {σ₂₁ : R₂ →+* R} →\n                        [inst_6 : RingHomInvPair σ₁₂ σ₂₁] →\n                          [inst_7 : RingHomInvPair σ₂₁ σ₁₂] →\n                            [Subsingleton M] → [Subsingleton M₂] → Unique (M ≃ₛₗ[σ₁₂] M₂)","typeReadable":"{R : Type u_1} →\n  {R₂ : Type u_2} →\n    {M : Type u_5} →\n      {M₂ : Type u_7} →\n        [inst : Semiring R] →\n          [inst_1 : Semiring R₂] →\n            [inst_2 : AddCommMonoid M] →\n              [inst_3 : AddCommMonoid M₂] →\n                [inst_4 : Module R M] →\n                  [inst_5 : Module R₂ M₂] →\n                    {σ₁₂ : R →+* R₂} →\n                      {σ₂₁ : R₂ →+* R} →\n                        [inst_6 : RingHomInvPair σ₁₂ σ₂₁] →\n                          [inst_7 : RingHomInvPair σ₂₁ σ₁₂] →\n                            [Subsingleton M] → [Subsingleton M₂] → Unique (M ≃ₛₗ[σ₁₂] M₂)","typeReferences":[["Unique"],["RingHom"],["Subsingleton"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["Module"],["LinearEquiv"],["RingHomInvPair"],["Semiring"]],"valueReferences":[["Inhabited","mk"],["LinearEquiv","instZero"],["Unique","mk"],["Zero","toOfNat0"],["LinearEquiv"],["LinearEquiv","instUnique","_proof_1"],["OfNat","ofNat"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","automorphismGroup","_proof_8"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 : Module.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19] (x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.56 : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.58 : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.60 : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25), Eq.{succ u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (HMul.hMul.{u_2, u_2, u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (instHMul.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (LinearEquiv.automorphismGroup._proof_7.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (LinearEquiv.automorphismGroup._proof_7.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f))) (HMul.hMul.{u_2, u_2, u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (instHMul.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (LinearEquiv.automorphismGroup._proof_7.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (LinearEquiv.automorphismGroup._proof_7.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f))) x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.56 x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.58) x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.60) (HMul.hMul.{u_2, u_2, u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (instHMul.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (LinearEquiv.automorphismGroup._proof_7.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (LinearEquiv.automorphismGroup._proof_7.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f))) (HMul.hMul.{u_2, u_2, u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f))) x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.56 x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.58) x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.60)","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 : M ≃ₗ[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 : M ≃ₗ[R] M), x * x_1 * x_2 = x * x_1 * x_2","typeReferences":[["Mul","mk"],["Module"],["HMul","hMul"],["LinearEquiv","automorphismGroup","_proof_7"],["LinearEquiv"],["LinearEquiv","trans"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["RingHomInvPair","ids"],["instHMul"],["Eq"],["Semiring"]],"valueReferences":[["Mul","mk"],["rfl"],["LinearEquiv","trans"],["Semiring","toNonAssocSemiring"],["RingHomCompTriple","ids"],["RingHom","id"],["RingHomInvPair","ids"],["instHMul"],["HMul","hMul"],["LinearEquiv"]]},{"isProp":true,"kind":"theorem","name":["AddEquiv","toIntLinearEquiv_trans"],"typeFallback":"forall {M : Type.{u_5}} {M₂ : Type.{u_7}} {M₃ : Type.{u_8}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4289648846._hygCtx._hyg.10 : AddCommGroup.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4289648846._hygCtx._hyg.13 : AddCommGroup.{u_7} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4289648846._hygCtx._hyg.16 : AddCommGroup.{u_8} M₃] {modM : Module.{0, u_5} Int M Int.instSemiring 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(AddCommSemigroup.toAddCommMagma.{u_7} M₂ (AddCommMonoid.toAddCommSemigroup.{u_7} M₂ (AddCommGroup.toAddCommMonoid.{u_7} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4289648846._hygCtx._hyg.13)))) (AddCommMagma.toAdd.{u_8} M₃ (AddCommSemigroup.toAddCommMagma.{u_8} M₃ (AddCommMonoid.toAddCommSemigroup.{u_8} M₃ (AddCommGroup.toAddCommMonoid.{u_8} M₃ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4289648846._hygCtx._hyg.16))))), Eq.{max (succ u_5) (succ u_8)} (LinearEquiv.{0, 0, u_5, u_8} Int Int Int.instSemiring Int.instSemiring (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int Int.instSemiring)) (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int Int.instSemiring)) (RingHomInvPair.ids.{0} Int Int.instSemiring) (RingHomInvPair.ids.{0} Int Int.instSemiring) M M₃ (AddCommGroup.toAddCommMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4289648846._hygCtx._hyg.10) (AddCommGroup.toAddCommMonoid.{u_8} M₃ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4289648846._hygCtx._hyg.16) modM modM₃) (AddEquiv.toIntLinearEquiv.{u_5, u_8} M M₃ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4289648846._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4289648846._hygCtx._hyg.16 modM modM₃ (AddEquiv.trans.{u_5, u_7, u_8} M M₂ M₃ (AddCommMagma.toAdd.{u_5} M (AddCommSemigroup.toAddCommMagma.{u_5} M (AddCommMonoid.toAddCommSemigroup.{u_5} M (AddCommGroup.toAddCommMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4289648846._hygCtx._hyg.10)))) (AddCommMagma.toAdd.{u_7} M₂ (AddCommSemigroup.toAddCommMagma.{u_7} M₂ (AddCommMonoid.toAddCommSemigroup.{u_7} M₂ (AddCommGroup.toAddCommMonoid.{u_7} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4289648846._hygCtx._hyg.13)))) (AddCommMagma.toAdd.{u_8} M₃ (AddCommSemigroup.toAddCommMagma.{u_8} M₃ (AddCommMonoid.toAddCommSemigroup.{u_8} M₃ (AddCommGroup.toAddCommMonoid.{u_8} M₃ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4289648846._hygCtx._hyg.16)))) e e₂)) (LinearEquiv.trans.{0, 0, 0, u_5, u_7, u_8} Int Int Int M M₂ M₃ 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[inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.19 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.22 : AddCommMonoid.{u_7} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.25 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.29 : Module.{u_1, u_7} R M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.33 : Subsingleton.{succ u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.36 : Subsingleton.{succ u_7} M₂] 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.refl.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25)) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f)) (Inv.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.symm.{u_1, u_1, u_2, u_2} R R M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) f)) (npowRec.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (One.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.refl.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25)) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f))) (Nat.cast.{0} Int instNatCastInt (Nat.succ n)) a) (HMul.hMul.{u_2, u_2, u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (instHMul.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f))) (zpowRec.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (One.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.refl.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25)) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f)) (Inv.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.symm.{u_1, u_1, u_2, u_2} R R M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) f)) (npowRec.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (One.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25)) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R 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u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (n : ℕ)\n  (a : M ≃ₗ[R] M), zpowRec npowRec (↑n.succ) a = zpowRec npowRec (↑n) a * 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19)","typeFull":"∀ {A : Type u_2} {B : Type u_1} [inst : AddCommGroup A] [inst_1 : AddCommGroup B],\n  Function.LeftInverse LinearMap.toAddMonoidHom AddMonoidHom.toIntLinearMap","typeReadable":"∀ {A : Type u_2} {B : Type u_1} [inst : AddCommGroup A] [inst_1 : AddCommGroup B],\n  Function.LeftInverse LinearMap.toAddMonoidHom 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{R : Type.{u_1}} {M : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 : Module.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19] (a : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (b : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25), Eq.{succ u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (HDiv.hDiv.{u_2, u_2, u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (instHDiv.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Div.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (DivInvMonoid.div'.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Monoid.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Semigroup.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f)) (fun (x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.56 : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.58 : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.60 : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => rfl.{succ u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (HMul.hMul.{u_2, u_2, u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (instHMul.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f))) (HMul.hMul.{u_2, u_2, u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (instHMul.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f))) x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.56 x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.58) x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.60))) (One.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.refl.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25)) (fun (x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.68 : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.ext.{u_1, u_1, u_2, u_2} R R M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (HMul.hMul.{u_2, u_2, u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (instHMul.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f))) (OfNat.ofNat.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) 1 (One.toOfNat1.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (One.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.refl.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25)))) x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.68) x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.68 (fun (x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.73 : M) => rfl.{succ u_2} M (DFunLike.coe.{succ u_2, succ u_2, succ u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (EquivLike.toFunLike.{succ u_2, succ u_2, succ u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) M M (LinearEquiv.instEquivLike.{u_1, u_1, u_2, u_2} R R M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (HMul.hMul.{u_2, u_2, u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (instHMul.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f))) (OfNat.ofNat.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) 1 (One.toOfNat1.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (One.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.refl.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25)))) x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.68) x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.73))) (fun (x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.78 : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.ext.{u_1, u_1, u_2, u_2} R R M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (HMul.hMul.{u_2, u_2, u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (instHMul.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f))) x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.78 (OfNat.ofNat.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) 1 (One.toOfNat1.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (One.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.refl.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25))))) x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.78 (fun (x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.83 : M) => rfl.{succ u_2} M (DFunLike.coe.{succ u_2, succ u_2, succ u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (EquivLike.toFunLike.{succ u_2, succ u_2, succ u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) M M (LinearEquiv.instEquivLike.{u_1, u_1, u_2, u_2} R R M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (HMul.hMul.{u_2, u_2, u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (instHMul.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f))) x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.78 (OfNat.ofNat.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) 1 (One.toOfNat1.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (One.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.refl.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25))))) x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.83))) (npowRecAuto.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Semigroup.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f)) (fun (x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.56 : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.58 : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.60 : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => rfl.{succ u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (HMul.hMul.{u_2, u_2, u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (instHMul.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f))) (HMul.hMul.{u_2, u_2, u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (instHMul.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f))) x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.56 x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.58) x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.60))) (One.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.refl.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25))) (LinearEquiv.automorphismGroup._proof_1.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.automorphismGroup._proof_2.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25)) (Inv.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.symm.{u_1, u_1, u_2, u_2} R R M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) f))))) a b) (HMul.hMul.{u_2, u_2, u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (instHMul.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10))) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f))) a (LinearEquiv.symm.{u_1, u_1, u_2, u_2} R R M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) b))","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 = a * b.symm","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 = a * b.symm","typeReferences":[["Mul","mk"],["Module"],["RingHomCompTriple","ids"],["Inv","mk"],["One","mk"],["HMul","hMul"],["Div","mk"],["LinearEquiv"],["DFunLike","coe"],["instHDiv"],["DivInvMonoid","div'"],["HDiv","hDiv"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["Semigroup","mk"],["LinearEquiv","ext"],["RingHom","id"],["EquivLike","toFunLike"],["LinearEquiv","instEquivLike"],["Eq"],["rfl"],["LinearEquiv","automorphismGroup","_proof_2"],["LinearEquiv","symm"],["OfNat","ofNat"],["LinearEquiv","trans"],["npowRecAuto"],["One","toOfNat1"],["RingHomInvPair","ids"],["Monoid","mk"],["instHMul"],["LinearEquiv","automorphismGroup","_proof_1"],["Semiring"],["LinearEquiv","refl"]],"valueReferences":[["Mul","mk"],["RingHomCompTriple","ids"],["Inv","mk"],["One","mk"],["HMul","hMul"],["Div","mk"],["LinearEquiv"],["instHDiv"],["DFunLike","coe"],["DivInvMonoid","div'"],["HDiv","hDiv"],["Semigroup","mk"],["Semiring","toNonAssocSemiring"],["LinearEquiv","ext"],["RingHom","id"],["EquivLike","toFunLike"],["LinearEquiv","instEquivLike"],["rfl"],["LinearEquiv","automorphismGroup","_proof_2"],["LinearEquiv","symm"],["OfNat","ofNat"],["LinearEquiv","trans"],["npowRecAuto"],["One","toOfNat1"],["Eq","refl"],["RingHomInvPair","ids"],["Monoid","mk"],["instHMul"],["LinearEquiv","automorphismGroup","_proof_1"],["LinearEquiv","refl"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","piApply","_proof_4"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13 : CommSemiring.{u_1} R], SMulCommClass.{u_1, u_1, max u_2 u_1} R R (M -> R) (Function.hasSMul.{u_2, u_1, u_1} M R R (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.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (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.Equiv.Basic.1550793534._hygCtx._hyg.13))) (DistribMulAction.toMulAction.{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.Equiv.Basic.1550793534._hygCtx._hyg.13))) (AddCommMonoid.toAddMonoid.{u_1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))))))","typeFull":"∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R], SMulCommClass R R (M → R)","typeReadable":"∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R], SMulCommClass R R (M → R)","typeReferences":[["CommSemiring"],["CommSemiring","toSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["SemigroupAction","toSMul"],["Semiring","toMonoidWithZero"],["AddCommMonoid","toAddMonoid"],["SMulCommClass"],["Function","hasSMul"],["Module","toDistribMulAction"],["Semiring","toNonAssocSemiring"],["MonoidWithZero","toMonoid"],["DistribMulAction","toMulAction"],["Monoid","toSemigroup"],["Semiring","toModule"],["MulAction","toSemigroupAction"]],"valueReferences":[["smulCommClass_self"],["CommMonoid","toMonoid"],["CommSemiring","toSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["SemigroupAction","toSMul"],["Semiring","toMonoidWithZero"],["AddCommMonoid","toAddMonoid"],["CommSemiring","toCommMonoid"],["Function","smulCommClass"],["Module","toDistribMulAction"],["Semiring","toNonAssocSemiring"],["MonoidWithZero","toMonoid"],["DistribMulAction","toMulAction"],["Monoid","toSemigroup"],["Semiring","toModule"],["MulAction","toSemigroupAction"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","smul_refl"],"typeFallback":"forall {R : Type.{u_1}} {S : Type.{u_4}} {M : Type.{u_5}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.13 : Semiring.{u_4} S] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.16 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.19 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.23 : Module.{u_4, u_5} S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.27 : SMulCommClass.{u_1, u_4, u_5} R S M (SMulZeroClass.toSMul.{u_1, u_5} R M (AddZero.toZero.{u_5} M (AddZeroClass.toAddZero.{u_5} 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(AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.16)))) (DistribSMul.toSMulZeroClass.{u_4, u_5} S M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.16)) (DistribMulAction.toDistribSMul.{u_4, u_5} S M (MonoidWithZero.toMonoid.{u_4} S (Semiring.toMonoidWithZero.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.13)) (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.16) (Module.toDistribMulAction.{u_4, u_5} S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.23))))] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.32 : SMul.{u_4, u_1} S R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.36 : IsScalarTower.{u_4, u_1, u_5} S R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.32 (SMulZeroClass.toSMul.{u_1, u_5} R M (AddZero.toZero.{u_5} M (AddZeroClass.toAddZero.{u_5} M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.16)))) (DistribSMul.toSMulZeroClass.{u_1, u_5} R M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.16)) (DistribMulAction.toDistribSMul.{u_1, u_5} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.16) (Module.toDistribMulAction.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.19)))) (SMulZeroClass.toSMul.{u_4, u_5} S M (AddZero.toZero.{u_5} M (AddZeroClass.toAddZero.{u_5} M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.16)))) (DistribSMul.toSMulZeroClass.{u_4, u_5} S M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.16)) (DistribMulAction.toDistribSMul.{u_4, u_5} S M (MonoidWithZero.toMonoid.{u_4} S (Semiring.toMonoidWithZero.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.13)) (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.16) (Module.toDistribMulAction.{u_4, u_5} S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.23))))] (α : Units.{u_4} S (MonoidWithZero.toMonoid.{u_4} S (Semiring.toMonoidWithZero.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.13))), Eq.{succ u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.19) (LinearEquiv.instSMulUnitsId.{u_4, u_1, u_5, u_5} S R M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.36)) α (LinearEquiv.refl.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.19)) (DistribMulAction.toLinearEquiv.{u_1, u_4, u_5} R (Units.{u_4} S (MonoidWithZero.toMonoid.{u_4} S (Semiring.toMonoidWithZero.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.13))) M 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.19)))) (Units.instSMul.{u_4, u_5} S M (MonoidWithZero.toMonoid.{u_4} S (Semiring.toMonoidWithZero.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.13)) (SMulZeroClass.toSMul.{u_4, u_5} S M (AddZero.toZero.{u_5} M (AddZeroClass.toAddZero.{u_5} M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.16)))) (DistribSMul.toSMulZeroClass.{u_4, u_5} S M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.16)) (DistribMulAction.toDistribSMul.{u_4, u_5} S M (MonoidWithZero.toMonoid.{u_4} S (Semiring.toMonoidWithZero.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.13)) (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.16) (Module.toDistribMulAction.{u_4, u_5} S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.23))))) (Units.smulCommClass_right.{u_1, u_4, u_5} R S M (MonoidWithZero.toMonoid.{u_4} S (Semiring.toMonoidWithZero.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.13)) (SMulZeroClass.toSMul.{u_1, u_5} R M (AddZero.toZero.{u_5} M (AddZeroClass.toAddZero.{u_5} M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.16)))) (DistribSMul.toSMulZeroClass.{u_1, u_5} R M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.16)) (DistribMulAction.toDistribSMul.{u_1, u_5} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.16) (Module.toDistribMulAction.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.19)))) (SMulZeroClass.toSMul.{u_4, u_5} S M (AddZero.toZero.{u_5} M (AddZeroClass.toAddZero.{u_5} M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.16)))) (DistribSMul.toSMulZeroClass.{u_4, u_5} S M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4089727367._hygCtx._hyg.16)) (DistribMulAction.toDistribSMul.{u_4, u_5} S M (MonoidWithZero.toMonoid.{u_4} 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AddCommMonoid M]\n  [inst_3 : Module R M] [inst_4 : Module S M] [inst_5 : SMulCommClass R S M] [inst_6 : SMul S R]\n  [inst_7 : IsScalarTower S R M] (α : Sˣ), α • LinearEquiv.refl R M = DistribMulAction.toLinearEquiv R M 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{R₁' : Type.{u_1}} {R₂' : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.59 : CommSemiring.{u_1} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.62 : CommSemiring.{u_2} R₂'] {σ₁'₂' : RingHom.{u_1, u_2} R₁' R₂' (Semiring.toNonAssocSemiring.{u_1} R₁' (CommSemiring.toSemiring.{u_1} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.59)) (Semiring.toNonAssocSemiring.{u_2} R₂' (CommSemiring.toSemiring.{u_2} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.62))} {σ₂'₁' : RingHom.{u_2, u_1} R₂' R₁' (Semiring.toNonAssocSemiring.{u_2} R₂' (CommSemiring.toSemiring.{u_2} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.62)) (Semiring.toNonAssocSemiring.{u_1} R₁' (CommSemiring.toSemiring.{u_1} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.59))} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.297 : RingHomInvPair.{u_2, u_1} R₂' R₁' 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R₁')","typeReadable":"∀ {R₁' : Type u_1} {R₂' : Type u_2} [inst : CommSemiring R₁'] [inst_1 : CommSemiring R₂'] {σ₁'₂' : R₁' →+* R₂'}\n  {σ₂'₁' : R₂' →+* R₁'} [RingHomInvPair σ₂'₁' σ₁'₂'], RingHomCompTriple σ₁'₂' σ₂'₁' (RingHom.id R₁')","typeReferences":[["RingHom"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["CommSemiring","toSemiring"],["CommSemiring"],["RingHomInvPair"],["RingHomCompTriple"]],"valueReferences":[["RingHomInvPair","triples₂"],["CommSemiring","toSemiring"]]},{"isProp":true,"kind":"theorem","name":["DistribMulAction","toLinearEquiv","_proof_4"],"typeFallback":"forall {S : Type.{u_2}} (M : Type.{u_1}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13 : AddCommMonoid.{u_1} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.20 : Group.{u_2} S] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.23 : DistribMulAction.{u_2, u_1} S M (DivInvMonoid.toMonoid.{u_2} S (Group.toDivInvMonoid.{u_2} S 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[inst_2 : DistribMulAction S M] (s : S),\n  Function.RightInverse (DistribMulAction.toAddEquiv M s).invFun (DistribMulAction.toAddEquiv M s).toFun","typeReferences":[["Group"],["AddCommMonoid","toAddMonoid"],["AddEquiv","toEquiv"],["Function","RightInverse"],["AddCommMonoid"],["DistribMulAction","toAddEquiv"],["DivInvMonoid","toMonoid"],["Equiv","invFun"],["AddMonoid","toAddSemigroup"],["Equiv","toFun"],["Group","toDivInvMonoid"],["DistribMulAction"],["AddSemigroup","toAdd"]],"valueReferences":[["DistribMulAction","toAddEquiv"],["AddMonoid","toAddSemigroup"],["Equiv","right_inv"],["AddCommMonoid","toAddMonoid"],["AddEquiv","toEquiv"],["AddSemigroup","toAdd"]]},{"isProp":true,"kind":"theorem","name":["Units","symm_mulLeftLinearEquiv"],"typeFallback":"forall {R : Type.{u_9}} {A : Type.{u_10}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 : Semiring.{u_9} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15 : Semiring.{u_10} A] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18 : Module.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15)))] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.22 : SMulCommClass.{u_9, u_10, u_10} R A A (SMulZeroClass.toSMul.{u_9, u_10} R A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_9, u_10} R A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A 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A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18) (Group.toDivInvMonoid.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18) (LinearEquiv.automorphismGroup.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18)))))) (Units.{u_10} A 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A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18) (MonoidHom.instFunLike.{u_10, u_10} (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 (RingHom.id.{u_9} R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18) (MulOneClass.toMulOne.{u_10} (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) (Units.instMulOneClass.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15)))) (MulOneClass.toMulOne.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18) (Monoid.toMulOneClass.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18) (DivInvMonoid.toMonoid.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18) (Group.toDivInvMonoid.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18) (LinearEquiv.automorphismGroup.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18)))))) (Units.mulLeftLinearEquiv.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.22) a)) (DFunLike.coe.{succ u_10, succ u_10, succ u_10} (MonoidHom.{u_10, u_10} (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18) (MulOneClass.toMulOne.{u_10} (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) (Units.instMulOneClass.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15)))) (MulOneClass.toMulOne.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18) (Monoid.toMulOneClass.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18) (DivInvMonoid.toMonoid.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18) (Group.toDivInvMonoid.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18) (LinearEquiv.automorphismGroup.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18)))))) (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) => LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18) (MonoidHom.instFunLike.{u_10, u_10} (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18) (MulOneClass.toMulOne.{u_10} (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) (Units.instMulOneClass.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15)))) (MulOneClass.toMulOne.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18) (Monoid.toMulOneClass.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18) (DivInvMonoid.toMonoid.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.18) (Group.toDivInvMonoid.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.742148405._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A 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(M : Type.{u_1}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2931425069._hygCtx._hyg.13 : AddCommMonoid.{u_1} M] {m : Type.{u_2}} {n : Type.{u_3}} (f : m -> n) (x._@.Mathlib.Algebra.Module.Equiv.Basic.2931425069._hygCtx._hyg.61 : n -> M) (x._@.Mathlib.Algebra.Module.Equiv.Basic.2931425069._hygCtx._hyg.63 : n -> M), Eq.{max (succ u_1) (succ u_2)} (m -> M) (Function.comp.{succ u_2, succ u_3, succ u_1} m n M (HAdd.hAdd.{max u_3 u_1, max u_3 u_1, max u_3 u_1} (n -> M) (n -> M) (n -> M) (instHAdd.{max u_3 u_1} (n -> M) (AddCommMagma.toAdd.{max u_3 u_1} (n -> M) (AddCommSemigroup.toAddCommMagma.{max u_3 u_1} (n -> M) (AddCommMonoid.toAddCommSemigroup.{max u_3 u_1} (n -> M) (Pi.addCommMonoid.{u_3, u_1} n (fun (a._@._internal._hyg.0 : n) => M) (fun (i : n) => inst._@.Mathlib.Algebra.Module.Equiv.Basic.2931425069._hygCtx._hyg.13)))))) x._@.Mathlib.Algebra.Module.Equiv.Basic.2931425069._hygCtx._hyg.61 x._@.Mathlib.Algebra.Module.Equiv.Basic.2931425069._hygCtx._hyg.63) f) (Function.comp.{succ 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f","typeReferences":[["HAdd","hAdd"],["AddCommMonoid"],["AddCommMonoid","toAddCommSemigroup"],["instHAdd"],["Pi","addCommMonoid"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Function","comp"],["Eq"]],"valueReferences":[["HAdd","hAdd"],["rfl"],["AddCommMonoid","toAddCommSemigroup"],["instHAdd"],["Pi","addCommMonoid"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Function","comp"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","domMulActCongrRight_symm_apply"],"typeFallback":"forall {S : Type.{u_4}} {R₁ : Type.{u_9}} {R₁' : Type.{u_11}} {R₂' : Type.{u_12}} {M₁ : Type.{u_13}} {M₁' : Type.{u_15}} {M₂' : Type.{u_16}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 : Semiring.{u_9} R₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 : Semiring.{u_11} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 : Semiring.{u_12} R₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 : AddCommMonoid.{u_13} M₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 : AddCommMonoid.{u_15} M₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 : AddCommMonoid.{u_16} M₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 : Module.{u_9, u_13} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 : Module.{u_11, u_15} R₁' M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 : Module.{u_12, u_16} R₂' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39] {σ₁'₂' : RingHom.{u_11, u_12} R₁' R₂' (Semiring.toNonAssocSemiring.{u_11} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24) (Semiring.toNonAssocSemiring.{u_12} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27)} {σ₂'₁' : RingHom.{u_12, u_11} R₂' R₁' (Semiring.toNonAssocSemiring.{u_12} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27) (Semiring.toNonAssocSemiring.{u_11} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24)} {σ₁₁' : RingHom.{u_9, u_11} R₁ R₁' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_11} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24)} {σ₁₂' : RingHom.{u_9, u_12} R₁ R₂' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_12} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27)} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.106 : RingHomInvPair.{u_11, u_12} R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁'₂' σ₂'₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.110 : RingHomInvPair.{u_12, u_11} R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₂'₁' σ₁'₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.114 : RingHomCompTriple.{u_9, u_11, u_12} R₁ R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₁' σ₁'₂' σ₁₂'] 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.110 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (a._@._internal._hyg.0 : LinearMap.{u_9, u_12, u_13, u_16} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54), Eq.{max (succ u_13) (succ u_15)} (LinearMap.{u_9, u_11, u_13, u_15} 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (LinearMap.{u_9, u_11, u_13, u_15} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.addCommMonoid.{u_9, u_12, u_13, u_16} R₁ R₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂') (LinearMap.addCommMonoid.{u_9, u_11, u_13, u_15} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁') (LinearMap.instModuleDomMulActOfSMulCommClass.{u_9, u_12, u_4, u_13, u_16} R₁ R₂' S M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.137 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.141) (LinearMap.instModuleDomMulActOfSMulCommClass.{u_9, u_11, u_4, u_13, u_15} R₁ R₁' S M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.137 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.141)) (LinearMap.{u_9, u_12, u_13, u_16} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : LinearMap.{u_9, u_12, u_13, u_16} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) => LinearMap.{u_9, u_11, u_13, u_15} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (EquivLike.toFunLike.{max (succ (max u_15 u_13)) (succ (max u_16 u_13)), succ (max u_16 u_13), succ (max u_15 u_13)} (LinearEquiv.{u_4, u_4, max u_16 u_13, max u_15 u_13} (DomMulAct.{u_4} S) (DomMulAct.{u_4} S) (DomMulAct.instSemiringOfMulOpposite.{u_4} S (MulOpposite.instSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)) (DomMulAct.instSemiringOfMulOpposite.{u_4} S (MulOpposite.instSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)) (RingHom.id.{u_4} (DomMulAct.{u_4} S) (Semiring.toNonAssocSemiring.{u_4} (DomMulAct.{u_4} S) (DomMulAct.instSemiringOfMulOpposite.{u_4} S (MulOpposite.instSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)))) (RingHom.id.{u_4} (DomMulAct.{u_4} S) (DomMulAct.instNonAssocSemiringOfMulOpposite.{u_4} S (MulOpposite.instNonAssocSemiring.{u_4} S (Semiring.toNonAssocSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)))) (RingHomInvPair.ids.{u_4} (DomMulAct.{u_4} S) (DomMulAct.instSemiringOfMulOpposite.{u_4} S (MulOpposite.instSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134))) (RingHomInvPair.ids.{u_4} (DomMulAct.{u_4} S) (DomMulAct.instSemiringOfMulOpposite.{u_4} S (MulOpposite.instSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134))) (LinearMap.{u_9, u_12, u_13, u_16} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (LinearMap.{u_9, u_11, u_13, u_15} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.addCommMonoid.{u_9, u_12, u_13, u_16} R₁ R₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂') (LinearMap.addCommMonoid.{u_9, u_11, u_13, u_15} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁') (LinearMap.instModuleDomMulActOfSMulCommClass.{u_9, u_12, u_4, u_13, u_16} R₁ R₂' S M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.137 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.141) (LinearMap.instModuleDomMulActOfSMulCommClass.{u_9, u_11, u_4, u_13, u_15} R₁ R₁' S M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.137 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.141)) (LinearMap.{u_9, u_12, u_13, u_16} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (LinearMap.{u_9, u_11, u_13, u_15} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearEquiv.instEquivLike.{u_4, u_4, max u_16 u_13, max u_15 u_13} (DomMulAct.{u_4} S) (DomMulAct.{u_4} S) (LinearMap.{u_9, u_12, u_13, u_16} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (LinearMap.{u_9, u_11, u_13, u_15} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (DomMulAct.instSemiringOfMulOpposite.{u_4} S (MulOpposite.instSemiring.{u_4} S 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁') (LinearMap.instModuleDomMulActOfSMulCommClass.{u_9, u_12, u_4, u_13, u_16} R₁ R₂' S M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.137 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.141) (LinearMap.instModuleDomMulActOfSMulCommClass.{u_9, 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.137 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.141) (RingHom.id.{u_4} (DomMulAct.{u_4} S) (DomMulAct.instNonAssocSemiringOfMulOpposite.{u_4} S (MulOpposite.instNonAssocSemiring.{u_4} S (Semiring.toNonAssocSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)))) (RingHom.id.{u_4} (DomMulAct.{u_4} S) (Semiring.toNonAssocSemiring.{u_4} (DomMulAct.{u_4} S) (DomMulAct.instSemiringOfMulOpposite.{u_4} S (MulOpposite.instSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)))) 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁'₂' σ₂'₁' σ₁₁' σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.137 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.141 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.146 e₂)) a._@._internal._hyg.0) (Equiv.invFun.{succ (max u_15 u_13), succ (max u_16 u_13)} (LinearMap.{u_9, u_11, u_13, u_15} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.{u_9, u_12, u_13, u_16} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (LinearMap.instAdd.{u_9, u_11, u_13, u_15} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁') (LinearMap.instAdd.{u_9, u_12, u_13, u_16} R₁ R₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂') (LinearEquiv.arrowCongrAddEquiv.{u_9, u_9, u_11, u_12, u_13, u_13, u_15, u_16} R₁ R₁ R₁' R₂' M₁ M₁ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 (RingHom.id.{u_9} R₁ (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18)) (RingHom.id.{u_9} R₁ (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18)) σ₁'₂' σ₂'₁' σ₁₁' σ₁₂' σ₁₁' σ₁₂' (RingHomInvPair.ids.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) (RingHomInvPair.ids.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.114 (RingHomCompTriple.ids.{u_9, u_12} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂') inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.146 (RingHomCompTriple.ids.{u_9, u_11} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁') (LinearEquiv.refl.{u_9, u_13} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42) e₂)) a._@._internal._hyg.0)","typeFull":"∀ {S : Type u_4} {R₁ : Type u_9} {R₁' : Type u_11} {R₂' : Type u_12} {M₁ : Type u_13} {M₁' : Type u_15}\n  {M₂' : Type u_16} [inst : Semiring R₁] [inst_1 : Semiring R₁'] [inst_2 : Semiring R₂'] [inst_3 : AddCommMonoid M₁]\n  [inst_4 : AddCommMonoid M₁'] [inst_5 : AddCommMonoid M₂'] [inst_6 : Module R₁ M₁] [inst_7 : Module R₁' M₁']\n  [inst_8 : Module R₂' M₂'] {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} {σ₁₁' : R₁ →+* R₁'} {σ₁₂' : R₁ →+* R₂'}\n  [inst_9 : RingHomInvPair σ₁'₂' σ₂'₁'] [inst_10 : RingHomInvPair σ₂'₁' σ₁'₂']\n  [inst_11 : RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_12 : Semiring S] [inst_13 : Module S M₁]\n  [inst_14 : SMulCommClass R₁ S M₁] [inst_15 : RingHomCompTriple σ₁₂' σ₂'₁' σ₁₁'] (e₂ : M₁' ≃ₛₗ[σ₁'₂'] M₂')\n  (a : M₁ →ₛₗ[σ₁₂'] M₂'), e₂.domMulActCongrRight.symm a = ((LinearEquiv.refl R₁ M₁).arrowCongrAddEquiv e₂).invFun a","typeReadable":"∀ {S : Type u_4} {R₁ : Type u_9} {R₁' : Type u_11} {R₂' : Type u_12} {M₁ : Type u_13} {M₁' : Type u_15}\n  {M₂' : Type u_16} [inst : Semiring R₁] [inst_1 : Semiring R₁'] [inst_2 : Semiring R₂'] [inst_3 : AddCommMonoid M₁]\n  [inst_4 : AddCommMonoid M₁'] [inst_5 : AddCommMonoid M₂'] [inst_6 : Module R₁ M₁] [inst_7 : Module R₁' M₁']\n  [inst_8 : Module R₂' M₂'] {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} {σ₁₁' : R₁ →+* R₁'} {σ₁₂' : R₁ →+* R₂'}\n  [inst_9 : RingHomInvPair σ₁'₂' σ₂'₁'] [inst_10 : RingHomInvPair σ₂'₁' σ₁'₂']\n  [inst_11 : RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_12 : Semiring S] [inst_13 : Module S M₁]\n  [inst_14 : SMulCommClass R₁ S M₁] [inst_15 : RingHomCompTriple σ₁₂' σ₂'₁' σ₁₁'] (e₂ : M₁' ≃ₛₗ[σ₁'₂'] M₂')\n  (a : M₁ →ₛₗ[σ₁₂'] M₂'), e₂.domMulActCongrRight.symm a = ((LinearEquiv.refl R₁ M₁).arrowCongrAddEquiv e₂).invFun a","typeReferences":[["RingHom"],["RingHomCompTriple","ids"],["Module"],["DomMulAct","instNonAssocSemiringOfMulOpposite"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["DFunLike","coe"],["RingHomCompTriple"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["LinearMap","instAdd"],["EquivLike","toFunLike"],["MonoidWithZero","toMonoid"],["LinearEquiv","instEquivLike"],["Eq"],["MulOpposite","instSemiring"],["DistribSMul","toSMulZeroClass"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["DomMulAct"],["AddEquiv","toEquiv"],["AddZeroClass","toAddZero"],["LinearMap"],["LinearEquiv","symm"],["LinearMap","instModuleDomMulActOfSMulCommClass"],["LinearMap","addCommMonoid"],["SMulCommClass"],["Module","toDistribMulAction"],["LinearEquiv","arrowCongrAddEquiv"],["Equiv","invFun"],["RingHomInvPair","ids"],["MulOpposite","instNonAssocSemiring"],["RingHomInvPair"],["LinearEquiv","domMulActCongrRight"],["AddZero","toZero"],["DomMulAct","instSemiringOfMulOpposite"],["LinearEquiv","refl"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["DomMulAct","instNonAssocSemiringOfMulOpposite"],["DomMulAct"],["LinearMap"],["LinearEquiv"],["LinearEquiv","symm"],["DFunLike","coe"],["LinearMap","instModuleDomMulActOfSMulCommClass"],["LinearMap","addCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Eq","refl"],["EquivLike","toFunLike"],["MulOpposite","instNonAssocSemiring"],["RingHomInvPair","ids"],["LinearEquiv","instEquivLike"],["LinearEquiv","domMulActCongrRight"],["DomMulAct","instSemiringOfMulOpposite"],["MulOpposite","instSemiring"]]},{"isProp":true,"kind":"theorem","name":["addMonoidEndRingEquivInt","_proof_4"],"typeFallback":"forall 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11)))))) (AddMonoid.End.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (SubNegMonoid.toAddMonoid.{u_1} A (AddGroup.toSubNegMonoid.{u_1} A (AddCommGroup.toAddGroup.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11)))))) (instHMul.{u_1} (AddMonoid.End.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (SubNegMonoid.toAddMonoid.{u_1} A (AddGroup.toSubNegMonoid.{u_1} A (AddCommGroup.toAddGroup.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11)))))) (AddMonoid.End.instMul.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (SubNegMonoid.toAddMonoid.{u_1} A (AddGroup.toSubNegMonoid.{u_1} A (AddCommGroup.toAddGroup.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11))))))) x._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.42 x._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.44))","typeFull":"∀ (A : Type u_1) [inst : AddCommGroup A] (x x_1 : AddMonoid.End A),\n  (↑(addMonoidHomLequivInt ℤ)).toFun (x * x_1) = (↑(addMonoidHomLequivInt ℤ)).toFun (x * x_1)","typeReadable":"∀ (A : Type u_1) [inst : AddCommGroup A] (x x_1 : AddMonoid.End A),\n  (↑(addMonoidHomLequivInt ℤ)).toFun (x * x_1) = (↑(addMonoidHomLequivInt ℤ)).toFun (x * x_1)","typeReferences":[["AddCommGroup","toAddGroup"],["HMul","hMul"],["LinearMap","toAddHom"],["AddMonoidHom","instModule"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["AddMonoidHom"],["addMonoidHomLequivInt"],["AddHom","toFun"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["AddMonoid","End","instMul"],["AddGroup","toSubNegMonoid"],["Eq"],["Module","End"],["LinearMap","module"],["LinearEquiv","toLinearMap"],["AddCommGroup"],["AddZeroClass","toAddZero"],["LinearMap"],["AddCommGroup","toIntModule"],["addMonoidEndRingEquivInt","_proof_1"],["Int"],["LinearMap","addCommMonoid"],["SubNegMonoid","toAddMonoid"],["AddCommMonoid","toAddCommSemigroup"],["Int","instSemiring"],["RingHomInvPair","ids"],["AddCommGroup","toAddCommMonoid"],["instHMul"],["AddMonoid","End"],["AddMonoidHom","instAddCommMonoid"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["AddCommGroup","toAddGroup"],["HMul","hMul"],["LinearMap","toAddHom"],["AddMonoidHom","instModule"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["AddMonoidHom"],["MonoidWithZero","toMonoid"],["addMonoidHomLequivInt"],["AddHom","toFun"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["AddMonoid","End","instMul"],["AddGroup","toSubNegMonoid"],["AddGroup","int_smulCommClass"],["rfl"],["Module","End"],["LinearMap","module"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["LinearEquiv","toLinearMap"],["AddZeroClass","toAddZero"],["LinearMap"],["AddCommGroup","toIntModule"],["Int"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["SubNegMonoid","toAddMonoid"],["AddCommMonoid","toAddCommSemigroup"],["Int","instSemiring"],["RingHomInvPair","ids"],["AddCommGroup","toAddCommMonoid"],["instHMul"],["AddMonoid","End"],["AddMonoidHom","instAddCommMonoid"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","arrowCongr_comp"],"typeFallback":"forall {R₁ : Type.{u_9}} {R₂ : Type.{u_10}} {R₁' : Type.{u_12}} {R₂' : Type.{u_13}} {R₁'' : Type.{u_15}} {R₂'' : Type.{u_16}} {M₁ : Type.{u_17}} {M₂ : Type.{u_18}} {M₁' : Type.{u_20}} {M₂' : Type.{u_21}} {M₁'' : Type.{u_23}} {M₂'' : Type.{u_24}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 : Semiring.{u_9} R₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 : Semiring.{u_10} R₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59 : CommSemiring.{u_12} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62 : CommSemiring.{u_13} R₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68 : CommSemiring.{u_15} R₁''] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71 : CommSemiring.{u_16} R₂''] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.74 : AddCommMonoid.{u_17} M₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.77 : AddCommMonoid.{u_18} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.83 : AddCommMonoid.{u_20} M₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.86 : AddCommMonoid.{u_21} M₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.92 : AddCommMonoid.{u_23} M₁''] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95 : AddCommMonoid.{u_24} M₂''] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.98 : Module.{u_9, u_17} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.74] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.102 : Module.{u_10, u_18} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.77] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.110 : Module.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.83] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.114 : Module.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.86] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122 : Module.{u_15, u_23} R₁'' M₁'' (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.92] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126 : Module.{u_16, u_24} R₂'' M₂'' (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95] {σ₁₂ : RingHom.{u_9, u_10} R₁ R₂ (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53)} {σ₂₁ : RingHom.{u_10, u_9} R₂ R₁ (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53) (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50)} {σ₁'₂' : RingHom.{u_12, u_13} R₁' R₂' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59)) (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62))} {σ₂'₁' : RingHom.{u_13, u_12} R₂' R₁' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62)) (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59))} {σ₁''₂'' : RingHom.{u_15, u_16} R₁'' R₂'' (Semiring.toNonAssocSemiring.{u_15} R₁'' (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68)) (Semiring.toNonAssocSemiring.{u_16} R₂'' (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71))} {σ₂''₁'' : RingHom.{u_16, u_15} R₂'' R₁'' (Semiring.toNonAssocSemiring.{u_16} R₂'' (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71)) (Semiring.toNonAssocSemiring.{u_15} R₁'' (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68))} {σ₁₁' : RingHom.{u_9, u_12} R₁ R₁' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59))} {σ₂₂' : RingHom.{u_10, u_13} R₂ R₂' (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53) (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62))} {σ₁'₁'' : RingHom.{u_12, u_15} R₁' R₁'' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59)) (Semiring.toNonAssocSemiring.{u_15} R₁'' (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68))} {σ₂'₂'' : RingHom.{u_13, u_16} R₂' R₂'' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62)) (Semiring.toNonAssocSemiring.{u_16} R₂'' (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71))} {σ₁₁'' : RingHom.{u_9, u_15} R₁ R₁'' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_15} R₁'' (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68))} {σ₂₂'' : RingHom.{u_10, u_16} R₂ R₂'' (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53) (Semiring.toNonAssocSemiring.{u_16} R₂'' (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71))} {σ₂₁' : RingHom.{u_10, u_12} R₂ R₁' (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53) (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59))} {σ₁₂' : RingHom.{u_9, u_13} R₁ R₂' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62))} {σ₂'₁'' : RingHom.{u_13, u_15} R₂' R₁'' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62)) (Semiring.toNonAssocSemiring.{u_15} R₁'' (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68))} {σ₁'₂'' : RingHom.{u_12, u_16} R₁' R₂'' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59)) (Semiring.toNonAssocSemiring.{u_16} R₂'' (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71))} {σ₂₁'' : RingHom.{u_10, u_15} R₂ R₁'' (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53) (Semiring.toNonAssocSemiring.{u_15} R₁'' (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68))} {σ₁₂'' : RingHom.{u_9, u_16} R₁ R₂'' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_16} R₂'' (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71))} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.285 : RingHomInvPair.{u_9, u_10} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 σ₁₂ σ₂₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.289 : RingHomInvPair.{u_10, u_9} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 σ₂₁ σ₁₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.293 : RingHomInvPair.{u_12, u_13} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) σ₁'₂' σ₂'₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.297 : RingHomInvPair.{u_13, u_12} R₂' R₁' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) σ₂'₁' σ₁'₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.333 : RingHomInvPair.{u_15, u_16} R₁'' R₂'' (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) σ₁''₂'' σ₂''₁''] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.337 : RingHomInvPair.{u_16, u_15} R₂'' R₁'' (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) σ₂''₁'' σ₁''₂''] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.341 : RingHomCompTriple.{u_9, u_12, u_15} R₁ R₁' R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) σ₁₁' σ₁'₁'' σ₁₁''] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.346 : RingHomCompTriple.{u_10, u_13, u_16} R₂ R₂' R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) σ₂₂' σ₂'₂'' σ₂₂''] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.351 : RingHomCompTriple.{u_9, u_12, u_13} R₁ R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) σ₁₁' σ₁'₂' σ₁₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.356 : RingHomCompTriple.{u_10, u_9, u_13} R₂ R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) σ₂₁ σ₁₂' σ₂₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.361 : RingHomCompTriple.{u_10, u_13, u_12} R₂ R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) σ₂₂' σ₂'₁' σ₂₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.366 : RingHomCompTriple.{u_9, u_10, u_12} R₁ R₂ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) σ₁₂ σ₂₁' σ₁₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.411 : RingHomCompTriple.{u_9, u_15, u_16} R₁ R₁'' R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) σ₁₁'' σ₁''₂'' σ₁₂''] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.416 : RingHomCompTriple.{u_10, u_9, u_16} R₂ R₁ R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) σ₂₁ σ₁₂'' σ₂₂''] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.421 : RingHomCompTriple.{u_10, u_16, u_15} R₂ R₂'' R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) σ₂₂'' σ₂''₁'' σ₂₁''] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.426 : RingHomCompTriple.{u_9, u_10, u_15} R₁ R₂ R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) σ₁₂ σ₂₁'' σ₁₁''] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.431 : RingHomCompTriple.{u_12, u_15, u_16} R₁' R₁'' R₂'' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) σ₁'₁'' σ₁''₂'' σ₁'₂''] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.436 : RingHomCompTriple.{u_13, u_12, u_16} R₂' R₁' R₂'' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) σ₂'₁' σ₁'₂'' σ₂'₂''] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.441 : RingHomCompTriple.{u_13, u_16, u_15} R₂' R₂'' R₁'' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) σ₂'₂'' σ₂''₁'' σ₂'₁''] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.446 : RingHomCompTriple.{u_12, u_13, u_15} R₁' R₂' R₁'' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) σ₁'₂' σ₂'₁'' σ₁'₁''] (e₁ : LinearEquiv.{u_9, u_10, u_17, u_18} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.285 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.289 M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.102) (e₂ : LinearEquiv.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.297 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.114) (e₃ : LinearEquiv.{u_15, u_16, u_23, u_24} R₁'' R₂'' (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) σ₁''₂'' σ₂''₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.333 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.337 M₁'' M₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126) (f : LinearMap.{u_9, u_12, u_17, u_20} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.110) (g : LinearMap.{u_12, u_15, u_20, u_23} R₁' R₁'' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) σ₁'₁'' M₁' M₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122), Eq.{max (succ u_18) (succ u_24)} (LinearMap.{u_10, u_16, u_18, u_24} R₂ R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) σ₂₂'' M₂ M₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126) (DFunLike.coe.{max (max (max (succ u_17) (succ u_18)) (succ u_23)) (succ u_24), max (succ u_17) (succ u_23), max (succ u_18) (succ u_24)} (LinearEquiv.{u_15, u_16, max u_23 u_17, max u_24 u_18} R₁'' R₂'' (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) σ₁''₂'' σ₂''₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.333 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.337 (LinearMap.{u_9, u_15, u_17, u_23} R₁ R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) σ₁₁'' M₁ M₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122) (LinearMap.{u_10, u_16, u_18, u_24} R₂ R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) σ₂₂'' M₂ M₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126) (LinearMap.addCommMonoid.{u_9, u_15, u_17, u_23} R₁ R₁'' M₁ M₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122 σ₁₁'') (LinearMap.addCommMonoid.{u_10, u_16, u_18, u_24} R₂ R₂'' M₂ M₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126 σ₂₂'') (LinearMap.module.{u_9, u_15, u_15, u_17, u_23} R₁ R₁'' R₁'' M₁ M₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122 σ₁₁'' (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122 (smulCommClass_self.{u_15, u_23} R₁'' M₁'' (CommSemiring.toCommMonoid.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) (DistribMulAction.toMulAction.{u_15, u_23} R₁'' M₁'' (CommMonoid.toMonoid.{u_15} R₁'' (CommSemiring.toCommMonoid.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68)) (AddCommMonoid.toAddMonoid.{u_23} M₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.92) (Module.toDistribMulAction.{u_15, u_23} R₁'' M₁'' (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122)))) (LinearMap.module.{u_10, u_16, u_16, u_18, u_24} R₂ R₂'' R₂'' M₂ M₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126 σ₂₂'' (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126 (smulCommClass_self.{u_16, u_24} R₂'' M₂'' (CommSemiring.toCommMonoid.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) (DistribMulAction.toMulAction.{u_16, u_24} R₂'' M₂'' (CommMonoid.toMonoid.{u_16} R₂'' (CommSemiring.toCommMonoid.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71)) (AddCommMonoid.toAddMonoid.{u_24} M₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95) (Module.toDistribMulAction.{u_16, u_24} R₂'' M₂'' (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126))))) (LinearMap.{u_9, u_15, u_17, u_23} R₁ R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) σ₁₁'' M₁ M₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : LinearMap.{u_9, u_15, u_17, u_23} R₁ R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) σ₁₁'' M₁ M₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122) => LinearMap.{u_10, u_16, u_18, u_24} R₂ R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) σ₂₂'' M₂ M₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126) (EquivLike.toFunLike.{max (max (max (succ u_17) (succ u_18)) (succ u_23)) (succ u_24), max (succ u_17) (succ u_23), max (succ u_18) (succ u_24)} (LinearEquiv.{u_15, u_16, max u_23 u_17, max u_24 u_18} R₁'' R₂'' (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) σ₁''₂'' σ₂''₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.333 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.337 (LinearMap.{u_9, u_15, u_17, u_23} R₁ R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) σ₁₁'' M₁ M₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122) (LinearMap.{u_10, u_16, u_18, u_24} R₂ R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) σ₂₂'' M₂ M₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126) (LinearMap.addCommMonoid.{u_9, u_15, u_17, u_23} R₁ R₁'' M₁ M₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122 σ₁₁'') (LinearMap.addCommMonoid.{u_10, u_16, u_18, u_24} R₂ R₂'' M₂ M₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126 σ₂₂'') (LinearMap.module.{u_9, u_15, u_15, u_17, u_23} R₁ R₁'' R₁'' M₁ M₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122 σ₁₁'' (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122 (smulCommClass_self.{u_15, u_23} R₁'' M₁'' (CommSemiring.toCommMonoid.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) (DistribMulAction.toMulAction.{u_15, u_23} R₁'' M₁'' (CommMonoid.toMonoid.{u_15} R₁'' (CommSemiring.toCommMonoid.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68)) (AddCommMonoid.toAddMonoid.{u_23} M₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.92) (Module.toDistribMulAction.{u_15, u_23} R₁'' M₁'' (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122)))) (LinearMap.module.{u_10, u_16, u_16, u_18, u_24} R₂ R₂'' R₂'' M₂ M₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126 σ₂₂'' (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126 (smulCommClass_self.{u_16, u_24} R₂'' M₂'' (CommSemiring.toCommMonoid.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) (DistribMulAction.toMulAction.{u_16, u_24} R₂'' M₂'' (CommMonoid.toMonoid.{u_16} R₂'' (CommSemiring.toCommMonoid.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71)) (AddCommMonoid.toAddMonoid.{u_24} M₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95) (Module.toDistribMulAction.{u_16, u_24} R₂'' M₂'' (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126))))) (LinearMap.{u_9, u_15, u_17, u_23} R₁ R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) σ₁₁'' M₁ M₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122) (LinearMap.{u_10, u_16, u_18, u_24} R₂ R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) σ₂₂'' M₂ M₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126) (LinearEquiv.instEquivLike.{u_15, u_16, max u_17 u_23, max u_18 u_24} R₁'' R₂'' (LinearMap.{u_9, u_15, u_17, u_23} R₁ R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) σ₁₁'' M₁ M₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122) (LinearMap.{u_10, u_16, u_18, u_24} R₂ R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) σ₂₂'' M₂ M₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126) (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) (LinearMap.addCommMonoid.{u_9, u_15, u_17, u_23} R₁ R₁'' M₁ M₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122 σ₁₁'') (LinearMap.addCommMonoid.{u_10, u_16, u_18, u_24} R₂ R₂'' M₂ M₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126 σ₂₂'') (LinearMap.module.{u_9, u_15, u_15, u_17, u_23} R₁ R₁'' R₁'' M₁ M₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122 σ₁₁'' (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122 (smulCommClass_self.{u_15, u_23} R₁'' M₁'' (CommSemiring.toCommMonoid.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) (DistribMulAction.toMulAction.{u_15, u_23} R₁'' M₁'' (CommMonoid.toMonoid.{u_15} R₁'' (CommSemiring.toCommMonoid.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68)) (AddCommMonoid.toAddMonoid.{u_23} M₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.92) (Module.toDistribMulAction.{u_15, u_23} R₁'' M₁'' (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122)))) (LinearMap.module.{u_10, u_16, u_16, u_18, u_24} R₂ R₂'' R₂'' M₂ M₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126 σ₂₂'' (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126 (smulCommClass_self.{u_16, u_24} R₂'' M₂'' (CommSemiring.toCommMonoid.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) (DistribMulAction.toMulAction.{u_16, u_24} R₂'' M₂'' (CommMonoid.toMonoid.{u_16} R₂'' (CommSemiring.toCommMonoid.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71)) (AddCommMonoid.toAddMonoid.{u_24} M₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95) (Module.toDistribMulAction.{u_16, u_24} R₂'' M₂'' (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126)))) σ₁''₂'' σ₂''₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.333 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.337)) (LinearEquiv.arrowCongr.{u_9, u_10, u_15, u_16, u_17, u_18, u_23, u_24} R₁ R₂ R₁'' R₂'' M₁ M₂ M₁'' M₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126 σ₁₂ σ₂₁ σ₁''₂'' σ₂''₁'' σ₁₁'' σ₂₂'' σ₂₁'' σ₁₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.285 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.289 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.333 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.337 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.411 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.416 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.421 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.426 e₁ e₃) (LinearMap.comp.{u_9, u_12, u_15, u_17, u_20, u_23} R₁ R₁' R₁'' M₁ M₁' M₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122 σ₁₁' σ₁'₁'' σ₁₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.341 g f)) (LinearMap.comp.{u_10, u_13, u_16, u_18, u_21, u_24} R₂ R₂' R₂'' M₂ M₂' M₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126 σ₂₂' σ₂'₂'' σ₂₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.346 (DFunLike.coe.{max (max (max (succ u_20) (succ u_21)) (succ u_23)) (succ u_24), max (succ u_20) (succ u_23), max (succ u_21) (succ u_24)} (LinearEquiv.{u_15, u_16, max u_23 u_20, max u_24 u_21} R₁'' R₂'' (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) σ₁''₂'' σ₂''₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.333 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.337 (LinearMap.{u_12, u_15, u_20, u_23} R₁' R₁'' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) σ₁'₁'' M₁' M₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122) (LinearMap.{u_13, u_16, u_21, u_24} R₂' R₂'' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) σ₂'₂'' M₂' M₂'' 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122)))) (LinearMap.module.{u_13, u_16, u_16, u_21, u_24} R₂' R₂'' R₂'' M₂' M₂'' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126 σ₂'₂'' (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126 (smulCommClass_self.{u_16, u_24} R₂'' M₂'' (CommSemiring.toCommMonoid.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) 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(CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) σ₂'₂'' M₂' M₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126) (EquivLike.toFunLike.{max (max (max (succ u_20) (succ u_21)) (succ u_23)) (succ u_24), max (succ u_20) (succ u_23), max (succ u_21) (succ u_24)} (LinearEquiv.{u_15, u_16, max u_23 u_20, max u_24 u_21} R₁'' R₂'' (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) σ₁''₂'' σ₂''₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.333 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.337 (LinearMap.{u_12, 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126) (LinearMap.addCommMonoid.{u_12, u_15, u_20, u_23} R₁' R₁'' M₁' M₁'' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122 σ₁'₁'') (LinearMap.addCommMonoid.{u_13, u_16, u_21, u_24} R₂' R₂'' M₂' M₂'' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126 σ₂'₂'') (LinearMap.module.{u_12, u_15, u_15, u_20, u_23} R₁' R₁'' R₁'' M₁' M₁'' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122 σ₁'₁'' (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122 (smulCommClass_self.{u_15, u_23} R₁'' M₁'' (CommSemiring.toCommMonoid.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) (DistribMulAction.toMulAction.{u_15, u_23} R₁'' M₁'' (CommMonoid.toMonoid.{u_15} R₁'' (CommSemiring.toCommMonoid.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68)) (AddCommMonoid.toAddMonoid.{u_23} M₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.92) (Module.toDistribMulAction.{u_15, u_23} R₁'' M₁'' (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122)))) (LinearMap.module.{u_13, u_16, u_16, u_21, u_24} R₂' R₂'' R₂'' M₂' M₂'' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126 σ₂'₂'' (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126 (smulCommClass_self.{u_16, u_24} R₂'' M₂'' (CommSemiring.toCommMonoid.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) (DistribMulAction.toMulAction.{u_16, u_24} R₂'' M₂'' (CommMonoid.toMonoid.{u_16} R₂'' (CommSemiring.toCommMonoid.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71)) 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R₂' R₂'' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) σ₂'₂'' M₂' M₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126) (LinearEquiv.instEquivLike.{u_15, u_16, max u_20 u_23, max u_21 u_24} R₁'' R₂'' (LinearMap.{u_12, u_15, u_20, u_23} R₁' R₁'' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) σ₁'₁'' M₁' M₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122) (LinearMap.{u_13, u_16, u_21, u_24} R₂' R₂'' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) σ₂'₂'' M₂' M₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126) (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) (LinearMap.addCommMonoid.{u_12, u_15, u_20, u_23} R₁' R₁'' M₁' M₁'' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122 σ₁'₁'') (LinearMap.addCommMonoid.{u_13, u_16, u_21, u_24} R₂' R₂'' M₂' M₂'' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126 σ₂'₂'') (LinearMap.module.{u_12, u_15, u_15, u_20, u_23} R₁' R₁'' R₁'' M₁' M₁'' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122 σ₁'₁'' (CommSemiring.toSemiring.{u_15} R₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122 (smulCommClass_self.{u_15, u_23} R₁'' M₁'' (CommSemiring.toCommMonoid.{u_15} R₁'' 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126 σ₂'₂'' (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126 (smulCommClass_self.{u_16, u_24} R₂'' M₂'' (CommSemiring.toCommMonoid.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) (DistribMulAction.toMulAction.{u_16, u_24} R₂'' M₂'' (CommMonoid.toMonoid.{u_16} R₂'' (CommSemiring.toCommMonoid.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71)) (AddCommMonoid.toAddMonoid.{u_24} M₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95) (Module.toDistribMulAction.{u_16, u_24} R₂'' M₂'' (CommSemiring.toSemiring.{u_16} R₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126)))) σ₁''₂'' σ₂''₁'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.333 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.337)) (LinearEquiv.arrowCongr.{u_12, u_13, u_15, u_16, u_20, u_21, u_23, u_24} R₁' R₂' R₁'' R₂'' M₁' M₂' M₁'' M₂'' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.71 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.95 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.122 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.126 σ₁'₂' σ₂'₁' σ₁''₂'' σ₂''₁'' σ₁'₁'' σ₂'₂'' σ₂'₁'' σ₁'₂'' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.297 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.333 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.337 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.431 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.436 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.441 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.446 e₂ e₃) g) (DFunLike.coe.{max (max (max (succ u_17) (succ u_18)) (succ u_20)) (succ u_21), max (succ u_17) (succ u_20), max (succ u_18) (succ u_21)} (LinearEquiv.{u_12, u_13, max u_20 u_17, max u_21 u_18} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.297 (LinearMap.{u_9, u_12, u_17, u_20} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.74 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(Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.110)))) (LinearMap.module.{u_10, u_13, u_13, u_18, u_21} R₂ R₂' R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.114 σ₂₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.114))))) (LinearMap.{u_9, u_12, u_17, u_20} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.110) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : LinearMap.{u_9, u_12, u_17, u_20} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.110) => LinearMap.{u_10, u_13, u_18, u_21} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.114) (EquivLike.toFunLike.{max (max (max (succ u_17) (succ u_18)) (succ u_20)) (succ u_21), max (succ u_17) (succ u_20), max (succ u_18) (succ u_21)} (LinearEquiv.{u_12, u_13, max u_20 u_17, max u_21 u_18} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.297 (LinearMap.{u_9, u_12, u_17, u_20} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.110) (LinearMap.{u_10, u_13, u_18, u_21} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.114) (LinearMap.addCommMonoid.{u_9, u_12, u_17, u_20} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.110 σ₁₁') (LinearMap.addCommMonoid.{u_10, u_13, u_18, u_21} R₂ R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.114 σ₂₂') (LinearMap.module.{u_9, u_12, u_12, u_17, u_20} R₁ R₁' R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.110 σ₁₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.110)))) (LinearMap.module.{u_10, u_13, u_13, u_18, u_21} R₂ R₂' R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.114 σ₂₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.114))))) (LinearMap.{u_9, u_12, u_17, u_20} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.110) (LinearMap.{u_10, u_13, u_18, u_21} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.114) (LinearEquiv.instEquivLike.{u_12, u_13, max u_17 u_20, max u_18 u_21} R₁' R₂' (LinearMap.{u_9, u_12, u_17, u_20} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.110) (LinearMap.{u_10, u_13, u_18, u_21} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.114) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) (LinearMap.addCommMonoid.{u_9, u_12, u_17, u_20} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.110 σ₁₁') (LinearMap.addCommMonoid.{u_10, u_13, u_18, u_21} R₂ R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.114 σ₂₂') (LinearMap.module.{u_9, u_12, u_12, u_17, u_20} R₁ R₁' R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.110 σ₁₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.110)))) (LinearMap.module.{u_10, u_13, u_13, u_18, u_21} R₂ R₂' R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.114 σ₂₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.114)))) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.297)) (LinearEquiv.arrowCongr.{u_9, u_10, u_12, u_13, u_17, u_18, u_20, u_21} R₁ R₂ R₁' R₂' M₁ M₂ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.59 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.62 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.114 σ₁₂ σ₂₁ σ₁'₂' σ₂'₁' σ₁₁' σ₂₂' σ₂₁' σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.285 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.289 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.297 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.351 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.356 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.361 inst._@.Mathlib.Algebra.Module.Equiv.Basic.217044241._hygCtx._hyg.366 e₁ e₂) f))","typeFull":"∀ {R₁ : Type u_9} {R₂ : Type u_10} {R₁' : Type u_12} {R₂' : Type u_13} {R₁'' : Type u_15} {R₂'' : Type u_16}\n  {M₁ : Type u_17} {M₂ : Type u_18} {M₁' : Type u_20} {M₂' : Type u_21} {M₁'' : Type u_23} {M₂'' : Type u_24}\n  [inst : Semiring R₁] [inst_1 : Semiring R₂] [inst_2 : CommSemiring R₁'] [inst_3 : CommSemiring R₂']\n  [inst_4 : CommSemiring R₁''] [inst_5 : CommSemiring R₂''] [inst_6 : AddCommMonoid M₁] [inst_7 : AddCommMonoid M₂]\n  [inst_8 : AddCommMonoid M₁'] [inst_9 : AddCommMonoid M₂'] [inst_10 : AddCommMonoid M₁'']\n  [inst_11 : AddCommMonoid M₂''] [inst_12 : Module R₁ M₁] [inst_13 : Module R₂ M₂] [inst_14 : Module R₁' M₁']\n  [inst_15 : Module R₂' M₂'] [inst_16 : Module R₁'' M₁''] [inst_17 : Module R₂'' M₂''] {σ₁₂ : R₁ →+* R₂}\n  {σ₂₁ : R₂ →+* R₁} {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} {σ₁''₂'' : R₁'' →+* R₂''} {σ₂''₁'' : R₂'' →+* R₁''}\n  {σ₁₁' : R₁ →+* R₁'} {σ₂₂' : R₂ →+* R₂'} {σ₁'₁'' : R₁' →+* R₁''} {σ₂'₂'' : R₂' →+* R₂''} {σ₁₁'' : R₁ →+* R₁''}\n  {σ₂₂'' : R₂ →+* R₂''} {σ₂₁' : R₂ →+* R₁'} {σ₁₂' : R�� →+* R₂'} {σ₂'₁'' : R₂' →+* R₁''} {σ₁'₂'' : R₁' →+* R₂''}\n  {σ₂₁'' : R₂ →+* R₁''} {σ₁₂'' : R₁ →+* R₂''} [inst_18 : RingHomInvPair σ₁₂ σ₂₁] [inst_19 : RingHomInvPair σ₂₁ σ₁₂]\n  [inst_20 : RingHomInvPair σ₁'₂' σ₂'₁'], ⋯","typeReadable":"∀ {R₁ : Type u_9} {R₂ : Type u_10} {R₁' : Type u_12} {R₂' : Type u_13} {R₁'' : Type u_15} {R₂'' : Type u_16}\n  {M₁ : Type u_17} {M₂ : Type u_18} {M₁' : Type u_20} {M₂' : Type u_21} {M₁'' : Type u_23} {M₂'' : Type u_24}\n  [inst : Semiring R₁] [inst_1 : Semiring R₂] [inst_2 : CommSemiring R₁'] [inst_3 : CommSemiring R₂']\n  [inst_4 : CommSemiring R₁''] [inst_5 : CommSemiring R₂''] [inst_6 : AddCommMonoid M₁] [inst_7 : AddCommMonoid M₂]\n  [inst_8 : AddCommMonoid M₁'] [inst_9 : AddCommMonoid M₂'] [inst_10 : AddCommMonoid M₁'']\n  [inst_11 : AddCommMonoid M₂''] [inst_12 : Module R₁ M₁] [inst_13 : Module R₂ M₂] [inst_14 : Module R₁' M₁']\n  [inst_15 : Module R₂' M₂'] [inst_16 : Module R₁'' M₁''] [inst_17 : Module R₂'' M₂''] {σ₁₂ : R₁ →+* R₂}\n  {σ₂₁ : R₂ →+* R₁} {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} {σ₁''₂'' : R₁'' →+* R₂''} {σ₂''₁'' : R₂'' →+* R₁''}\n  {σ₁₁' : R₁ →+* R₁'} {σ₂₂' : R₂ →+* R₂'} {σ₁'₁'' : R₁' →+* R₁''} {σ₂'₂'' : R₂' →+* R₂''} {σ₁₁'' : R₁ →+* R₁''}\n  {σ₂₂'' : R₂ →+* R₂''} {σ₂₁' : R₂ →+* R₁'} {σ₁₂' : R₁ →+* R₂'} {σ₂'₁'' : R₂' →+* R₁''} {σ₁'₂'' : R₁' →+* R₂''}\n  {σ₂₁'' : R₂ →+* R₁''} {σ₁₂'' : R₁ →+* R₂''} [inst_18 : RingHomInvPair σ₁₂ σ₂₁] [inst_19 : RingHomInvPair σ₂₁ σ₁₂]\n  [inst_20 : RingHomInvPair σ₁'₂' σ₂'₁'], ⋯","typeReferences":[["RingHom"],["smulCommClass_self"],["CommMonoid","toMonoid"],["Module"],["CommSemiring"],["LinearMap","comp"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["DFunLike","coe"],["RingHomCompTriple"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["EquivLike","toFunLike"],["DistribMulAction","toMulAction"],["Eq"],["LinearEquiv","instEquivLike"],["CommSemiring","toSemiring"],["LinearMap","module"],["LinearMap"],["CommSemiring","toCommMonoid"],["LinearEquiv","arrowCongr"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["RingHomInvPair"],["Semiring"]],"valueReferences":[["smulCommClass_self"],["CommMonoid","toMonoid"],["LinearMap","instFunLike"],["Eq","trans"],["LinearEquiv","symm_apply_apply"],["LinearMap","comp"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["DFunLike","coe"],["congrArg"],["LinearMap","ext"],["EquivLike","toFunLike"],["DistribMulAction","toMulAction"],["LinearEquiv","instEquivLike"],["Eq"],["True"],["LinearMap","module"],["CommSemiring","toSemiring"],["LinearMap"],["LinearEquiv","symm"],["CommSemiring","toCommMonoid"],["LinearEquiv","arrowCongr"],["LinearMap","addCommMonoid"],["eq_self"],["Module","toDistribMulAction"],["of_eq_true"]]},{"isProp":true,"kind":"theorem","name":["Units","mulLeftLinearEquiv","_proof_1"],"typeFallback":"forall (R : Type.{u_2}) (A : Type.{u_1}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 : Semiring.{u_2} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15 : Semiring.{u_1} A] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 : Module.{u_2, u_1} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.22 : SMulCommClass.{u_2, u_1, u_1} R A A (SMulZeroClass.toSMul.{u_2, u_1} R A (AddZero.toZero.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddMonoidWithOne.toAddMonoid.{u_1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_2, u_1} R A (AddMonoid.toAddZeroClass.{u_1} A (AddMonoidWithOne.toAddMonoid.{u_1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))))) (DistribMulAction.toDistribSMul.{u_2, u_1} R A (MonoidWithZero.toMonoid.{u_2} R (Semiring.toMonoidWithZero.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (AddMonoidWithOne.toAddMonoid.{u_1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))) (Module.toDistribMulAction.{u_2, u_1} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18)))) (SMulZeroClass.toSMul.{u_1, u_1} A A (AddZero.toZero.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddMonoidWithOne.toAddMonoid.{u_1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_1, u_1} A A (AddMonoid.toAddZeroClass.{u_1} A (AddMonoidWithOne.toAddMonoid.{u_1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))))) (instDistribSMul.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))))] (a : Units.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (x : A) (y : A), Eq.{succ u_1} A (AddHom.toFun.{u_1, u_1} A A (AddCommMagma.toAdd.{u_1} A (AddCommSemigroup.toAddCommMagma.{u_1} A (AddCommMonoid.toAddCommSemigroup.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))))) (AddCommMagma.toAdd.{u_1} A (AddCommSemigroup.toAddCommMagma.{u_1} A (AddCommMonoid.toAddCommSemigroup.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))))) (LinearMap.toAddHom.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 (LinearMap.mulLeft.{u_2, u_1} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.22 (Units.val.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)) a))) (HAdd.hAdd.{u_1, u_1, u_1} A A A (instHAdd.{u_1} A (AddCommMagma.toAdd.{u_1} A (AddCommSemigroup.toAddCommMagma.{u_1} A (AddCommMonoid.toAddCommSemigroup.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))))))) x y)) (HAdd.hAdd.{u_1, u_1, u_1} A A A (instHAdd.{u_1} A (AddCommMagma.toAdd.{u_1} A (AddCommSemigroup.toAddCommMagma.{u_1} A (AddCommMonoid.toAddCommSemigroup.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))))))) (AddHom.toFun.{u_1, u_1} A A (AddCommMagma.toAdd.{u_1} A (AddCommSemigroup.toAddCommMagma.{u_1} A (AddCommMonoid.toAddCommSemigroup.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))))) (AddCommMagma.toAdd.{u_1} A (AddCommSemigroup.toAddCommMagma.{u_1} A (AddCommMonoid.toAddCommSemigroup.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))))) (LinearMap.toAddHom.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 (LinearMap.mulLeft.{u_2, u_1} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.22 (Units.val.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)) a))) x) (AddHom.toFun.{u_1, u_1} A A (AddCommMagma.toAdd.{u_1} A (AddCommSemigroup.toAddCommMagma.{u_1} A (AddCommMonoid.toAddCommSemigroup.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))))) (AddCommMagma.toAdd.{u_1} A (AddCommSemigroup.toAddCommMagma.{u_1} A (AddCommMonoid.toAddCommSemigroup.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))))) (LinearMap.toAddHom.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 (LinearMap.mulLeft.{u_2, u_1} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.22 (Units.val.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)) a))) y))","typeFull":"∀ (R : Type u_2) (A : Type u_1) [inst : Semiring R] [inst_1 : Semiring A] [inst_2 : Module R A]\n  [inst_3 : SMulCommClass R A A] (a : Aˣ) (x y : A),\n  (LinearMap.mulLeft R ↑a).toFun (x + y) = (LinearMap.mulLeft R ↑a).toFun x + (LinearMap.mulLeft R ↑a).toFun y","typeReadable":"∀ (R : Type u_2) (A : Type u_1) [inst : Semiring R] [inst_1 : Semiring A] [inst_2 : Module R A]\n  [inst_3 : SMulCommClass R A A] (a : Aˣ) (x y : A),\n  (LinearMap.mulLeft R ↑a).toFun (x + y) = (LinearMap.mulLeft R ↑a).toFun x + (LinearMap.mulLeft R ↑a).toFun y","typeReferences":[["Module"],["LinearMap","toAddHom"],["SMulZeroClass","toSMul"],["AddMonoidWithOne","toAddMonoid"],["instDistribSMul"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["AddHom","toFun"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["LinearMap","mulLeft"],["Eq"],["NonAssocSemiring","toAddCommMonoidWithOne"],["Units"],["DistribSMul","toSMulZeroClass"],["instHAdd"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["HAdd","hAdd"],["SMulCommClass"],["Module","toDistribMulAction"],["AddCommMonoid","toAddCommSemigroup"],["Units","val"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["LinearMap","toAddHom"],["Semiring","toMonoidWithZero"],["AddHom","map_add'"],["Semiring","toNonAssocSemiring"],["AddCommMonoid","toAddCommSemigroup"],["RingHom","id"],["Units","val"],["MonoidWithZero","toMonoid"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["LinearMap","mulLeft"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","automorphismGroup","toLinearMapMonoidHom","_proof_2"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 : Module.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19] (x._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.66 : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (x._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.68 : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25), Eq.{succ u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (LinearEquiv.toLinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (instHMul.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (MulOne.toMul.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (MulOneClass.toMulOne.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (Monoid.toMulOneClass.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (DivInvMonoid.toMonoid.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (Group.toDivInvMonoid.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (LinearEquiv.automorphismGroup.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25))))))) x._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.66 x._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.68)) (LinearEquiv.toLinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 (HMul.hMul.{u_2, u_2, u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (instHMul.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (MulOne.toMul.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (MulOneClass.toMulOne.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (Monoid.toMulOneClass.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (DivInvMonoid.toMonoid.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (Group.toDivInvMonoid.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (LinearEquiv.automorphismGroup.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25))))))) x._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.66 x._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.68))","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 : M ≃ₗ[R] M), ↑(x * x_1) = ↑(x * x_1)","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 : M ≃ₗ[R] M), ↑(x * x_1) = ↑(x * x_1)","typeReferences":[["MulOneClass","toMulOne"],["Module"],["HMul","hMul"],["LinearEquiv","toLinearMap"],["LinearEquiv"],["LinearMap"],["LinearEquiv","automorphismGroup"],["AddCommMonoid"],["MulOne","toMul"],["Semiring","toNonAssocSemiring"],["DivInvMonoid","toMonoid"],["RingHom","id"],["Monoid","toMulOneClass"],["RingHomInvPair","ids"],["instHMul"],["Eq"],["Group","toDivInvMonoid"],["Semiring"]],"valueReferences":[["rfl"],["MulOneClass","toMulOne"],["HMul","hMul"],["LinearEquiv","toLinearMap"],["LinearMap"],["LinearEquiv"],["LinearEquiv","automorphismGroup"],["MulOne","toMul"],["Semiring","toNonAssocSemiring"],["DivInvMonoid","toMonoid"],["RingHom","id"],["Monoid","toMulOneClass"],["RingHomInvPair","ids"],["instHMul"],["Group","toDivInvMonoid"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","conj","_proof_2"],"typeFallback":"forall {R₁' : Type.{u_2}} {R₂' : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.59 : CommSemiring.{u_2} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.62 : CommSemiring.{u_1} R₂'] {σ₁'₂' : RingHom.{u_2, u_1} R₁' R₂' (Semiring.toNonAssocSemiring.{u_2} R₁' (CommSemiring.toSemiring.{u_2} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.59)) (Semiring.toNonAssocSemiring.{u_1} R₂' (CommSemiring.toSemiring.{u_1} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.62))} {σ₂'₁' : RingHom.{u_1, u_2} R₂' R₁' (Semiring.toNonAssocSemiring.{u_1} R₂' (CommSemiring.toSemiring.{u_1} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.62)) (Semiring.toNonAssocSemiring.{u_2} R₁' (CommSemiring.toSemiring.{u_2} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.59))} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.293 : RingHomInvPair.{u_2, u_1} R₁' R₂' (CommSemiring.toSemiring.{u_2} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_1} 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: R₂' →+* R₁'} [RingHomInvPair σ₁'₂' σ₂'₁'], RingHomCompTriple σ₂'₁' σ₁'₂' (RingHom.id R₂')","typeReferences":[["RingHom"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["CommSemiring","toSemiring"],["CommSemiring"],["RingHomInvPair"],["RingHomCompTriple"]],"valueReferences":[["RingHomInvPair","triples₂"],["CommSemiring","toSemiring"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","ofLinear_symm_apply"],"typeFallback":"forall {R : Type.{u_1}} {R₂ : Type.{u_2}} {M : Type.{u_5}} {M₂ : Type.{u_7}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.13 : Semiring.{u_2} R₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.16 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.19 : AddCommMonoid.{u_7} M₂] {module_M : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.16} {module_M₂ : Module.{u_2, u_7} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.19} {σ₁₂ : RingHom.{u_1, u_2} R R₂ (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.10) (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.13)} {σ₂₁ : RingHom.{u_2, u_1} R₂ R (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.13) (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.10)} {re₁₂ : RingHomInvPair.{u_1, u_2} R R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.13 σ₁₂ σ₂₁} {re₂₁ : RingHomInvPair.{u_2, u_1} R₂ R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.10 σ₂₁ σ₁₂} (f : LinearMap.{u_1, u_2, u_5, u_7} R R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.13 σ₁₂ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.19 module_M module_M₂) (g : LinearMap.{u_2, u_1, u_7, u_5} R₂ R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.10 σ₂₁ M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.16 module_M₂ module_M) {h₁ : Eq.{succ u_7} (LinearMap.{u_2, u_2, u_7, u_7} R₂ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.13 (RingHom.id.{u_2} R₂ (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.13)) M₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.19 module_M₂ module_M₂) (LinearMap.comp.{u_2, u_1, u_2, u_7, u_5, u_7} R₂ R R₂ M₂ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.19 module_M₂ module_M module_M₂ σ₂₁ σ₁₂ (RingHom.id.{u_2} R₂ (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.13)) (RingHomInvPair.triples₂.{u_1, u_2} R R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.13 σ₁₂ σ₂₁ re₁₂) f g) (LinearMap.id.{u_2, u_7} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.19 module_M₂)} {h₂ : Eq.{succ u_5} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.16 module_M module_M) (LinearMap.comp.{u_1, u_2, u_1, u_5, u_7, u_5} R R₂ R M M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.16 module_M module_M₂ module_M σ₁₂ σ₂₁ (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.10)) (RingHomInvPair.triples₂.{u_2, u_1} R₂ R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.10 σ₂₁ σ₁₂ re₂₁) g f) (LinearMap.id.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.16 module_M)} (x : M₂), Eq.{succ u_5} M (DFunLike.coe.{max (succ u_5) (succ u_7), succ u_7, succ u_5} (LinearEquiv.{u_2, u_1, u_7, u_5} R₂ R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.10 σ₂₁ σ₁₂ re₂₁ re₁₂ M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.16 module_M₂ module_M) M₂ (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M₂) => M) (EquivLike.toFunLike.{max (succ u_5) (succ u_7), succ u_7, succ u_5} (LinearEquiv.{u_2, u_1, u_7, u_5} R₂ R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.10 σ₂₁ σ₁₂ re₂₁ re₁₂ M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.16 module_M₂ module_M) M₂ M (LinearEquiv.instEquivLike.{u_2, u_1, u_7, u_5} R₂ R M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.16 module_M₂ module_M σ₂₁ σ₁₂ re₂₁ re₁₂)) (LinearEquiv.symm.{u_1, u_2, u_5, u_7} R R₂ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.19 module_M module_M₂ σ₁₂ σ₂₁ re₁₂ re₂₁ (LinearEquiv.ofLinear.{u_1, u_2, u_5, u_7} R R₂ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.19 module_M module_M₂ σ₁₂ σ₂₁ re₁₂ re₂₁ f g h₁ h₂)) x) (DFunLike.coe.{max (succ u_5) (succ u_7), succ u_7, succ u_5} (LinearMap.{u_2, u_1, u_7, u_5} R₂ R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.10 σ₂₁ M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.16 module_M₂ module_M) M₂ (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M₂) => M) (LinearMap.instFunLike.{u_2, u_1, u_7, u_5} R₂ R M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1101695653._hygCtx._hyg.16 module_M₂ module_M σ₂₁) g x)","typeFull":"∀ {R : Type u_1} {R₂ : Type u_2} {M : Type u_5} {M₂ : Type u_7} [inst : Semiring R] [inst_1 : Semiring R₂]\n  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] {module_M : Module R M} {module_M₂ : Module R₂ M₂}\n  {σ₁₂ : R →+* R₂} {σ₂₁ : R₂ →+* R} {re₁₂ : RingHomInvPair σ₁₂ σ₂₁} {re₂₁ : RingHomInvPair σ₂₁ σ₁₂} (f : M →ₛₗ[σ₁₂] M₂)\n  (g : M₂ →ₛₗ[σ₂₁] M) {h₁ : f ∘ₛₗ g = LinearMap.id} {h₂ : g ∘ₛₗ f = LinearMap.id} (x : M₂),\n  (LinearEquiv.ofLinear f g h₁ h₂).symm x = g x","typeReadable":"∀ {R : Type u_1} {R₂ : Type u_2} {M : Type u_5} {M₂ : Type u_7} [inst : Semiring R] [inst_1 : Semiring R₂]\n  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] {module_M : Module R M} {module_M₂ : Module R₂ M₂}\n  {σ₁₂ : R →+* R₂} {σ₂₁ : R₂ →+* R} {re₁₂ : RingHomInvPair σ₁₂ σ₂₁} {re₂₁ : RingHomInvPair σ₂₁ σ₁₂} (f : M →ₛₗ[σ₁₂] M₂)\n  (g : M₂ →ₛₗ[σ₂₁] M) {h₁ : f ∘ₛₗ g = LinearMap.id} {h₂ : g ∘ₛₗ f = LinearMap.id} (x : M₂),\n  (LinearEquiv.ofLinear f g h₁ h₂).symm x = g x","typeReferences":[["RingHomInvPair","triples₂"],["RingHom"],["LinearMap","instFunLike"],["Module"],["LinearMap","comp"],["LinearEquiv"],["LinearMap"],["LinearEquiv","symm"],["LinearMap","id"],["DFunLike","coe"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["LinearEquiv","ofLinear"],["EquivLike","toFunLike"],["LinearEquiv","instEquivLike"],["RingHomInvPair"],["Eq"],["Semiring"]],"valueReferences":[["rfl"],["LinearEquiv","ofLinear"],["EquivLike","toFunLike"],["LinearEquiv","instEquivLike"],["LinearEquiv"],["LinearEquiv","symm"],["DFunLike","coe"]]},{"isProp":true,"kind":"theorem","name":["DistribMulAction","toLinearEquiv","_proof_2"],"typeFallback":"forall (R : Type.{u_2}) {S : Type.{u_3}} (M : Type.{u_1}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10 : Semiring.{u_2} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13 : AddCommMonoid.{u_1} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.16 : Module.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.20 : Group.{u_3} S] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.23 : DistribMulAction.{u_3, u_1} S M (DivInvMonoid.toMonoid.{u_3} S (Group.toDivInvMonoid.{u_3} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.20)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13)] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._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.Equiv.Basic.2719555651._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.Equiv.Basic.2719555651._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_3, u_1} S M (DivInvMonoid.toMonoid.{u_3} S (Group.toDivInvMonoid.{u_3} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.20)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._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.Equiv.Basic.2719555651._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.Equiv.Basic.2719555651._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.Equiv.Basic.2719555651._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13) (Module.toDistribMulAction.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.16))))] (s : S) (m : R) (x : M), Eq.{succ u_1} M (AddHom.toFun.{u_1, u_1} M M (AddCommMagma.toAdd.{u_1} M (AddCommSemigroup.toAddCommMagma.{u_1} M (AddCommMonoid.toAddCommSemigroup.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13))) (AddCommMagma.toAdd.{u_1} M (AddCommSemigroup.toAddCommMagma.{u_1} M (AddCommMonoid.toAddCommSemigroup.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13))) (LinearMap.toAddHom.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.16 (DistribSMul.toLinearMap.{u_2, u_3, u_1} R S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.16 (DistribMulAction.toDistribSMul.{u_3, u_1} S M (DivInvMonoid.toMonoid.{u_3} S (Group.toDivInvMonoid.{u_3} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.20)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.23) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.27 s)) (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.Equiv.Basic.2719555651._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.Equiv.Basic.2719555651._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.Equiv.Basic.2719555651._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13) (Module.toDistribMulAction.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.16))))) m x)) (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.Equiv.Basic.2719555651._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.Equiv.Basic.2719555651._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.Equiv.Basic.2719555651._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13) (Module.toDistribMulAction.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.16))))) (DFunLike.coe.{succ u_2, succ u_2, succ u_2} (RingHom.{u_2, u_2} R R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10) (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10)) R (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : R) => R) (RingHom.instFunLike.{u_2, u_2} R R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10) (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10)) m) (AddHom.toFun.{u_1, u_1} M M (AddCommMagma.toAdd.{u_1} M (AddCommSemigroup.toAddCommMagma.{u_1} M (AddCommMonoid.toAddCommSemigroup.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13))) (AddCommMagma.toAdd.{u_1} M (AddCommSemigroup.toAddCommMagma.{u_1} M (AddCommMonoid.toAddCommSemigroup.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13))) (LinearMap.toAddHom.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.16 (DistribSMul.toLinearMap.{u_2, u_3, u_1} R S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.16 (DistribMulAction.toDistribSMul.{u_3, u_1} S M (DivInvMonoid.toMonoid.{u_3} S (Group.toDivInvMonoid.{u_3} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.20)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.23) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.27 s)) x))","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 : Group S] [inst_4 : DistribMulAction S M] [inst_5 : SMulCommClass S R M] (s : S) (m : R) (x : M),\n  (DistribSMul.toLinearMap R M s).toFun (m • x) = (RingHom.id R) m • (DistribSMul.toLinearMap R M s).toFun x","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 : Group S] [inst_4 : DistribMulAction S M] [inst_5 : SMulCommClass S R M] (s : S) (m : R) (x : M),\n  (DistribSMul.toLinearMap R M s).toFun (m • x) = (RingHom.id R) m • (DistribSMul.toLinearMap R M s).toFun x","typeReferences":[["RingHom"],["Module"],["RingHom","instFunLike"],["LinearMap","toAddHom"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["DistribSMul","toLinearMap"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["instHSMul"],["AddHom","toFun"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Eq"],["Group","toDivInvMonoid"],["DistribMulAction"],["DistribSMul","toSMulZeroClass"],["Group"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["SMulCommClass"],["Module","toDistribMulAction"],["DivInvMonoid","toMonoid"],["AddCommMonoid","toAddCommSemigroup"],["HSMul","hSMul"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["Semiring","toNonAssocSemiring"],["DivInvMonoid","toMonoid"],["RingHom","id"],["DistribMulAction","toDistribSMul"],["AddCommMonoid","toAddMonoid"],["LinearMap","map_smul'"],["Group","toDivInvMonoid"],["DistribSMul","toLinearMap"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","congrLeft","_proof_2"],"typeFallback":"forall (M : Type.{u_3}) {M₂ : Type.{u_2}} {M₃ : Type.{u_4}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 : AddCommMonoid.{u_3} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 : AddCommMonoid.{u_2} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.19 : AddCommMonoid.{u_4} M₃] {R : Type.{u_1}} (S : Type.{u_5}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.39 : Semiring.{u_5} S] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 : Module.{u_1, u_2} R M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.46 : Module.{u_1, u_4} R M₃ inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50 : Module.{u_1, u_3} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.54 : Module.{u_5, u_3} S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.58 : SMulCommClass.{u_1, u_5, u_3} R S M (SMulZeroClass.toSMul.{u_1, u_3} R M (AddZero.toZero.{u_3} M (AddZeroClass.toAddZero.{u_3} M (AddMonoid.toAddZeroClass.{u_3} M (AddCommMonoid.toAddMonoid.{u_3} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_1, u_3} R M (AddMonoid.toAddZeroClass.{u_3} M (AddCommMonoid.toAddMonoid.{u_3} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_1, u_3} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (AddCommMonoid.toAddMonoid.{u_3} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_3} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50)))) (SMulZeroClass.toSMul.{u_5, u_3} S M (AddZero.toZero.{u_3} M (AddZeroClass.toAddZero.{u_3} M (AddMonoid.toAddZeroClass.{u_3} M (AddCommMonoid.toAddMonoid.{u_3} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_5, u_3} S M (AddMonoid.toAddZeroClass.{u_3} M (AddCommMonoid.toAddMonoid.{u_3} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_5, u_3} S M (MonoidWithZero.toMonoid.{u_5} S (Semiring.toMonoidWithZero.{u_5} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.39)) (AddCommMonoid.toAddMonoid.{u_3} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13) (Module.toDistribMulAction.{u_5, u_3} S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.54))))] (e : LinearEquiv.{u_1, u_1, u_2, u_4} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50), Eq.{max (succ u_3) (succ u_4)} (LinearMap.{u_1, u_1, u_4, u_3} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) M₃ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50) (Equiv.toFun.{succ (max u_3 u_2), succ (max u_3 u_4)} (LinearMap.{u_1, u_1, u_2, u_3} R R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50) (MonoidWithZero.toMonoid.{u_5} S (Semiring.toMonoidWithZero.{u_5} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.39)) (AddCommMonoid.toAddMonoid.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)))) (Module.toDistribMulAction.{u_5, max u_3 u_2} S (LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50) inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.39 (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36))) (LinearMap.module.{u_1, u_1, u_5, u_2, u_3} R R S M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.54 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.58)))))) x._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.118 x._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.120))","typeFull":"∀ (M : Type u_3) {M₂ : Type u_2} {M₃ : Type u_4} [inst : AddCommMonoid M] [inst_1 : AddCommMonoid M₂]\n  [inst_2 : AddCommMonoid M₃] {R : Type u_1} (S : Type u_5) [inst_3 : Semiring R] [inst_4 : Semiring S]\n  [inst_5 : Module R M₂] [inst_6 : Module R M₃] [inst_7 : Module R M] [inst_8 : Module S M]\n  [inst_9 : SMulCommClass R S M] (e : M₂ ≃ₗ[R] M₃) (x : S) (x_1 : M₂ →ₗ[R] M),\n  (e.arrowCongrAddEquiv (LinearEquiv.refl R M)).toFun (x • x_1) =\n    (e.arrowCongrAddEquiv (LinearEquiv.refl R M)).toFun (x • x_1)","typeReadable":"∀ (M : Type u_3) {M₂ : Type u_2} {M₃ : Type u_4} [inst : AddCommMonoid M] [inst_1 : AddCommMonoid M₂]\n  [inst_2 : AddCommMonoid M₃] {R : Type u_1} (S : Type u_5) [inst_3 : Semiring R] [inst_4 : Semiring S]\n  [inst_5 : Module R M₂] [inst_6 : Module R M₃] [inst_7 : Module R M] [inst_8 : Module S M]\n  [inst_9 : SMulCommClass R S M] (e : M₂ ≃ₗ[R] M₃) (x : S) (x_1 : M₂ →ₗ[R] M),\n  (e.arrowCongrAddEquiv (LinearEquiv.refl R M)).toFun (x • x_1) =\n    (e.arrowCongrAddEquiv (LinearEquiv.refl R M)).toFun (x • x_1)","typeReferences":[["Module"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["LinearMap","instAdd"],["instHSMul"],["Equiv","toFun"],["Eq"],["DistribSMul","toSMulZeroClass"],["LinearMap","module"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["LinearEquiv","automorphismGroup","_proof_7"],["AddZeroClass","toAddZero"],["LinearMap"],["AddEquiv","toEquiv"],["LinearMap","addCommMonoid"],["SMulCommClass"],["Module","toDistribMulAction"],["LinearEquiv","arrowCongrAddEquiv"],["HSMul","hSMul"],["RingHomInvPair","ids"],["AddZero","toZero"],["LinearEquiv","refl"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["RingHomCompTriple","ids"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["LinearMap","instAdd"],["MonoidWithZero","toMonoid"],["instHSMul"],["Equiv","toFun"],["DistribSMul","toSMulZeroClass"],["rfl"],["LinearMap","module"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddEquiv","toEquiv"],["LinearMap"],["AddZeroClass","toAddZero"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["LinearEquiv","arrowCongrAddEquiv"],["HSMul","hSMul"],["RingHomInvPair","ids"],["AddZero","toZero"],["LinearEquiv","refl"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["Units","mulRightLinearEquiv","_proof_2"],"typeFallback":"forall (R : Type.{u_2}) {A : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12 : Semiring.{u_2} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15 : Semiring.{u_1} A] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.18 : Module.{u_2, u_1} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15)))] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.22 : IsScalarTower.{u_2, u_1, u_1} R A A (SMulZeroClass.toSMul.{u_2, u_1} R A (AddZero.toZero.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddMonoidWithOne.toAddMonoid.{u_1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_2, u_1} R A (AddMonoid.toAddZeroClass.{u_1} A (AddMonoidWithOne.toAddMonoid.{u_1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))))) (DistribMulAction.toDistribSMul.{u_2, u_1} R A (MonoidWithZero.toMonoid.{u_2} R (Semiring.toMonoidWithZero.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12)) (AddMonoidWithOne.toAddMonoid.{u_1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15)))) (Module.toDistribMulAction.{u_2, u_1} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.18)))) (SMulZeroClass.toSMul.{u_1, u_1} A A (AddZero.toZero.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddMonoidWithOne.toAddMonoid.{u_1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_1, u_1} A A (AddMonoid.toAddZeroClass.{u_1} A (AddMonoidWithOne.toAddMonoid.{u_1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))))) (instDistribSMul.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))))) (SMulZeroClass.toSMul.{u_2, u_1} R A (AddZero.toZero.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddMonoidWithOne.toAddMonoid.{u_1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_2, u_1} R A (AddMonoid.toAddZeroClass.{u_1} A (AddMonoidWithOne.toAddMonoid.{u_1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))))) (DistribMulAction.toDistribSMul.{u_2, u_1} R A (MonoidWithZero.toMonoid.{u_2} R (Semiring.toMonoidWithZero.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12)) (AddMonoidWithOne.toAddMonoid.{u_1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15)))) (Module.toDistribMulAction.{u_2, u_1} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.18))))] (a : Units.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))) (m : R) (x : A), Eq.{succ u_1} A (AddHom.toFun.{u_1, u_1} A A (AddCommMagma.toAdd.{u_1} A (AddCommSemigroup.toAddCommMagma.{u_1} A (AddCommMonoid.toAddCommSemigroup.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15)))))) (AddCommMagma.toAdd.{u_1} A (AddCommSemigroup.toAddCommMagma.{u_1} A (AddCommMonoid.toAddCommSemigroup.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15)))))) (LinearMap.toAddHom.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12)) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.18 (LinearMap.mulRight.{u_2, u_1} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15)) inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.22 (Units.val.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15)) a))) (HSMul.hSMul.{u_2, u_1, u_1} R A A (instHSMul.{u_2, u_1} R A (SMulZeroClass.toSMul.{u_2, u_1} R A (AddZero.toZero.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddCommMonoid.toAddMonoid.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_2, u_1} R A (AddMonoid.toAddZeroClass.{u_1} A (AddCommMonoid.toAddMonoid.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))))) (DistribMulAction.toDistribSMul.{u_2, u_1} R A (MonoidWithZero.toMonoid.{u_2} R (Semiring.toMonoidWithZero.{u_2} R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.22 (Units.val.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15)) a))) x))","typeFull":"∀ (R : Type u_2) {A : Type u_1} [inst : Semiring R] [inst_1 : Semiring A] [inst_2 : Module R A]\n  [inst_3 : IsScalarTower R A A] (a : Aˣ) (m : R) (x : A),\n  (LinearMap.mulRight R ↑a).toFun (m • x) = (RingHom.id R) m • (LinearMap.mulRight R ↑a).toFun x","typeReadable":"∀ (R : Type u_2) {A : Type u_1} [inst : Semiring R] [inst_1 : Semiring A] [inst_2 : Module R A]\n  [inst_3 : IsScalarTower R A A] (a : Aˣ) (m : R) (x : A),\n  (LinearMap.mulRight R ↑a).toFun (m • x) = (RingHom.id R) m • (LinearMap.mulRight R ↑a).toFun 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{R : Type.{u_2}} {R₂ : Type.{u_3}} {M : Type.{u_1}} {M₂ : Type.{u_4}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10 : Semiring.{u_2} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 : Semiring.{u_3} R₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.16 : AddCommMonoid.{u_1} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19 : AddCommMonoid.{u_4} M₂] {module_M : Module.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.16} {module_M₂ : Module.{u_3, u_4} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19} {σ₁₂ : RingHom.{u_2, u_3} R R₂ (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10) (Semiring.toNonAssocSemiring.{u_3} R₂ 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.16 module_M module_M₂ module_M σ₁₂ σ₂₁ (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10)) (RingHomInvPair.triples₂.{u_3, u_2} R₂ R inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10 σ₂₁ σ₁₂ re₂₁) g f) x) (DFunLike.coe.{succ u_1, succ u_1, succ u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.16 module_M) x))","typeFull":"∀ {R : Type u_2} {R₂ : Type u_3} {M : Type u_1} {M₂ : Type u_4} [inst : Semiring R] [inst_1 : Semiring R₂]\n  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] {module_M : Module R M} {module_M₂ : Module R₂ M₂}\n  {σ₁₂ : R →+* R₂} {σ₂₁ : R₂ →+* R} {re₂₁ : RingHomInvPair σ₂₁ σ₁₂} (f : M →ₛₗ[σ₁₂] M₂) (g : M₂ →ₛₗ[σ₂₁] M),\n  g ∘ₛₗ f = LinearMap.id → ∀ (x : M), (g ∘ₛₗ f) x = LinearMap.id x","typeReadable":"∀ {R : Type u_2} {R₂ : Type u_3} {M : Type u_1} {M₂ : Type u_4} [inst : Semiring R] [inst_1 : Semiring R₂]\n  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] {module_M : Module R M} {module_M₂ : Module R₂ M₂}\n  {σ₁₂ : R →+* R₂} {σ₂₁ : R₂ →+* R} {re₂₁ : RingHomInvPair σ₂₁ σ₁₂} (f : M →ₛₗ[σ₁₂] M₂) (g : M₂ →ₛₗ[σ₂₁] M),\n  g ∘ₛₗ f = LinearMap.id → ∀ (x : M), (g ∘ₛₗ f) x = LinearMap.id 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g","typeReferences":[["LinearMap","instFunLike"],["Module"],["Pi","addCommMonoid"],["LinearMap"],["DFunLike","coe"],["Pi","Function","module"],["LinearMap","funLeft"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["id"],["Eq"],["Semiring"]],"valueReferences":[["rfl"],["LinearMap","funLeft"],["Semiring","toNonAssocSemiring"],["LinearMap","instFunLike"],["RingHom","id"],["Pi","addCommMonoid"],["id"],["LinearMap"],["DFunLike","coe"],["Pi","Function","module"]]},{"isProp":false,"kind":"definition","name":["DistribMulAction","toModuleAut"],"typeFallback":"forall (R : Type.{u_1}) {S : Type.{u_4}} (M : Type.{u_5}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.16 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.20 : Group.{u_4} S] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.23 : DistribMulAction.{u_4, u_5} S M (DivInvMonoid.toMonoid.{u_4} S (Group.toDivInvMonoid.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.20)) (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13)] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.27 : SMulCommClass.{u_4, u_1, u_5} S R M (SMulZeroClass.toSMul.{u_4, u_5} S M (AddZero.toZero.{u_5} M (AddZeroClass.toAddZero.{u_5} M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_4, u_5} S M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.16))))], MonoidHom.{u_4, u_5} S (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10) 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.16) (Monoid.toMulOneClass.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R 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  [inst_3 : Group S] → [inst_4 : DistribMulAction S M] → [SMulCommClass S R M] → S →* M ≃ₗ[R] M","typeReadable":"(R : Type u_1) →\n  {S : Type u_4} →\n    (M : Type u_5) →\n      [inst : Semiring R] →\n        [inst_1 : AddCommMonoid M] →\n          [inst_2 : Module R M] →\n            [inst_3 : Group S] → [inst_4 : DistribMulAction S M] → [SMulCommClass S R M] → S →* M ≃ₗ[R] 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{R : Type.{u_3}} {R₂ : Type.{u_2}} {M : Type.{u_4}} {M₂ : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10 : Semiring.{u_3} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 : Semiring.{u_2} R₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.16 : AddCommMonoid.{u_4} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19 : AddCommMonoid.{u_1} M₂] {module_M : Module.{u_3, u_4} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.16} {module_M₂ : Module.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19} {σ₁₂ : RingHom.{u_3, u_2} R R₂ (Semiring.toNonAssocSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10) (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13)} {σ₂₁ : RingHom.{u_2, u_3} R₂ R (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13) (Semiring.toNonAssocSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10)} {re₁₂ : RingHomInvPair.{u_3, u_2} R R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 σ₁₂ σ₂₁} (f : LinearMap.{u_3, u_2, u_4, u_1} R R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 σ₁₂ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19 module_M module_M₂) (g : LinearMap.{u_2, u_3, u_1, u_4} R₂ R inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10 σ₂₁ M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.16 module_M₂ module_M), (Eq.{succ u_1} (LinearMap.{u_2, u_2, u_1, u_1} R₂ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 (RingHom.id.{u_2} R₂ (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13)) M₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19 module_M₂ module_M₂) (LinearMap.comp.{u_2, u_3, u_2, u_1, u_4, u_1} R₂ R R₂ M₂ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19 module_M₂ module_M module_M₂ σ₂₁ σ₁₂ (RingHom.id.{u_2} R₂ (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13)) (RingHomInvPair.triples₂.{u_3, u_2} R R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 σ₁₂ σ₂₁ re₁₂) f g) (LinearMap.id.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19 module_M₂)) -> (forall (x : M₂), Eq.{succ u_1} M₂ (DFunLike.coe.{succ u_1, succ u_1, succ u_1} (LinearMap.{u_2, u_2, u_1, u_1} R₂ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 (RingHom.id.{u_2} R₂ (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13)) M₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19 module_M₂ module_M₂) M₂ (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M₂) => M₂) (LinearMap.instFunLike.{u_2, u_2, u_1, u_1} R₂ R₂ M₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19 module_M₂ module_M₂ (RingHom.id.{u_2} R₂ (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13))) (LinearMap.comp.{u_2, u_3, u_2, u_1, u_4, u_1} R₂ R R₂ M₂ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19 module_M₂ module_M module_M₂ σ₂₁ σ₁₂ (RingHom.id.{u_2} R₂ (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13)) (RingHomInvPair.triples₂.{u_3, u_2} R R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 σ₁₂ σ₂₁ re₁₂) f g) x) (DFunLike.coe.{succ u_1, succ u_1, succ u_1} (LinearMap.{u_2, u_2, u_1, u_1} R₂ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 (RingHom.id.{u_2} R₂ (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13)) M₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19 module_M₂ module_M₂) M₂ (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M₂) => M₂) (LinearMap.instFunLike.{u_2, u_2, u_1, u_1} R₂ R₂ M₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19 module_M₂ module_M₂ (RingHom.id.{u_2} R₂ (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13))) (LinearMap.id.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19 module_M₂) x))","typeFull":"∀ {R : Type u_3} {R₂ : Type u_2} {M : Type u_4} {M₂ : Type u_1} [inst : Semiring R] [inst_1 : Semiring R₂]\n  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] {module_M : Module R M} {module_M₂ : Module R₂ M₂}\n  {σ₁₂ : R →+* R₂} {σ₂₁ : R₂ →+* R} {re₁₂ : RingHomInvPair σ₁₂ σ₂₁} (f : M →ₛₗ[σ₁₂] M₂) (g : M₂ →ₛₗ[σ₂₁] M),\n  f ∘ₛₗ g = LinearMap.id → ∀ (x : M₂), (f ∘ₛₗ g) x = LinearMap.id x","typeReadable":"∀ {R : Type u_3} {R₂ : Type u_2} {M : Type u_4} {M₂ : Type u_1} [inst : Semiring R] [inst_1 : Semiring R₂]\n  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] {module_M : Module R M} {module_M₂ : Module R₂ M₂}\n  {σ₁₂ : R →+* R₂} {σ₂₁ : R₂ →+* R} {re₁₂ : RingHomInvPair σ₁₂ σ₂₁} (f : M →ₛₗ[σ₁₂] M₂) (g : M₂ →ₛₗ[σ₂₁] M),\n  f ∘ₛₗ g = LinearMap.id → ∀ (x : M₂), (f ∘ₛₗ g) x = LinearMap.id x","typeReferences":[["RingHomInvPair","triples₂"],["RingHom"],["LinearMap","instFunLike"],["Module"],["LinearMap","comp"],["LinearMap"],["LinearMap","id"],["DFunLike","coe"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["RingHomInvPair"],["Eq"],["Semiring"]],"valueReferences":[["RingHomInvPair","triples₂"],["Semiring","toNonAssocSemiring"],["LinearMap","instFunLike"],["RingHom","id"],["LinearMap","ext_iff"],["Iff","mp"],["LinearMap","comp"],["LinearMap"],["Eq"],["DFunLike","coe"],["LinearMap","id"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","smulOfUnit","_proof_1"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2078068047._hygCtx._hyg.10 : CommSemiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2078068047._hygCtx._hyg.13 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2078068047._hygCtx._hyg.22 : Module.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2078068047._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2078068047._hygCtx._hyg.13], SMulCommClass.{u_1, u_1, u_2} (Units.{u_1} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2078068047._hygCtx._hyg.10)))) R M (Units.instSMul.{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.Equiv.Basic.2078068047._hygCtx._hyg.10))) (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.Equiv.Basic.2078068047._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.Equiv.Basic.2078068047._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.Equiv.Basic.2078068047._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2078068047._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2078068047._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2078068047._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2078068047._hygCtx._hyg.22))))) (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.Equiv.Basic.2078068047._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.Equiv.Basic.2078068047._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.Equiv.Basic.2078068047._hygCtx._hyg.10))) (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2078068047._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2078068047._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2078068047._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2078068047._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  SMulCommClass Rˣ R M","typeReadable":"∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],\n  SMulCommClass Rˣ R M","typeReferences":[["Module"],["CommSemiring"],["CommSemiring","toSemiring"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["SMulCommClass"],["Module","toDistribMulAction"],["AddCommMonoid"],["MonoidWithZero","toMonoid"],["Units","instSMul"],["AddZero","toZero"],["Units"],["DistribSMul","toSMulZeroClass"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["smulCommClass_self"],["Units","smulCommClass_left"],["CommMonoid","toMonoid"],["CommSemiring","toSemiring"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["CommSemiring","toCommMonoid"],["Module","toDistribMulAction"],["MonoidWithZero","toMonoid"],["DistribMulAction","toMulAction"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["DistribSMul","toSMulZeroClass"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","ringLmapEquivSelf","_proof_5"],"typeFallback":"forall (R : Type.{u_1}) (M : Type.{u_2}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.16 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.19 : Module.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.16], 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 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10))) (MulAction.toSemigroupAction.{u_1, u_1} R R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10)) (Monoid.toMulAction.{u_1} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._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 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10))) (MulAction.toSemigroupAction.{u_1, u_2} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10)) (DistribMulAction.toMulAction.{u_1, u_2} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.16) (Module.toDistribMulAction.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.19)))) (SemigroupAction.toSMul.{u_1, u_2} R M (Monoid.toSemigroup.{u_1} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10))) (MulAction.toSemigroupAction.{u_1, u_2} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10)) (DistribMulAction.toMulAction.{u_1, u_2} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_2} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.16) (Module.toDistribMulAction.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.19))))","typeFull":"∀ (R : Type u_1) (M : Type u_2) [inst : Semiring 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 : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],\n  IsScalarTower R R M","typeReferences":[["Module"],["IsScalarTower"],["SemigroupAction","toSMul"],["Semiring","toMonoidWithZero"],["AddCommMonoid","toAddMonoid"],["Monoid","toMulAction"],["AddCommMonoid"],["Module","toDistribMulAction"],["MonoidWithZero","toMonoid"],["DistribMulAction","toMulAction"],["Monoid","toSemigroup"],["MulAction","toSemigroupAction"],["Semiring"]],"valueReferences":[["Module","toDistribMulAction"],["IsScalarTower","left"],["MonoidWithZero","toMonoid"],["DistribMulAction","toMulAction"],["Semiring","toMonoidWithZero"],["AddCommMonoid","toAddMonoid"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","restrictScalars_apply"],"typeFallback":"forall (R : Type.{u_1}) {S : Type.{u_4}} {M : Type.{u_5}} {M₂ : Type.{u_7}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 : Semiring.{u_4} S] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22 : AddCommMonoid.{u_7} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.25 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.29 : Module.{u_1, u_7} R M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.33 : Module.{u_4, u_5} S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.37 : Module.{u_4, u_7} S M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.41 : LinearMap.CompatibleSMul.{u_5, u_7, u_1, u_4} M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22 R S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 (SMulZeroClass.toSMul.{u_1, u_5} R M (AddZero.toZero.{u_5} M (AddZeroClass.toAddZero.{u_5} M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19)))) (DistribSMul.toSMulZeroClass.{u_1, u_5} R M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19)) (DistribMulAction.toDistribSMul.{u_1, u_5} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R 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(MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_7} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22) (Module.toDistribMulAction.{u_1, u_7} R M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.29)))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.37] (f : LinearEquiv.{u_4, u_4, u_5, u_7} S S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 (RingHom.id.{u_4} S (Semiring.toNonAssocSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13)) (RingHom.id.{u_4} S (Semiring.toNonAssocSemiring.{u_4} S 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.37 (RingHom.id.{u_4} S (Semiring.toNonAssocSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13)) (RingHom.id.{u_4} S (Semiring.toNonAssocSemiring.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13)) (RingHomInvPair.ids.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13) (RingHomInvPair.ids.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13))) f a)","typeFull":"∀ (R : Type u_1) {S : Type u_4} {M : Type u_5} {M₂ : Type u_7} [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 M] [inst_7 : Module S M₂] [inst_8 : LinearMap.CompatibleSMul M M₂ R S] (f : M ≃ₗ[S] M₂) (a : M),\n  (LinearEquiv.restrictScalars R f) a = f a","typeReadable":"∀ (R : Type u_1) {S : Type u_4} {M : Type u_5} {M₂ : Type u_7} [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 M] [inst_7 : Module S M₂] [inst_8 : LinearMap.CompatibleSMul M M₂ R S] (f : M ≃ₗ[S] M₂) (a : M),\n  (LinearEquiv.restrictScalars R f) a = f 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[inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.16 : AddCommMonoid.{u_1} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2736031858._hygCtx._hyg.48 : Subsingleton.{succ u_1} M] (b : M), Eq.{succ u_1} 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.Equiv.Basic.2736031858._hygCtx._hyg.16)))).1) b","typeFull":"∀ {M : Type u_1} [inst : AddCommMonoid M] [Subsingleton M] (b : M), inst.toAddZeroClass.toZero.1 = b","typeReadable":"∀ {M : Type u_1} [inst : AddCommMonoid M] [Subsingleton M] (b : M), inst.toAddZeroClass.toZero.1 = b","typeReferences":[["Subsingleton"],["AddCommMonoid"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["Eq"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["Subsingleton","elim"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","arrowCongrAddEquiv","congr_simp"],"typeFallback":"forall {R₁ : Type.{u_9}} {R₂ : Type.{u_10}} {R₁' : Type.{u_11}} {R₂' : Type.{u_12}} {M₁ : Type.{u_13}} {M₂ : Type.{u_14}} {M₁' : Type.{u_15}} {M₂' : Type.{u_16}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 : Semiring.{u_9} R₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 : Semiring.{u_10} R₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 : Semiring.{u_11} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 : Semiring.{u_12} R₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 : AddCommMonoid.{u_13} M₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 : AddCommMonoid.{u_14} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 : AddCommMonoid.{u_15} M₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 : AddCommMonoid.{u_16} M₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 : Module.{u_9, u_13} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 : Module.{u_10, u_14} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 : Module.{u_11, u_15} R₁' M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 : Module.{u_12, u_16} R₂' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39] {σ₁₂ : RingHom.{u_9, u_10} R₁ R₂ (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21)} {σ₂₁ : RingHom.{u_10, u_9} R₂ R₁ (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21) (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18)} {σ₁'₂' : RingHom.{u_11, u_12} R₁' R₂' (Semiring.toNonAssocSemiring.{u_11} R₁' 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(Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21) (Semiring.toNonAssocSemiring.{u_11} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24)} {σ₂₁'_1 : RingHom.{u_10, u_11} R₂ R₁' (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21) (Semiring.toNonAssocSemiring.{u_11} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24)} (e_σ₂₁' : Eq.{max (succ u_10) (succ u_11)} (RingHom.{u_10, u_11} R₂ R₁' (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21) (Semiring.toNonAssocSemiring.{u_11} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24)) σ₂₁' σ₂₁'_1) {σ₁₂' : RingHom.{u_9, u_12} R₁ R₂' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_12} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27)} {σ₁₂'_1 : RingHom.{u_9, u_12} R₁ R₂' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_12} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27)} (e_σ₁₂' : Eq.{max (succ u_9) (succ u_12)} (RingHom.{u_9, u_12} R₁ R₂' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_12} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27)) σ₁₂' σ₁₂'_1) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 : RingHomInvPair.{u_9, u_10} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 σ₁₂ σ₂₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 : RingHomInvPair.{u_10, u_9} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 σ₂₁ σ₁₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 : RingHomInvPair.{u_11, u_12} R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₁'₂' σ₂'₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 : RingHomInvPair.{u_12, u_11} R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₂'₁' σ₁'₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.114 : RingHomCompTriple.{u_9, u_11, u_12} R₁ R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₁₁' ��₁'₂' σ₁₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.119 : RingHomCompTriple.{u_10, u_9, u_12} R₂ R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₂₁ σ₁₂' σ₂₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.124 : RingHomCompTriple.{u_10, u_12, u_11} R₂ R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₂₂' σ₂'₁' σ₂₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.129 : RingHomCompTriple.{u_9, u_10, u_11} R₁ R₂ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₂ σ₂₁' σ₁₁'] (e₁ : LinearEquiv.{u_9, u_10, u_13, u_14} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46) (e₁_1 : LinearEquiv.{u_9, u_10, u_13, u_14} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46), (Eq.{max (succ u_13) (succ u_14)} (LinearEquiv.{u_9, u_10, u_13, u_14} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46) e₁ e₁_1) -> (forall (e₂ : LinearEquiv.{u_11, u_12, u_15, u_16} R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54) (e₂_1 : LinearEquiv.{u_11, u_12, u_15, u_16} R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54), (Eq.{max (succ u_15) (succ u_16)} (LinearEquiv.{u_11, u_12, u_15, u_16} R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54) e₂ e₂_1) -> (Eq.{max (succ (max u_16 u_14)) (succ (max u_15 u_13))} (AddEquiv.{max u_15 u_13, max u_16 u_14} (LinearMap.{u_9, u_11, u_13, u_15} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50) (LinearMap.{u_10, u_12, u_14, u_16} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54) (LinearMap.instAdd.{u_9, u_11, u_13, u_15} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 σ₁₁') (LinearMap.instAdd.{u_10, u_12, u_14, u_16} R₂ R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 σ₂₂')) (LinearEquiv.arrowCongrAddEquiv.{u_9, u_10, u_11, u_12, u_13, u_14, u_15, u_16} R₁ R₂ R₁' R₂' M₁ M₂ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 σ₁₂ σ₂₁ σ₁'₂' σ₂'₁' σ₁₁' σ₂₂' σ₂₁' σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.119 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.124 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.129 e₁ e₂) (LinearEquiv.arrowCongrAddEquiv.{u_9, u_10, u_11, u_12, u_13, u_14, u_15, u_16} R₁ R₂ R₁' R₂' M₁ M₂ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 σ₁₂ σ₂₁ σ₁'₂' σ₂'₁' σ₁₁' σ₂₂' σ₂₁'_1 σ₁₂'_1 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 (Eq.ndrec.{0, max (succ u_9) (succ u_12)} (RingHom.{u_9, u_12} R₁ R₂' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_12} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27)) σ₁₂' (fun {σ₁₂' : RingHom.{u_9, u_12} R₁ R₂' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_12} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27)} => RingHomCompTriple.{u_9, u_11, u_12} R₁ R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₁₁' σ₁'₂' σ₁₂') inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.114 σ₁₂'_1 e_σ₁₂') (Eq.ndrec.{0, max (succ u_9) (succ u_12)} (RingHom.{u_9, u_12} R₁ R₂' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_12} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27)) σ₁₂' (fun {σ₁₂' : RingHom.{u_9, u_12} R₁ R₂' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_12} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27)} => RingHomCompTriple.{u_10, u_9, u_12} R₂ R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₂₁ σ₁₂' σ₂₂') inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.119 σ₁₂'_1 e_σ₁₂') (Eq.ndrec.{0, max (succ u_10) (succ u_11)} (RingHom.{u_10, u_11} R₂ R₁' (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21) (Semiring.toNonAssocSemiring.{u_11} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24)) σ₂₁' (fun {σ₂₁' : RingHom.{u_10, u_11} R₂ R₁' (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21) (Semiring.toNonAssocSemiring.{u_11} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24)} => RingHomCompTriple.{u_10, u_12, u_11} R₂ R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₂₂' σ₂'₁' σ₂₁') inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.124 σ₂₁'_1 e_σ₂₁') (Eq.ndrec.{0, max (succ u_10) (succ u_11)} (RingHom.{u_10, u_11} R₂ R₁' (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21) (Semiring.toNonAssocSemiring.{u_11} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24)) σ₂₁' (fun {σ₂₁' : RingHom.{u_10, u_11} R₂ R₁' (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21) (Semiring.toNonAssocSemiring.{u_11} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24)} => RingHomCompTriple.{u_9, u_10, u_11} R₁ R₂ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₂ σ₂₁' σ₁₁') inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.129 σ₂₁'_1 e_σ₂₁') e₁_1 e₂_1)))","typeFull":"∀ {R₁ : Type u_9} {R₂ : Type u_10} {R₁' : Type u_11} {R₂' : Type u_12} {M₁ : Type u_13} {M₂ : Type u_14}\n  {M₁' : Type u_15} {M₂' : Type u_16} [inst : Semiring R₁] [inst_1 : Semiring R₂] [inst_2 : Semiring R₁']\n  [inst_3 : Semiring R₂'] [inst_4 : AddCommMonoid M₁] [inst_5 : AddCommMonoid M₂] [inst_6 : AddCommMonoid M₁']\n  [inst_7 : AddCommMonoid M₂'] [inst_8 : Module R₁ M₁] [inst_9 : Module R₂ M₂] [inst_10 : Module R₁' M₁']\n  [inst_11 : Module R₂' M₂'] {σ₁₂ : R₁ →+* R₂} {σ₂₁ : R₂ →+* R₁} {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'}\n  {σ₁₁' : R₁ →+* R₁'} {σ₂₂' : R₂ →+* R₂'} {σ₂₁' σ₂₁'_1 : R₂ →+* R₁'} (e_σ₂₁' : σ₂₁' = σ₂₁'_1) {σ₁₂' σ₁₂'_1 : R₁ →+* R₂'}\n  (e_σ₁₂' : σ₁₂' = σ₁₂'_1) [inst_12 : RingHomInvPair σ₁₂ σ₂₁] [inst_13 : RingHomInvPair σ₂₁ σ₁₂]\n  [inst_14 : RingHomInvPair σ₁'₂' σ₂'₁'] [inst_15 : RingHomInvPair σ₂'₁' σ₁'₂']\n  [inst_16 : RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_17 : RingHomCompTriple σ₂₁ σ₁₂' σ₂₂']\n  [inst_18 : RingHomCompTriple 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RingHomInvPair σ₁'₂' σ₂'₁'] [inst_15 : RingHomInvPair σ₂'₁' σ₁'₂']\n  [inst_16 : RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_17 : RingHomCompTriple σ₂₁ σ₁₂' σ₂₂']\n  [inst_18 : RingHomCompTriple σ₂₂' σ₂'₁' σ₂₁'] [inst_19 : RingHomCompTriple σ₁₂ σ₂₁' σ₁₁'] (e₁ e₁_1 : M₁ ≃ₛₗ[σ₁₂] M₂),\n  e₁ = e₁_1 → ∀ (e₂ e₂_1 : M₁' ≃ₛₗ[σ₁'₂'] M₂'), e₂ = e₂_1 → e₁.arrowCongrAddEquiv e₂ = e₁_1.arrowCongrAddEquiv e₂_1","typeReferences":[["RingHom"],["Module"],["LinearEquiv"],["LinearMap"],["AddEquiv"],["RingHomCompTriple"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["LinearEquiv","arrowCongrAddEquiv"],["LinearMap","instAdd"],["Eq","ndrec"],["Eq"],["RingHomInvPair"],["Semiring"]],"valueReferences":[["RingHom"],["LinearEquiv"],["LinearMap"],["AddEquiv"],["RingHomCompTriple"],["Semiring","toNonAssocSemiring"],["LinearEquiv","arrowCongrAddEquiv"],["Eq","refl"],["LinearMap","instAdd"],["Eq","rec"],["Eq"],["RingHomInvPair"],["Eq","ndrec"]]},{"isProp":true,"kind":"theorem","name":["_private","Mathlib","Algebra","Module","Equiv","Basic",0,"LinearEquiv","ofSubsingleton_self","_simp_1_1"],"typeFallback":"forall {α : Sort.{u_1}} [inst._@.Init.Core.2795499514._hygCtx._hyg.9 : Subsingleton.{u_1} α] (x : α) (y : α), Eq.{1} Prop (Eq.{u_1} α x y) True","typeFull":"∀ {α : Sort u_1} [Subsingleton α] (x y : α), (x = y) = True","typeReadable":"∀ {α : Sort u_1} [Subsingleton α] (x y : α), (x = y) = True","typeReferences":[["Subsingleton"],["True"],["Eq"]],"valueReferences":[["True"],["eq_iff_true_of_subsingleton"],["Eq"],["propext"]]},{"isProp":false,"kind":"definition","name":["LinearEquiv","arrowCongrAddEquiv"],"typeFallback":"forall {R₁ : Type.{u_9}} {R₂ : Type.{u_10}} {R₁' : Type.{u_11}} {R₂' : Type.{u_12}} {M₁ : Type.{u_13}} {M₂ : Type.{u_14}} {M₁' : Type.{u_15}} {M₂' : Type.{u_16}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 : Semiring.{u_9} R₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 : Semiring.{u_10} R₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 : Semiring.{u_11} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 : Semiring.{u_12} R₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 : AddCommMonoid.{u_13} M₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 : AddCommMonoid.{u_14} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 : AddCommMonoid.{u_15} M₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 : AddCommMonoid.{u_16} M₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 : Module.{u_9, u_13} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 : Module.{u_10, u_14} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 : Module.{u_11, u_15} R₁' M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 : Module.{u_12, u_16} R₂' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39] {σ₁₂ : RingHom.{u_9, u_10} R₁ R₂ (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21)} {σ₂₁ : RingHom.{u_10, u_9} R₂ R₁ (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21) (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18)} {σ₁'₂' : RingHom.{u_11, u_12} R₁' R₂' (Semiring.toNonAssocSemiring.{u_11} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24) (Semiring.toNonAssocSemiring.{u_12} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27)} {σ₂'₁' : RingHom.{u_12, u_11} R₂' R₁' (Semiring.toNonAssocSemiring.{u_12} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27) (Semiring.toNonAssocSemiring.{u_11} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24)} {σ₁₁' : RingHom.{u_9, u_11} R₁ R₁' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_11} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24)} {σ₂₂' : RingHom.{u_10, u_12} R₂ R₂' (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21) (Semiring.toNonAssocSemiring.{u_12} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27)} {σ₂₁' : RingHom.{u_10, u_11} R₂ R₁' (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21) (Semiring.toNonAssocSemiring.{u_11} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24)} {σ₁₂' : RingHom.{u_9, u_12} R₁ R₂' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_12} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27)} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 : RingHomInvPair.{u_9, u_10} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 σ₁₂ σ₂₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 : RingHomInvPair.{u_10, u_9} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 σ₂₁ σ₁₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 : RingHomInvPair.{u_11, u_12} R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₁'₂' σ₂'₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 : RingHomInvPair.{u_12, u_11} R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₂'₁' σ₁'₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.114 : RingHomCompTriple.{u_9, u_11, u_12} R₁ R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₁₁' σ₁'₂' σ₁₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.119 : RingHomCompTriple.{u_10, u_9, u_12} R₂ R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₂₁ σ₁₂' σ₂₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.124 : RingHomCompTriple.{u_10, u_12, u_11} R₂ R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₂₂' σ₂'₁' σ₂₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.129 : RingHomCompTriple.{u_9, u_10, u_11} R₁ R₂ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₂ σ₂₁' σ₁₁'], (LinearEquiv.{u_9, u_10, u_13, u_14} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46) -> (LinearEquiv.{u_11, u_12, u_15, u_16} R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54) -> (AddEquiv.{max u_15 u_13, max u_16 u_14} (LinearMap.{u_9, u_11, u_13, u_15} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50) (LinearMap.{u_10, u_12, u_14, u_16} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54) (LinearMap.instAdd.{u_9, u_11, u_13, u_15} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 σ₁₁') (LinearMap.instAdd.{u_10, u_12, u_14, u_16} R₂ R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 σ₂₂'))","typeFull":"{R₁ : Type u_9} →\n  {R₂ : Type u_10} →\n    {R₁' : Type u_11} →\n      {R₂' : Type u_12} →\n        {M₁ : Type u_13} →\n          {M₂ : Type u_14} →\n            {M₁' : Type u_15} →\n              {M₂' : Type u_16} →\n                [inst : Semiring R₁] →\n                  [inst_1 : Semiring R₂] →\n                    [inst_2 : Semiring R₁'] →\n                      [inst_3 : Semiring R₂'] →\n                        [inst_4 : AddCommMonoid M₁] →\n                          [inst_5 : AddCommMonoid M₂] →\n                            [inst_6 : AddCommMonoid M₁'] →\n                              [inst_7 : AddCommMonoid M₂'] →\n                                [inst_8 : Module R₁ M₁] →\n                                  [inst_9 : Module R₂ M₂] →\n                                    [inst_10 : Module R₁' M₁'] →\n                                      [inst_11 : Module R₂' M₂'] →\n                                        {σ₁₂ : R₁ →+* R₂} →\n                                          {σ₂₁ : R₂ →+* R₁} →\n                                            {σ₁'₂' : R₁' →+* R₂'} →\n                                              {σ₂'₁' : R₂' →+* R₁'} →\n                                                {σ₁₁' : R₁ →+* R₁'} →\n                                                  {σ₂₂' : R₂ →+* R₂'} →\n                                                    {σ₂₁' : R₂ →+* R₁'} →\n                                                      {σ₁₂' : R₁ →+* R₂'} →\n                                                        [inst_12 : RingHomInvPair σ₁₂ σ₂₁] →\n                                                          [inst_13 : RingHomInvPair σ₂₁ σ₁₂] →\n                                                            [inst_14 : RingHomInvPair σ₁'₂' σ₂'₁'] →\n                                                              [inst_15 : RingHomInvPair σ₂'₁' σ₁'₂'] →\n                                                                [RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] →\n                                                                  [RingHomCompTriple σ₂₁ σ₁₂' σ₂₂'] →\n                                                                    [RingHomCompTriple σ₂₂' σ₂'₁' σ₂₁'] →\n                                                                      [RingHomCompTriple σ₁₂ σ₂₁' σ₁₁'] →\n                                                                        (M₁ ≃ₛₗ[σ₁₂] M₂) →\n                                                                          (M₁' ≃ₛₗ[σ₁'₂'] M₂') →\n                                                                            (M₁ →ₛₗ[σ₁₁'] M₁') ≃+ (M₂ →ₛₗ[σ₂₂'] M₂')","typeReadable":"{R₁ : Type u_9} →\n  {R₂ : Type u_10} →\n    {R₁' : Type u_11} →\n      {R₂' : Type u_12} →\n        {M₁ : Type u_13} →\n          {M₂ : Type u_14} →\n            {M₁' : Type u_15} →\n              {M₂' : Type u_16} →\n                [inst : Semiring R₁] →\n                  [inst_1 : Semiring R₂] →\n                    [inst_2 : Semiring R₁'] →\n                      [inst_3 : Semiring R₂'] →\n                        [inst_4 : AddCommMonoid M₁] →\n                          [inst_5 : AddCommMonoid M₂] →\n                            [inst_6 : AddCommMonoid M₁'] →\n                              [inst_7 : AddCommMonoid M₂'] →\n                                [inst_8 : Module R₁ M₁] →\n                                  [inst_9 : Module R₂ M₂] →\n                                    [inst_10 : Module R₁' M₁'] →\n                                      [inst_11 : Module R₂' M₂'] →\n                                        {σ₁₂ : R₁ →+* R₂} →\n                                          {σ₂₁ : R₂ →+* R₁} →\n                                            {σ₁'₂' : R₁' →+* R₂'} →\n                                              {σ₂'₁' : R₂' →+* R₁'} →\n                                                {σ₁₁' : R₁ →+* R₁'} →\n                                                  {σ₂₂' : R₂ →+* R₂'} →\n                                                    {σ₂₁' : R₂ →+* R₁'} →\n                                                      {σ₁₂' : R₁ →+* R₂'} →\n                                                        [inst_12 : RingHomInvPair σ₁₂ σ₂₁] →\n                                                          [inst_13 : RingHomInvPair σ₂₁ σ₁₂] →\n                                                            [inst_14 : RingHomInvPair σ₁'₂' σ₂'₁'] →\n                                                              [inst_15 : RingHomInvPair σ₂'₁' σ₁'₂'] →\n                                                                [RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] →\n                                                                  [RingHomCompTriple σ₂₁ σ₁₂' σ₂₂'] →\n                                                                    [RingHomCompTriple σ₂₂' σ₂'₁' σ₂₁'] →\n                                                                      [RingHomCompTriple σ₁₂ σ₂₁' σ₁₁'] →\n                                                                        (M₁ ≃ₛₗ[σ₁₂] M₂) →\n                                                                          (M₁' ≃ₛₗ[σ₁'₂'] M₂') →\n                                                                            (M₁ →ₛₗ[σ₁₁'] M₁') ≃+ (M₂ →ₛₗ[σ₂₂'] M₂')","typeReferences":[["RingHom"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["Module"],["LinearMap","instAdd"],["LinearMap"],["LinearEquiv"],["RingHomInvPair"],["AddEquiv"],["RingHomCompTriple"],["Semiring"]],"valueReferences":[["AddEquiv","mk"],["LinearEquiv","arrowCongrAddEquiv","_proof_2"],["Equiv","mk"],["LinearMap","instAdd"],["LinearMap","comp"],["LinearEquiv","toLinearMap"],["LinearMap"],["LinearEquiv","symm"],["LinearEquiv","arrowCongrAddEquiv","_proof_1"],["LinearEquiv","arrowCongrAddEquiv","_proof_3"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","piUnique","_proof_2"],"typeFallback":"forall {α : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1979755013._hygCtx._hyg.11 : Unique.{succ u_2} α] (R : Type.{u_3}) 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x._@.Mathlib.Algebra.Module.Equiv.Basic.1979755013._hygCtx._hyg.82 x._@.Mathlib.Algebra.Module.Equiv.Basic.1979755013._hygCtx._hyg.84)) (Equiv.toFun.{max (succ u_2) (succ u_1), succ u_1} (forall (i : α), f i) (f (Inhabited.default.{succ u_2} α (Unique.instInhabited.{succ u_2} α inst._@.Mathlib.Algebra.Module.Equiv.Basic.1979755013._hygCtx._hyg.11))) (Equiv.piUnique.{succ u_2, succ u_1} α inst._@.Mathlib.Algebra.Module.Equiv.Basic.1979755013._hygCtx._hyg.11 f) (HSMul.hSMul.{u_3, max u_1 u_2, max u_1 u_2} R (forall (t : α), f t) (forall (t : α), f t) (instHSMul.{u_3, max u_1 u_2} R (forall (t : α), f t) (SMulZeroClass.toSMul.{u_3, max u_1 u_2} R (forall (t : α), f t) (AddZero.toZero.{max u_1 u_2} (forall (t : α), f t) (AddZeroClass.toAddZero.{max u_1 u_2} (forall (t : α), f t) (AddMonoid.toAddZeroClass.{max u_1 u_2} (forall (t : α), f t) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (forall (t : α), f t) (Pi.addCommMonoid.{u_2, u_1} α f 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x_1) = (Equiv.piUnique f).toFun (x • x_1)","typeReferences":[["Unique"],["Equiv","piUnique"],["Module"],["Pi","addCommMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["Pi","module"],["Inhabited","default"],["Module","toDistribMulAction"],["AddCommMonoid"],["MonoidWithZero","toMonoid"],["HSMul","hSMul"],["instHSMul"],["Equiv","toFun"],["Eq"],["AddZero","toZero"],["DistribSMul","toSMulZeroClass"],["AddMonoid","toAddZeroClass"],["Semiring"],["Unique","instInhabited"]],"valueReferences":[["rfl"],["Equiv","piUnique"],["Pi","addCommMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["Pi","module"],["Inhabited","default"],["Module","toDistribMulAction"],["MonoidWithZero","toMonoid"],["HSMul","hSMul"],["instHSMul"],["Equiv","toFun"],["AddZero","toZero"],["DistribSMul","toSMulZeroClass"],["Unique","instInhabited"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["AddEquiv","toIntLinearEquiv_toAddEquiv"],"typeFallback":"forall 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AddCommGroup M₂] {modM : Module ℤ M}\n  {modM₂ : Module ℤ M₂} (e : M ≃+ M₂), ↑e.toIntLinearEquiv = 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(AddCommMagma.toAdd.{u_1} (LinearMap.{0, 0, u_1, u_1} Int Int Int.instSemiring Int.instSemiring (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int Int.instSemiring)) A A (AddCommGroup.toAddCommMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (AddCommGroup.toAddCommMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (AddCommGroup.toIntModule.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (AddCommGroup.toIntModule.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11)) (AddCommSemigroup.toAddCommMagma.{u_1} (LinearMap.{0, 0, u_1, u_1} Int Int Int.instSemiring Int.instSemiring (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int Int.instSemiring)) A A (AddCommGroup.toAddCommMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (AddCommGroup.toAddCommMonoid.{u_1} A 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(AddCommGroup.toAddCommMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (AddCommGroup.toAddCommMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (AddCommGroup.toIntModule.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (AddCommGroup.toIntModule.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int Int.instSemiring)))))) (LinearMap.toAddHom.{0, 0, u_1, u_1} Int Int Int.instSemiring Int.instSemiring (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int Int.instSemiring)) (AddMonoidHom.{u_1, u_1} A A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (SubNegMonoid.toAddMonoid.{u_1} A (AddGroup.toSubNegMonoid.{u_1} A (AddCommGroup.toAddGroup.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11))))) (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (SubNegMonoid.toAddMonoid.{u_1} A (AddGroup.toSubNegMonoid.{u_1} A (AddCommGroup.toAddGroup.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11)))))) (LinearMap.{0, 0, u_1, u_1} Int Int Int.instSemiring Int.instSemiring (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int Int.instSemiring)) A A (AddCommGroup.toAddCommMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (AddCommGroup.toAddCommMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (AddCommGroup.toIntModule.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (AddCommGroup.toIntModule.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11)) (AddMonoidHom.instAddCommMonoid.{u_1, u_1} A A (AddMonoid.toAddZeroClass.{u_1} A (SubNegMonoid.toAddMonoid.{u_1} A (AddGroup.toSubNegMonoid.{u_1} A (AddCommGroup.toAddGroup.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11)))) (AddCommGroup.toAddCommMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11)) (LinearMap.addCommMonoid.{0, 0, u_1, u_1} Int Int A A Int.instSemiring Int.instSemiring (AddCommGroup.toAddCommMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (AddCommGroup.toAddCommMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (AddCommGroup.toIntModule.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (AddCommGroup.toIntModule.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int Int.instSemiring))) (AddMonoidHom.instModule.{0, u_1, u_1} Int A A Int.instSemiring (SubNegMonoid.toAddMonoid.{u_1} A (AddGroup.toSubNegMonoid.{u_1} A (AddCommGroup.toAddGroup.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11))) (AddCommGroup.toAddCommMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (AddCommGroup.toIntModule.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11)) (LinearMap.module.{0, 0, 0, u_1, u_1} Int Int Int A A Int.instSemiring Int.instSemiring (AddCommGroup.toAddCommMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (AddCommGroup.toAddCommMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (AddCommGroup.toIntModule.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (AddCommGroup.toIntModule.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int Int.instSemiring)) Int.instSemiring (AddCommGroup.toIntModule.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (addMonoidEndRingEquivInt._proof_1.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11)) (LinearEquiv.toLinearMap.{0, 0, u_1, u_1} Int Int Int.instSemiring Int.instSemiring (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int Int.instSemiring)) (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int Int.instSemiring)) (RingHomInvPair.ids.{0} Int Int.instSemiring) (RingHomInvPair.ids.{0} Int Int.instSemiring) (AddMonoidHom.{u_1, u_1} A A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (SubNegMonoid.toAddMonoid.{u_1} A (AddGroup.toSubNegMonoid.{u_1} A (AddCommGroup.toAddGroup.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11))))) (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (SubNegMonoid.toAddMonoid.{u_1} A (AddGroup.toSubNegMonoid.{u_1} A (AddCommGroup.toAddGroup.{u_1} A 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a","typeReferences":[["Module"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["AddEquiv","instEquivLike"],["EquivLike","toFunLike"],["MonoidWithZero","toMonoid"],["instHSMul"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Eq"],["DistribSMul","toSMulZeroClass"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddCommGroup"],["AddZeroClass","toAddZero"],["AddEquiv"],["Int"],["Module","toDistribMulAction"],["AddCommMonoid","toAddCommSemigroup"],["Int","instSemiring"],["HSMul","hSMul"],["AddCommGroup","toAddCommMonoid"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["AddCommGroup","toAddGroup"],["SemigroupAction","toSMul"],["SMulZeroClass","toSMul"],["AddEquiv","toAddMonoidHom"],["AddMonoidHom"],["eq_of_heq"],["Eq","symm"],["DistribMulAction","toMulAction"],["AddMonoidHom","instFunLike"],["AddGroup","toSubNegMonoid"],["Monoid","toSemigroup"],["Eq","ndrec"],["DistribSMul","toSMulZeroClass"],["DistribMulAction","toDistribSMul"],["AddZeroClass","toAddZero"],["AddEquiv"],["SubtractionMonoid","toSubNegMonoid"],["Eq","refl"],["HSMul","hSMul"],["AddCommGroup","toAddCommMonoid"],["HEq"],["id"],["Eq","mpr"],["SubNegMonoid","toZSMul"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["SubtractionCommMonoid","toSubtractionMonoid"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["AddEquiv","instEquivLike"],["congrArg"],["MonoidWithZero","toMonoid"],["EquivLike","toFunLike"],["instHSMul"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Eq"],["HEq","refl"],["Semiring","toMonoidWithZero"],["Eq","casesOn"],["Int"],["AddMonoidHom","map_zsmul"],["Module","toDistribMulAction"],["AddCommMonoid","toAddCommSemigroup"],["SubNegMonoid","toAddMonoid"],["AddCommGroup","toDivisionAddCommMonoid"],["Int","instSemiring"],["int_smul_eq_zsmul"],["SMul","smul"],["MulAction","toSemigroupAction"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","domMulActCongrRight","_proof_4"],"typeFallback":"forall {S : Type.{u_1}} {R₁ : Type.{u_2}} {R₁' : Type.{u_3}} {R₂' : Type.{u_7}} {M₁ : Type.{u_4}} {M₁' : Type.{u_5}} {M₂' : Type.{u_6}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 : Semiring.{u_2} R₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 : Semiring.{u_3} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 : Semiring.{u_7} R₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 : AddCommMonoid.{u_4} M₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 : AddCommMonoid.{u_5} M₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 : AddCommMonoid.{u_6} M₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 : Module.{u_2, u_4} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 : Module.{u_3, u_5} R₁' M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 : Module.{u_7, u_6} R₂' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39] {σ₁'₂' : RingHom.{u_3, u_7} R₁' R₂' (Semiring.toNonAssocSemiring.{u_3} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24) (Semiring.toNonAssocSemiring.{u_7} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27)} {σ₂'₁' : RingHom.{u_7, u_3} R₂' R₁' (Semiring.toNonAssocSemiring.{u_7} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27) (Semiring.toNonAssocSemiring.{u_3} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24)} {σ₁₁' : RingHom.{u_2, u_3} R₁ R₁' (Semiring.toNonAssocSemiring.{u_2} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_3} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24)} {σ₁₂' : RingHom.{u_2, u_7} R₁ R₂' (Semiring.toNonAssocSemiring.{u_2} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_7} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27)} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.106 : RingHomInvPair.{u_3, u_7} R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁'₂' σ₂'₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.110 : RingHomInvPair.{u_7, u_3} R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₂'₁' σ₁'₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.114 : RingHomCompTriple.{u_2, u_3, u_7} R₁ R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₁' σ₁'₂' σ₁₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134 : Semiring.{u_1} S] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.137 : Module.{u_1, u_4} S M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.141 : SMulCommClass.{u_2, u_1, u_4} R₁ S M₁ (SMulZeroClass.toSMul.{u_2, u_4} R₁ M₁ (AddZero.toZero.{u_4} M₁ (AddZeroClass.toAddZero.{u_4} M₁ (AddMonoid.toAddZeroClass.{u_4} M₁ (AddCommMonoid.toAddMonoid.{u_4} M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30)))) (DistribSMul.toSMulZeroClass.{u_2, u_4} R₁ M₁ (AddMonoid.toAddZeroClass.{u_4} M₁ (AddCommMonoid.toAddMonoid.{u_4} M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30)) (DistribMulAction.toDistribSMul.{u_2, u_4} R₁ M₁ (MonoidWithZero.toMonoid.{u_2} R₁ (Semiring.toMonoidWithZero.{u_2} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18)) (AddCommMonoid.toAddMonoid.{u_4} M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30) (Module.toDistribMulAction.{u_2, u_4} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42)))) (SMulZeroClass.toSMul.{u_1, u_4} S M₁ (AddZero.toZero.{u_4} M₁ (AddZeroClass.toAddZero.{u_4} M₁ (AddMonoid.toAddZeroClass.{u_4} M₁ (AddCommMonoid.toAddMonoid.{u_4} M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30)))) (DistribSMul.toSMulZeroClass.{u_1, u_4} S M₁ (AddMonoid.toAddZeroClass.{u_4} M₁ (AddCommMonoid.toAddMonoid.{u_4} M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30)) (DistribMulAction.toDistribSMul.{u_1, u_4} S M₁ (MonoidWithZero.toMonoid.{u_1} S (Semiring.toMonoidWithZero.{u_1} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)) (AddCommMonoid.toAddMonoid.{u_4} M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30) (Module.toDistribMulAction.{u_1, u_4} S M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.137))))] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.146 : RingHomCompTriple.{u_2, u_7, u_3} R₁ R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₂' σ₂'₁' σ₁₁'] (e₂ : LinearEquiv.{u_3, u_7, u_5, u_6} R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.110 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (b : DomMulAct.{u_1} S) (x : LinearMap.{u_2, u_3, u_4, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50), Eq.{succ (max u_4 u_6)} (LinearMap.{u_2, u_7, u_4, u_6} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (Equiv.toFun.{succ (max u_5 u_4), succ (max u_6 u_4)} (LinearMap.{u_2, u_3, u_4, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.{u_2, u_7, u_4, u_6} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (AddEquiv.toEquiv.{max u_5 u_4, max u_6 u_4} (LinearMap.{u_2, u_3, u_4, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.{u_2, u_7, u_4, u_6} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (LinearMap.instAdd.{u_2, u_3, u_4, u_5} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁') (LinearMap.instAdd.{u_2, u_7, u_4, u_6} R₁ R₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂') (LinearEquiv.arrowCongrAddEquiv.{u_2, u_2, u_3, u_7, u_4, u_4, u_5, u_6} R₁ R₁ R₁' R₂' M₁ M₁ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 (RingHom.id.{u_2} R₁ (Semiring.toNonAssocSemiring.{u_2} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18)) (RingHom.id.{u_2} R₁ (Semiring.toNonAssocSemiring.{u_2} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18)) σ₁'₂' σ₂'₁' σ₁₁' σ₁₂' σ₁₁' σ₁₂' (RingHomInvPair.ids.{u_2} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) (RingHomInvPair.ids.{u_2} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.114 (RingHomCompTriple.ids.{u_2, u_7} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂') inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.146 (RingHomCompTriple.ids.{u_2, u_3} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁') (LinearEquiv.refl.{u_2, u_4} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42) e₂)) (HSMul.hSMul.{u_1, max u_4 u_5, max u_4 u_5} (DomMulAct.{u_1} S) (LinearMap.{u_2, u_3, u_4, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.{u_2, u_3, u_4, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (instHSMul.{u_1, max u_4 u_5} (DomMulAct.{u_1} S) (LinearMap.{u_2, u_3, u_4, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (SMulZeroClass.toSMul.{u_1, max u_4 u_5} (DomMulAct.{u_1} S) (LinearMap.{u_2, u_3, u_4, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (AddZero.toZero.{max u_4 u_5} (LinearMap.{u_2, u_3, u_4, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (AddZeroClass.toAddZero.{max u_4 u_5} (LinearMap.{u_2, u_3, u_4, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (AddMonoid.toAddZeroClass.{max u_4 u_5} (LinearMap.{u_2, u_3, u_4, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (AddCommMonoid.toAddMonoid.{max u_4 u_5} (LinearMap.{u_2, u_3, u_4, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.addCommMonoid.{u_2, u_3, u_4, u_5} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁'))))) (DistribSMul.toSMulZeroClass.{u_1, max u_4 u_5} (DomMulAct.{u_1} S) (LinearMap.{u_2, u_3, u_4, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (AddMonoid.toAddZeroClass.{max u_4 u_5} (LinearMap.{u_2, u_3, u_4, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (AddCommMonoid.toAddMonoid.{max u_4 u_5} (LinearMap.{u_2, u_3, u_4, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.addCommMonoid.{u_2, u_3, u_4, u_5} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁'))) (DistribMulAction.toDistribSMul.{u_1, max u_4 u_5} (DomMulAct.{u_1} S) (LinearMap.{u_2, u_3, u_4, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (MonoidWithZero.toMonoid.{u_1} (DomMulAct.{u_1} S) (Semiring.toMonoidWithZero.{u_1} (DomMulAct.{u_1} S) (DomMulAct.instSemiringOfMulOpposite.{u_1} S (MulOpposite.instSemiring.{u_1} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)))) (AddCommMonoid.toAddMonoid.{max u_4 u_5} (LinearMap.{u_2, u_3, u_4, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.addCommMonoid.{u_2, u_3, u_4, u_5} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁')) (Module.toDistribMulAction.{u_1, max u_4 u_5} (DomMulAct.{u_1} S) (LinearMap.{u_2, u_3, u_4, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (DomMulAct.instSemiringOfMulOpposite.{u_1} S (MulOpposite.instSemiring.{u_1} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)) (LinearMap.addCommMonoid.{u_2, u_3, u_4, u_5} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁') (LinearMap.instModuleDomMulActOfSMulCommClass.{u_2, u_3, u_1, u_4, u_5} R₁ R₁' S M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.137 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.141)))))) b x)) (HSMul.hSMul.{u_1, max u_4 u_6, max u_4 u_6} (DomMulAct.{u_1} S) (LinearMap.{u_2, u_7, u_4, u_6} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (LinearMap.{u_2, u_7, u_4, u_6} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (instHSMul.{u_1, max u_4 u_6} (DomMulAct.{u_1} S) (LinearMap.{u_2, u_7, u_4, u_6} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (SMulZeroClass.toSMul.{u_1, max u_4 u_6} (DomMulAct.{u_1} S) (LinearMap.{u_2, u_7, u_4, u_6} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (AddZero.toZero.{max u_4 u_6} (LinearMap.{u_2, u_7, u_4, u_6} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (AddZeroClass.toAddZero.{max u_4 u_6} (LinearMap.{u_2, u_7, u_4, u_6} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (AddMonoid.toAddZeroClass.{max u_4 u_6} (LinearMap.{u_2, u_7, u_4, u_6} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (AddCommMonoid.toAddMonoid.{max u_4 u_6} (LinearMap.{u_2, u_7, u_4, u_6} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (LinearMap.addCommMonoid.{u_2, u_7, u_4, u_6} R₁ R₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂'))))) (DistribSMul.toSMulZeroClass.{u_1, max u_4 u_6} (DomMulAct.{u_1} S) (LinearMap.{u_2, u_7, u_4, u_6} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (AddMonoid.toAddZeroClass.{max u_4 u_6} (LinearMap.{u_2, u_7, u_4, u_6} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (AddCommMonoid.toAddMonoid.{max u_4 u_6} (LinearMap.{u_2, u_7, u_4, u_6} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (LinearMap.addCommMonoid.{u_2, u_7, u_4, u_6} R₁ R₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂'))) (DistribMulAction.toDistribSMul.{u_1, max u_4 u_6} (DomMulAct.{u_1} S) (LinearMap.{u_2, u_7, u_4, u_6} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (MonoidWithZero.toMonoid.{u_1} (DomMulAct.{u_1} S) (Semiring.toMonoidWithZero.{u_1} (DomMulAct.{u_1} S) (DomMulAct.instSemiringOfMulOpposite.{u_1} S (MulOpposite.instSemiring.{u_1} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)))) (AddCommMonoid.toAddMonoid.{max u_4 u_6} (LinearMap.{u_2, u_7, u_4, u_6} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (LinearMap.addCommMonoid.{u_2, u_7, u_4, u_6} R₁ R₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂')) (Module.toDistribMulAction.{u_1, max u_4 u_6} (DomMulAct.{u_1} S) (LinearMap.{u_2, u_7, u_4, u_6} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (DomMulAct.instSemiringOfMulOpposite.{u_1} S (MulOpposite.instSemiring.{u_1} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)) (LinearMap.addCommMonoid.{u_2, u_7, u_4, u_6} R₁ R₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂') (LinearMap.instModuleDomMulActOfSMulCommClass.{u_2, u_7, u_1, u_4, u_6} R₁ R₂' S M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.137 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.141)))))) (DFunLike.coe.{succ u_1, succ u_1, succ u_1} (RingHom.{u_1, u_1} (DomMulAct.{u_1} S) (DomMulAct.{u_1} S) (Semiring.toNonAssocSemiring.{u_1} (DomMulAct.{u_1} S) (DomMulAct.instSemiringOfMulOpposite.{u_1} S (MulOpposite.instSemiring.{u_1} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134))) (Semiring.toNonAssocSemiring.{u_1} (DomMulAct.{u_1} S) (DomMulAct.instSemiringOfMulOpposite.{u_1} S (MulOpposite.instSemiring.{u_1} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)))) (DomMulAct.{u_1} S) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : DomMulAct.{u_1} S) => DomMulAct.{u_1} S) (RingHom.instFunLike.{u_1, u_1} (DomMulAct.{u_1} S) (DomMulAct.{u_1} S) (Semiring.toNonAssocSemiring.{u_1} (DomMulAct.{u_1} S) (DomMulAct.instSemiringOfMulOpposite.{u_1} S (MulOpposite.instSemiring.{u_1} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134))) (Semiring.toNonAssocSemiring.{u_1} (DomMulAct.{u_1} S) (DomMulAct.instSemiringOfMulOpposite.{u_1} S (MulOpposite.instSemiring.{u_1} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)))) (RingHom.id.{u_1} (DomMulAct.{u_1} S) (DomMulAct.instNonAssocSemiringOfMulOpposite.{u_1} S (MulOpposite.instNonAssocSemiring.{u_1} S (Semiring.toNonAssocSemiring.{u_1} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.134)))) b) (Equiv.toFun.{succ (max u_5 u_4), succ (max u_6 u_4)} (LinearMap.{u_2, u_3, u_4, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.{u_2, u_7, u_4, u_6} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (AddEquiv.toEquiv.{max u_5 u_4, max u_6 u_4} (LinearMap.{u_2, u_3, u_4, u_5} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50) (LinearMap.{u_2, u_7, u_4, u_6} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54) (LinearMap.instAdd.{u_2, u_3, u_4, u_5} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 σ₁₁') (LinearMap.instAdd.{u_2, u_7, u_4, u_6} R₁ R₂' M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 σ₁₂') (LinearEquiv.arrowCongrAddEquiv.{u_2, u_2, u_3, u_7, u_4, u_4, u_5, u_6} R₁ R₁ R₁' R₂' M₁ M₁ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.54 (RingHom.id.{u_2} R₁ (Semiring.toNonAssocSemiring.{u_2} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18)) (RingHom.id.{u_2} R₁ (Semiring.toNonAssocSemiring.{u_2} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18)) σ₁'₂' σ₂'₁' σ₁₁' σ₁₂' σ₁₁' σ₁₂' (RingHomInvPair.ids.{u_2} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) (RingHomInvPair.ids.{u_2} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.114 (RingHomCompTriple.ids.{u_2, u_7} R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.27 σ₁₂') inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.146 (RingHomCompTriple.ids.{u_2, u_3} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.24 σ₁₁') (LinearEquiv.refl.{u_2, u_4} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1952284028._hygCtx._hyg.42) e₂)) x))","typeFull":"∀ {S : Type u_1} {R₁ : Type u_2} {R₁' : Type u_3} {R₂' : Type u_7} {M₁ : Type u_4} {M₁' : Type u_5} {M₂' : Type u_6}\n  [inst : Semiring R₁] [inst_1 : Semiring R₁'] [inst_2 : Semiring R₂'] [inst_3 : AddCommMonoid M₁]\n  [inst_4 : AddCommMonoid M₁'] [inst_5 : AddCommMonoid M₂'] [inst_6 : Module R₁ M₁] [inst_7 : Module R₁' M₁']\n  [inst_8 : Module R₂' M₂'] {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} {σ₁₁' : R₁ →+* R₁'} {σ₁₂' : R₁ →+* R₂'}\n  [inst_9 : RingHomInvPair σ₁'₂' σ₂'₁'] [inst_10 : RingHomInvPair σ₂'₁' σ₁'₂']\n  [inst_11 : RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_12 : Semiring S] [inst_13 : Module S M₁]\n  [inst_14 : SMulCommClass R₁ S M₁] [inst_15 : RingHomCompTriple σ₁₂' σ₂'₁' σ₁₁'] (e₂ : M₁' ≃ₛₗ[σ₁'₂'] M₂') (b : Sᵈᵐᵃ)\n  (x : M₁ →ₛₗ[σ₁₁'] M₁'),\n  ((LinearEquiv.refl R₁ M₁).arrowCongrAddEquiv e₂).toFun (b • x) =\n    (RingHom.id Sᵈᵐᵃ) b • ((LinearEquiv.refl R₁ M₁).arrowCongrAddEquiv e₂).toFun x","typeReadable":"∀ {S : Type u_1} {R₁ : Type u_2} {R₁' : Type u_3} {R₂' : Type u_7} {M₁ : Type u_4} {M₁' : Type u_5} {M₂' : Type u_6}\n  [inst : Semiring R₁] [inst_1 : Semiring R₁'] [inst_2 : Semiring R₂'] [inst_3 : AddCommMonoid M₁]\n  [inst_4 : AddCommMonoid M₁'] [inst_5 : AddCommMonoid M₂'] [inst_6 : Module R₁ M₁] [inst_7 : Module R₁' M₁']\n  [inst_8 : Module R₂' M₂'] {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} {σ₁₁' : R₁ →+* R₁'} {σ₁₂' : R₁ →+* R₂'}\n  [inst_9 : RingHomInvPair σ₁'₂' σ₂'₁'] [inst_10 : RingHomInvPair σ₂'₁' σ₁'₂']\n  [inst_11 : RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_12 : Semiring S] [inst_13 : Module S M₁]\n  [inst_14 : SMulCommClass R₁ S M₁] [inst_15 : RingHomCompTriple σ₁₂' σ₂'₁' σ₁₁'] (e₂ : M₁' ≃ₛₗ[σ₁'₂'] M₂') (b : Sᵈᵐᵃ)\n  (x : M₁ →ₛₗ[σ₁₁'] M₁'),\n  ((LinearEquiv.refl R₁ M₁).arrowCongrAddEquiv e₂).toFun (b • x) =\n    (RingHom.id Sᵈᵐᵃ) b • ((LinearEquiv.refl R₁ M₁).arrowCongrAddEquiv e₂).toFun 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(e : LinearEquiv.{u_1, u_1, u_2, u_4} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36) M₂ M₃ inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.46) (x : LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50) (y : LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50), Eq.{succ (max u_3 u_4)} (LinearMap.{u_1, u_1, u_4, u_3} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) M₃ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50) (Equiv.toFun.{succ (max u_3 u_2), succ (max u_3 u_4)} (LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50) (LinearMap.{u_1, u_1, u_4, u_3} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) M₃ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50) (AddEquiv.toEquiv.{max u_3 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50) (LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50) (LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50) (instHAdd.{max u_3 u_2} (LinearMap.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50) (LinearMap.instAdd.{u_1, u_1, u_2, u_3} R R M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)))) x y)) (HAdd.hAdd.{max u_3 u_4, max u_3 u_4, max u_3 u_4} (LinearMap.{u_1, u_1, u_4, u_3} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) M₃ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50) (LinearMap.{u_1, u_1, u_4, u_3} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) M₃ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50) (LinearMap.{u_1, u_1, u_4, u_3} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHom.id.{u_1} R 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(LinearEquiv.automorphismGroup._proof_7.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36) e (LinearEquiv.refl.{u_1, u_3} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50))) y))","typeFull":"∀ (M : Type u_3) {M₂ : Type u_2} {M₃ : Type u_4} [inst : AddCommMonoid M] [inst_1 : AddCommMonoid M₂]\n  [inst_2 : AddCommMonoid M₃] {R : Type u_1} [inst_3 : Semiring R] [inst_4 : Module R M₂] [inst_5 : Module R M₃]\n  [inst_6 : Module R M] (e : M₂ ≃ₗ[R] M₃) (x y : M₂ →ₗ[R] M),\n  (e.arrowCongrAddEquiv (LinearEquiv.refl R M)).toFun (x + y) =\n    (e.arrowCongrAddEquiv (LinearEquiv.refl R M)).toFun x + (e.arrowCongrAddEquiv (LinearEquiv.refl R M)).toFun y","typeReadable":"∀ (M : Type u_3) {M₂ : Type u_2} {M₃ : Type u_4} [inst : AddCommMonoid M] [inst_1 : AddCommMonoid M₂]\n  [inst_2 : AddCommMonoid M₃] {R : Type u_1} [inst_3 : Semiring R] [inst_4 : Module R M₂] [inst_5 : Module R M₃]\n  [inst_6 : Module R M] (e : M₂ ≃ₗ[R] M₃) (x y : M₂ →ₗ[R] M),\n  (e.arrowCongrAddEquiv (LinearEquiv.refl R M)).toFun (x + y) =\n    (e.arrowCongrAddEquiv (LinearEquiv.refl R M)).toFun x + (e.arrowCongrAddEquiv (LinearEquiv.refl R M)).toFun 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Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 : Module.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19] (x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.78 : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25), Eq.{succ u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (instHMul.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 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[inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.10 : Semiring.{u_3} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.19 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.22 : AddCommMonoid.{u_1} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.25 : Module.{u_3, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.29 : Module.{u_3, u_1} R M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.22] (x : M) (y : M), Eq.{succ u_1} M₂ (AddHom.toFun.{u_2, u_1} M M₂ (AddCommMagma.toAdd.{u_2} M (AddCommSemigroup.toAddCommMagma.{u_2} M (AddCommMonoid.toAddCommSemigroup.{u_2} M 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.10 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.29) 0 (Zero.toOfNat0.{max u_2 u_1} (LinearMap.{u_3, u_3, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.10 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.29) (LinearMap.instZero.{u_3, u_3, u_2, u_1} R R M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.29 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.10)))))) (HAdd.hAdd.{u_2, u_2, u_2} M M M (instHAdd.{u_2} M (AddCommMagma.toAdd.{u_2} M (AddCommSemigroup.toAddCommMagma.{u_2} M (AddCommMonoid.toAddCommSemigroup.{u_2} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.19)))) x y)) 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.29 (OfNat.ofNat.{max u_2 u_1} (LinearMap.{u_3, u_3, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.10 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.10)) M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.29) 0 (Zero.toOfNat0.{max u_2 u_1} (LinearMap.{u_3, u_3, u_2, u_1} R R 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y","typeReferences":[["LinearMap","instZero"],["instHAdd"],["Module"],["LinearMap","toAddHom"],["LinearMap"],["OfNat","ofNat"],["HAdd","hAdd"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["AddCommMonoid","toAddCommSemigroup"],["RingHom","id"],["Zero","toOfNat0"],["AddHom","toFun"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Eq"],["Semiring"]],"valueReferences":[["LinearMap","instZero"],["AddHom","map_add'"],["Semiring","toNonAssocSemiring"],["AddCommMonoid","toAddCommSemigroup"],["RingHom","id"],["LinearMap","toAddHom"],["Zero","toOfNat0"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["LinearMap"],["OfNat","ofNat"]]},{"isProp":true,"kind":"theorem","name":["addMonoidHomLequivNat","_proof_3"],"typeFallback":"forall {B : Type.{u_2}} (R : Type.{u_1}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.13 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19 : AddCommMonoid.{u_2} B] 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(CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.62))} {σ₂'₁' : RingHom.{u_13, u_12} R₂' R₁' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.62)) (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.59))} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.293 : RingHomInvPair.{u_12, u_13} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.62) σ₁'₂' σ₂'₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.297 : RingHomInvPair.{u_13, u_12} R₂' R₁' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.59) σ₂'₁' σ₁'₂'], (LinearEquiv.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.297 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.114) -> (LinearEquiv.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.297 (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.114) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.59)))) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.86 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.110)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.62))) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1461087409._hygCtx._hyg.114)))))","typeFull":"{R₁' : Type u_12} →\n  {R₂' : Type u_13} →\n    {M₁' : Type u_20} →\n      {M₂' : Type u_21} →\n        [inst : CommSemiring R₁'] →\n          [inst_1 : CommSemiring R₂'] →\n            [inst_2 : AddCommMonoid M₁'] →\n              [inst_3 : AddCommMonoid M₂'] →\n                [inst_4 : Module R₁' M₁'] →\n                  [inst_5 : Module R₂' M₂'] →\n                    {σ₁'₂' : R₁' →+* R₂'} →\n                      {σ₂'₁' : R₂' →+* R₁'} →\n                        [inst_6 : RingHomInvPair σ₁'₂' σ₂'₁'] →\n                          [inst_7 : RingHomInvPair σ₂'₁' σ₁'₂'] →\n                            (M₁' ≃ₛₗ[σ₁'₂'] M₂') → Module.End R₁' M₁' ≃ₛₗ[σ₁'₂'] Module.End R₂' M₂'","typeReadable":"{R₁' : Type u_12} →\n  {R₂' : Type u_13} →\n    {M₁' : Type u_20} →\n      {M₂' : Type u_21} →\n        [inst : CommSemiring R₁'] →\n          [inst_1 : CommSemiring R₂'] →\n            [inst_2 : AddCommMonoid M₁'] →\n              [inst_3 : AddCommMonoid M₂'] →\n                [inst_4 : Module R₁' M₁'] →\n                  [inst_5 : Module R₂' M₂'] →\n                    {σ₁'₂' : R₁' →+* R₂'} →\n                      {σ₂'₁' : R₂' →+* R₁'} →\n                        [inst_6 : RingHomInvPair σ₁'₂' σ₂'₁'] →\n                          [inst_7 : RingHomInvPair σ₂'₁' σ₁'₂'] →\n                            (M₁' ≃ₛₗ[σ₁'₂'] M₂') → Module.End R₁' M₁' ≃ₛₗ[σ₁'₂'] Module.End R₂' M₂'","typeReferences":[["RingHom"],["smulCommClass_self"],["Module","End"],["CommMonoid","toMonoid"],["Module"],["CommSemiring"],["CommSemiring","toSemiring"],["LinearMap","module"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["DistribMulAction","toMulAction"],["RingHomInvPair"]],"valueReferences":[["Semiring","toNonAssocSemiring"],["LinearEquiv","conj","_proof_1"],["RingHom","id"],["CommSemiring","toSemiring"],["LinearEquiv","conj","_proof_4"],["LinearEquiv","conj","_proof_3"],["LinearEquiv","conj","_proof_2"],["LinearEquiv","arrowCongr"]]},{"isProp":false,"kind":"definition","name":["AddEquiv","toNatLinearEquiv"],"typeFallback":"forall {M : Type.{u_5}} {M₂ : Type.{u_7}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3107006938._hygCtx._hyg.13 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3107006938._hygCtx._hyg.16 : AddCommMonoid.{u_7} M₂], (AddEquiv.{u_5, u_7} M M₂ (AddCommMagma.toAdd.{u_5} M (AddCommSemigroup.toAddCommMagma.{u_5} M (AddCommMonoid.toAddCommSemigroup.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3107006938._hygCtx._hyg.13))) (AddCommMagma.toAdd.{u_7} M₂ (AddCommSemigroup.toAddCommMagma.{u_7} M₂ (AddCommMonoid.toAddCommSemigroup.{u_7} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3107006938._hygCtx._hyg.16)))) -> (LinearEquiv.{0, 0, u_5, u_7} Nat Nat Nat.instSemiring Nat.instSemiring (RingHom.id.{0} Nat Nat.instNonAssocSemiring) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.instSemiring)) (RingHomInvPair.ids.{0} Nat Nat.instSemiring) (RingHomInvPair.ids.{0} Nat Nat.instSemiring) M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3107006938._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3107006938._hygCtx._hyg.16 (AddCommMonoid.toNatModule.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3107006938._hygCtx._hyg.13) (AddCommMonoid.toNatModule.{u_7} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3107006938._hygCtx._hyg.16))","typeFull":"{M : Type u_5} → {M₂ : Type u_7} → [inst : AddCommMonoid M] → [inst_1 : AddCommMonoid M₂] → M ≃+ M₂ → M ≃ₗ[ℕ] M₂","typeReadable":"{M : Type u_5} → {M₂ : Type u_7} → [inst : AddCommMonoid M] → [inst_1 : AddCommMonoid M₂] → M ≃+ M₂ → M ≃ₗ[ℕ] M₂","typeReferences":[["LinearEquiv"],["AddEquiv"],["AddCommMonoid"],["Nat"],["Semiring","toNonAssocSemiring"],["AddCommMonoid","toAddCommSemigroup"],["Nat","instSemiring"],["Nat","instNonAssocSemiring"],["RingHom","id"],["RingHomInvPair","ids"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["AddCommMonoid","toNatModule"]],"valueReferences":[["Nat"],["Nat","instSemiring"],["AddEquiv","toNatLinearEquiv","_proof_1"],["AddCommMonoid","toNatModule"],["AddEquiv","toLinearEquiv"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","conjRingEquiv_apply_apply"],"typeFallback":"forall {R₁ : Type.{u_9}} {R₂ : Type.{u_10}} {M₁ : Type.{u_13}} {M₂ : Type.{u_14}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 : Semiring.{u_9} R₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 : Semiring.{u_10} R₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 : AddCommMonoid.{u_13} M₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 : AddCommMonoid.{u_14} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 : Module.{u_9, u_13} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 : Module.{u_10, u_14} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33] {σ₁₂ : RingHom.{u_9, u_10} R₁ R₂ (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21)} {σ₂₁ : RingHom.{u_10, u_9} R₂ R₁ (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21) (Semiring.toNonAssocSemiring.{u_9} R₁ 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 (RingHom.id.{u_10} R₂ (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21))))) (LinearEquiv.conjRingEquiv.{u_9, u_10, u_13, u_14} R₁ R₂ M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.102 e) f) a._@._internal._hyg.0) (DFunLike.coe.{max (succ u_13) (succ u_14), succ u_13, succ u_14} (LinearEquiv.{u_9, u_10, u_13, u_14} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.102 M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46) M₁ (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M₁) => 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.102)) e (DFunLike.coe.{succ u_13, succ u_13, succ u_13} (LinearMap.{u_9, u_9, u_13, u_13} R₁ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 (RingHom.id.{u_9} R₁ (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18)) M₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42) M₁ 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42) M₂ M₁ (LinearEquiv.instEquivLike.{u_10, u_9, u_14, u_13} R₂ R₁ M₂ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 σ₂₁ σ₁₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.98)) (LinearEquiv.symm.{u_9, u_10, u_13, u_14} R₁ R₂ M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.102 e) a._@._internal._hyg.0)))","typeFull":"∀ {R₁ : Type u_9} {R₂ : Type u_10} {M₁ : Type u_13} {M₂ : Type u_14} [inst : Semiring R₁] [inst_1 : Semiring R₂]\n  [inst_2 : AddCommMonoid M₁] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R₁ M₁] [inst_5 : Module R₂ M₂]\n  {σ₁₂ : R₁ →+* R₂} {σ₂₁ : R₂ →+* R₁} [inst_6 : RingHomInvPair σ₁₂ σ₂₁] [inst_7 : RingHomInvPair σ₂₁ σ₁₂]\n  (e : M₁ ≃ₛₗ[σ₁₂] M₂) (f : M₁ →ₗ[R₁] M₁) (a : M₂), (e.conjRingEquiv f) a = e (f (e.symm a))","typeReadable":"∀ {R₁ : Type u_9} {R₂ : Type u_10} {M₁ : Type u_13} {M₂ : Type u_14} [inst : Semiring R₁] [inst_1 : Semiring R₂]\n  [inst_2 : AddCommMonoid M₁] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R₁ M₁] [inst_5 : Module R₂ M₂]\n  {σ₁₂ : R₁ →+* R₂} {σ₂₁ : R₂ →+* R₁} [inst_6 : RingHomInvPair σ₁₂ σ₂₁] [inst_7 : RingHomInvPair σ₂₁ σ₁₂]\n  (e : M₁ ≃ₛₗ[σ₁₂] M₂) (f : M₁ →ₗ[R₁] M₁) (a : M₂), (e.conjRingEquiv f) a = e (f (e.symm a))","typeReferences":[["RingHom"],["Module","End"],["LinearMap","instFunLike"],["Module"],["RingEquiv","instEquivLike"],["LinearEquiv"],["LinearMap"],["LinearEquiv","symm"],["DFunLike","coe"],["Module","End","instMul"],["LinearEquiv","conjRingEquiv"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["EquivLike","toFunLike"],["LinearMap","instAdd"],["RingEquiv"],["LinearEquiv","instEquivLike"],["RingHomInvPair"],["Eq"],["Semiring"]],"valueReferences":[["Module","End"],["LinearMap","instFunLike"],["RingEquiv","instEquivLike"],["LinearMap"],["DFunLike","coe"],["Module","End","instMul"],["LinearEquiv","conjRingEquiv"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Eq","refl"],["RingEquiv"],["LinearMap","instAdd"],["EquivLike","toFunLike"]]},{"isProp":true,"kind":"theorem","name":["addMonoidHomLequivInt","_proof_2"],"typeFallback":"forall {A : Type.{u_2}} {B : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16 : AddCommGroup.{u_2} 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19) (AddCommGroup.toIntModule.{u_2} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16) (AddCommGroup.toIntModule.{u_1} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19)) (LinearMap.toAddMonoidHom.{0, 0, u_2, u_1} Int Int A B Int.instSemiring Int.instSemiring (AddCommGroup.toAddCommMonoid.{u_2} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_1} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19) (AddCommGroup.toIntModule.{u_2} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16) (AddCommGroup.toIntModule.{u_1} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19) (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int Int.instSemiring))) (AddMonoidHom.toIntLinearMap.{u_2, u_1} A B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19)","typeFull":"∀ {A : Type u_2} {B : Type u_1} [inst : AddCommGroup A] [inst_1 : AddCommGroup B],\n  Function.RightInverse LinearMap.toAddMonoidHom AddMonoidHom.toIntLinearMap","typeReadable":"∀ {A : Type u_2} {B : Type u_1} [inst : AddCommGroup A] [inst_1 : AddCommGroup B],\n  Function.RightInverse LinearMap.toAddMonoidHom 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Type.{u_12}} {R₂' : Type.{u_13}} {M₁ : Type.{u_17}} {M₂ : Type.{u_18}} {M₁' : Type.{u_20}} {M₂' : Type.{u_21}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 : Semiring.{u_9} R₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 : Semiring.{u_10} R₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59 : CommSemiring.{u_12} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62 : CommSemiring.{u_13} R₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 : AddCommMonoid.{u_17} M₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 : AddCommMonoid.{u_18} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 : AddCommMonoid.{u_20} M₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 : AddCommMonoid.{u_21} M₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 : Module.{u_9, u_17} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 : Module.{u_10, u_18} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 : Module.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 : Module.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86] {σ₁₂ : RingHom.{u_9, u_10} R₁ R₂ 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59))} {σ₁₂' : RingHom.{u_9, u_13} R₁ R₂' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62))} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.285 : RingHomInvPair.{u_9, u_10} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 σ₁₂ σ₂₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.289 : RingHomInvPair.{u_10, u_9} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 σ₂₁ σ₁₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.293 : RingHomInvPair.{u_12, u_13} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₁'₂' σ₂'₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.297 : RingHomInvPair.{u_13, u_12} R₂' R₁' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₂'₁' σ₁'₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.351 : RingHomCompTriple.{u_9, u_12, u_13} R₁ R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₁₁' σ₁'₂' σ₁₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.356 : RingHomCompTriple.{u_10, u_9, u_13} R₂ R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₁ σ₁₂' σ₂₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.361 : RingHomCompTriple.{u_10, u_13, u_12} R₂ R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₂₂' σ₂'₁' σ₂₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.366 : RingHomCompTriple.{u_9, u_10, u_12} R₁ R₂ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₂ σ₂₁' σ₁₁'], (LinearEquiv.{u_9, u_10, u_17, u_18} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.285 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.289 M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102) -> (LinearEquiv.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.297 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) -> (LinearEquiv.{u_12, u_13, max u_20 u_17, max u_21 u_18} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.297 (LinearMap.{u_9, u_12, u_17, u_20} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (LinearMap.{u_10, u_13, u_18, u_21} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (LinearMap.addCommMonoid.{u_9, u_12, u_17, u_20} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 σ₁₁') (LinearMap.addCommMonoid.{u_10, u_13, u_18, u_21} R₂ R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 σ₂₂') (LinearMap.module.{u_9, u_12, u_12, u_17, u_20} R₁ R₁' R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 σ₁₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110)))) (LinearMap.module.{u_10, u_13, u_13, u_18, u_21} R₂ R₂' R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 σ₂₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114)))))","typeFull":"{R₁ : Type u_9} →\n  {R₂ : Type u_10} →\n    {R₁' : Type u_12} →\n      {R₂' : Type u_13} →\n        {M₁ : Type u_17} →\n          {M₂ : Type u_18} →\n            {M₁' : Type u_20} →\n              {M₂' : Type u_21} →\n                [inst : Semiring R₁] →\n                  [inst_1 : Semiring R₂] →\n                    [inst_2 : CommSemiring R₁'] →\n                      [inst_3 : CommSemiring R₂'] →\n                        [inst_4 : AddCommMonoid M₁] →\n                          [inst_5 : AddCommMonoid M₂] →\n                            [inst_6 : AddCommMonoid M₁'] →\n                              [inst_7 : AddCommMonoid M₂'] →\n                                [inst_8 : Module R₁ M₁] →\n                                  [inst_9 : Module R₂ M₂] →\n                                    [inst_10 : Module R₁' M₁'] →\n                                      [inst_11 : Module R₂' M₂'] →\n                                        {σ₁₂ : R₁ →+* R₂} →\n                                          {σ₂₁ : R��� →+* R₁} →\n                                            {σ₁'₂' : R₁' →+* R₂'} →\n                                              {σ₂'₁' : R₂' →+* R₁'} →\n                                                {σ₁₁' : R₁ →+* R₁'} →\n                                                  {σ₂₂' : R₂ →+* R₂'} →\n                                                    {σ₂₁' : R₂ →+* R₁'} →\n                                                      {σ₁₂' : R₁ →+* R₂'} →\n                                                        [inst_12 : RingHomInvPair σ₁₂ σ₂₁] →\n                                                          [inst_13 : RingHomInvPair σ₂₁ σ₁₂] →\n                                                            [inst_14 : RingHomInvPair σ₁'₂' σ₂'₁'] →\n                                                              [inst_15 : RingHomInvPair σ₂'₁' σ₁'₂'] →\n                                                                [RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] →\n                                                                  [RingHomCompTriple σ₂₁ σ₁₂' σ₂₂'] →\n                                                                    [RingHomCompTriple σ₂₂' σ₂'₁' σ₂₁'] →\n                                                                      [RingHomCompTriple σ₁₂ σ₂₁' σ₁₁'] →\n                                                                        (M₁ ≃ₛₗ[σ₁₂] M₂) →\n                                                                          (M₁' ≃ₛₗ[σ₁'₂'] M₂') →\n                                                                            (M₁ →ₛₗ[σ₁₁'] M₁') ≃ₛₗ[σ₁'₂']\n                                                                              M₂ →ₛₗ[σ₂₂'] M₂'","typeReadable":"{R₁ : Type u_9} →\n  {R₂ : Type u_10} →\n    {R₁' : Type u_12} →\n      {R₂' : Type u_13} →\n        {M₁ : Type u_17} →\n          {M₂ : Type u_18} →\n            {M₁' : Type u_20} →\n              {M₂' : Type u_21} →\n                [inst : Semiring R₁] →\n                  [inst_1 : Semiring R₂] →\n                    [inst_2 : CommSemiring R₁'] →\n                      [inst_3 : CommSemiring R₂'] →\n                        [inst_4 : AddCommMonoid M₁] →\n                          [inst_5 : AddCommMonoid M₂] →\n                            [inst_6 : AddCommMonoid M₁'] →\n                              [inst_7 : AddCommMonoid M₂'] →\n                                [inst_8 : Module R₁ M₁] →\n                                  [inst_9 : Module R₂ M₂] →\n                                    [inst_10 : Module R₁' M₁'] →\n                                      [inst_11 : Module R₂' M₂'] →\n                                        {σ₁₂ : R₁ →+* R₂} →\n                                          {σ₂₁ : R₂ →+* R₁} →\n                                            {σ₁'₂' : R₁' →+* R₂'} →\n                                              {σ₂'₁' : R₂' →+* R₁'} →\n                                                {σ₁₁' : R₁ →+* R₁'} →\n                                                  {σ₂₂' : R₂ →+* R₂'} →\n                                                    {σ₂₁' : R₂ →+* R₁'} →\n                                                      {σ₁₂' : R₁ →+* R₂'} →\n                                                        [inst_12 : RingHomInvPair σ₁₂ σ₂₁] →\n                                                          [inst_13 : RingHomInvPair σ₂₁ σ₁₂] →\n                                                            [inst_14 : RingHomInvPair σ₁'₂' σ₂'₁'] →\n                                                              [inst_15 : RingHomInvPair σ₂'₁' σ₁'₂'] →\n                                                                [RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] →\n                                                                  [RingHomCompTriple σ₂₁ σ₁₂' σ₂₂'] →\n                                                                    [RingHomCompTriple σ₂₂' σ₂'₁' σ₂₁'] →\n                                                                      [RingHomCompTriple σ₁₂ σ₂₁' σ₁₁'] →\n                                                                        (M₁ ≃ₛₗ[σ₁₂] M₂) →\n                                                                          (M₁' ≃ₛₗ[σ₁'₂'] M₂') →\n                                                                            (M₁ →ₛₗ[σ₁₁'] M₁') ≃ₛₗ[σ₁'₂']\n                                                                              M₂ →ₛₗ[σ₂₂'] M₂'","typeReferences":[["smulCommClass_self"],["RingHom"],["CommMonoid","toMonoid"],["Module"],["CommSemiring"],["CommSemiring","toSemiring"],["LinearMap","module"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["LinearMap"],["CommSemiring","toCommMonoid"],["RingHomCompTriple"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["DistribMulAction","toMulAction"],["RingHomInvPair"],["Semiring"]],"valueReferences":[["LinearEquiv","arrowCongr","_proof_1"],["LinearMap","mk"],["CommSemiring","toSemiring"],["LinearMap","module"],["AddHom","mk"],["LinearEquiv","arrowCongr","_proof_3"],["LinearEquiv","arrowCongr","_proof_5"],["AddEquiv","toEquiv"],["LinearMap"],["LinearMap","addCommMonoid"],["LinearEquiv","arrowCongrAddEquiv"],["AddCommMonoid","toAddCommSemigroup"],["LinearEquiv","arrowCongr","_proof_4"],["Equiv","invFun"],["LinearMap","instAdd"],["LinearEquiv","arrowCongr","_proof_2"],["LinearEquiv","mk"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Equiv","toFun"]]},{"isProp":true,"kind":"theorem","name":["Units","mulRightLinearEquiv","_proof_1"],"typeFallback":"forall (R : Type.{u_2}) {A : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12 : Semiring.{u_2} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15 : Semiring.{u_1} A] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.18 : Module.{u_2, u_1} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15)))] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.22 : IsScalarTower.{u_2, u_1, u_1} R A A (SMulZeroClass.toSMul.{u_2, u_1} R A (AddZero.toZero.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddMonoidWithOne.toAddMonoid.{u_1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_2, u_1} R A (AddMonoid.toAddZeroClass.{u_1} A (AddMonoidWithOne.toAddMonoid.{u_1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))))) (DistribMulAction.toDistribSMul.{u_2, u_1} R A (MonoidWithZero.toMonoid.{u_2} R (Semiring.toMonoidWithZero.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12)) (AddMonoidWithOne.toAddMonoid.{u_1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15)))) (Module.toDistribMulAction.{u_2, u_1} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.18)))) (SMulZeroClass.toSMul.{u_1, u_1} A A (AddZero.toZero.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddMonoidWithOne.toAddMonoid.{u_1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_1, u_1} A A (AddMonoid.toAddZeroClass.{u_1} A (AddMonoidWithOne.toAddMonoid.{u_1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))))) (instDistribSMul.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))))) (SMulZeroClass.toSMul.{u_2, u_1} R A (AddZero.toZero.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (AddMonoidWithOne.toAddMonoid.{u_1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_2, u_1} R A (AddMonoid.toAddZeroClass.{u_1} A (AddMonoidWithOne.toAddMonoid.{u_1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))))) (DistribMulAction.toDistribSMul.{u_2, u_1} R A (MonoidWithZero.toMonoid.{u_2} R (Semiring.toMonoidWithZero.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12)) (AddMonoidWithOne.toAddMonoid.{u_1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15)))) (Module.toDistribMulAction.{u_2, u_1} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.18))))] (a : Units.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))) (x : A) (y : A), Eq.{succ u_1} A (AddHom.toFun.{u_1, u_1} A A (AddCommMagma.toAdd.{u_1} A (AddCommSemigroup.toAddCommMagma.{u_1} A (AddCommMonoid.toAddCommSemigroup.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15)))))) (AddCommMagma.toAdd.{u_1} A (AddCommSemigroup.toAddCommMagma.{u_1} A (AddCommMonoid.toAddCommSemigroup.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15)))))) (LinearMap.toAddHom.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12)) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.18 (LinearMap.mulRight.{u_2, u_1} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15)) inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.22 (Units.val.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15)) a))) (HAdd.hAdd.{u_1, u_1, u_1} A A A (instHAdd.{u_1} A (AddCommMagma.toAdd.{u_1} A (AddCommSemigroup.toAddCommMagma.{u_1} A (AddCommMonoid.toAddCommSemigroup.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))))))) x y)) (HAdd.hAdd.{u_1, u_1, u_1} A A A (instHAdd.{u_1} A (AddCommMagma.toAdd.{u_1} A (AddCommSemigroup.toAddCommMagma.{u_1} A (AddCommMonoid.toAddCommSemigroup.{u_1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))))))) (AddHom.toFun.{u_1, u_1} A A (AddCommMagma.toAdd.{u_1} A (AddCommSemigroup.toAddCommMagma.{u_1} A 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.22 (Units.val.{u_1} A (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15)) a))) y))","typeFull":"∀ (R : Type u_2) {A : Type u_1} [inst : Semiring R] [inst_1 : Semiring A] [inst_2 : Module R A]\n  [inst_3 : IsScalarTower R A A] (a : Aˣ) (x y : A),\n  (LinearMap.mulRight R ↑a).toFun (x + y) = (LinearMap.mulRight R ↑a).toFun x + (LinearMap.mulRight R ↑a).toFun y","typeReadable":"∀ (R : Type u_2) {A : Type u_1} [inst : Semiring R] [inst_1 : Semiring A] [inst_2 : Module R A]\n  [inst_3 : IsScalarTower R A A] (a : Aˣ) (x y : A),\n  (LinearMap.mulRight R ↑a).toFun (x + y) = (LinearMap.mulRight R ↑a).toFun x + (LinearMap.mulRight R ↑a).toFun y","typeReferences":[["IsScalarTower"],["Module"],["LinearMap","toAddHom"],["SMulZeroClass","toSMul"],["AddMonoidWithOne","toAddMonoid"],["instDistribSMul"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["AddHom","toFun"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Eq"],["NonAssocSemiring","toAddCommMonoidWithOne"],["Units"],["DistribSMul","toSMulZeroClass"],["instHAdd"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["HAdd","hAdd"],["Module","toDistribMulAction"],["AddCommMonoid","toAddCommSemigroup"],["Units","val"],["LinearMap","mulRight"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["LinearMap","toAddHom"],["Semiring","toMonoidWithZero"],["AddHom","map_add'"],["Semiring","toNonAssocSemiring"],["AddCommMonoid","toAddCommSemigroup"],["RingHom","id"],["Units","val"],["MonoidWithZero","toMonoid"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["LinearMap","mulRight"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","restrictScalars","_proof_3"],"typeFallback":"forall {S : Type.{u_3}} {M : Type.{u_1}} {M₂ : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 : Semiring.{u_3} S] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19 : AddCommMonoid.{u_1} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22 : AddCommMonoid.{u_2} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.33 : Module.{u_3, u_1} S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.37 : Module.{u_3, u_2} S M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22] (f : LinearEquiv.{u_3, u_3, u_1, u_2} S S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13)) (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13)) (RingHomInvPair.ids.{u_3} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13) (RingHomInvPair.ids.{u_3} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13) M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.37), Function.LeftInverse.{succ u_1, succ u_2} M M₂ (LinearEquiv.invFun.{u_3, u_3, u_1, u_2} S S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13)) (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13)) (RingHomInvPair.ids.{u_3} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13) (RingHomInvPair.ids.{u_3} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13) M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.37 f) (AddHom.toFun.{u_1, u_2} M M₂ (AddCommMagma.toAdd.{u_1} M (AddCommSemigroup.toAddCommMagma.{u_1} M (AddCommMonoid.toAddCommSemigroup.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19))) (AddCommMagma.toAdd.{u_2} M₂ (AddCommSemigroup.toAddCommMagma.{u_2} M₂ (AddCommMonoid.toAddCommSemigroup.{u_2} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22))) (LinearMap.toAddHom.{u_3, u_3, u_1, u_2} S S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13)) M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.37 (LinearEquiv.toLinearMap.{u_3, u_3, u_1, u_2} S S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13 (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13)) (RingHom.id.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13)) (RingHomInvPair.ids.{u_3} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13) (RingHomInvPair.ids.{u_3} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.13) M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3287639652._hygCtx._hyg.37 f)))","typeFull":"∀ {S : Type u_3} {M : Type u_1} {M₂ : Type u_2} [inst : Semiring S] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₂] [inst_3 : Module S M] [inst_4 : Module S M₂] (f : M ≃ₗ[S] M₂),\n  Function.LeftInverse f.invFun (↑f).toFun","typeReadable":"∀ {S : Type u_3} {M : Type u_1} {M₂ : Type u_2} [inst : Semiring S] [inst_1 : AddCommMonoid M]\n  [inst_2 : AddCommMonoid M₂] [inst_3 : Module S M] [inst_4 : Module S M₂] (f : M ≃ₗ[S] M₂),\n  Function.LeftInverse f.invFun (↑f).toFun","typeReferences":[["Module"],["LinearMap","toAddHom"],["LinearEquiv","toLinearMap"],["LinearEquiv"],["LinearEquiv","invFun"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["AddCommMonoid","toAddCommSemigroup"],["RingHom","id"],["RingHomInvPair","ids"],["Function","LeftInverse"],["AddHom","toFun"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Semiring"]],"valueReferences":[["Semiring","toNonAssocSemiring"],["RingHom","id"],["RingHomInvPair","ids"],["LinearEquiv","left_inv"]]},{"isProp":true,"kind":"theorem","name":["AddEquiv","toIntLinearEquiv_refl"],"typeFallback":"forall {M : Type.{u_5}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2546266444._hygCtx._hyg.10 : AddCommGroup.{u_5} M] {modM : Module.{0, u_5} Int M Int.instSemiring (AddCommGroup.toAddCommMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2546266444._hygCtx._hyg.10)}, Eq.{succ u_5} (LinearEquiv.{0, 0, u_5, u_5} Int Int Int.instSemiring Int.instSemiring (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int Int.instSemiring)) (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int Int.instSemiring)) (RingHomInvPair.ids.{0} Int Int.instSemiring) (RingHomInvPair.ids.{0} Int Int.instSemiring) M M (AddCommGroup.toAddCommMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2546266444._hygCtx._hyg.10) (AddCommGroup.toAddCommMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2546266444._hygCtx._hyg.10) modM modM) (AddEquiv.toIntLinearEquiv.{u_5, u_5} M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2546266444._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2546266444._hygCtx._hyg.10 modM modM (AddEquiv.refl.{u_5} M (AddCommMagma.toAdd.{u_5} M (AddCommSemigroup.toAddCommMagma.{u_5} M (AddCommMonoid.toAddCommSemigroup.{u_5} M (AddCommGroup.toAddCommMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2546266444._hygCtx._hyg.10)))))) (LinearEquiv.refl.{0, u_5} Int M Int.instSemiring (AddCommGroup.toAddCommMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2546266444._hygCtx._hyg.10) modM)","typeFull":"∀ {M : Type u_5} [inst : AddCommGroup M] {modM : Module ℤ M}, (AddEquiv.refl M).toIntLinearEquiv = LinearEquiv.refl ℤ M","typeReadable":"∀ {M : Type u_5} [inst : AddCommGroup M] {modM : Module ℤ M}, (AddEquiv.refl M).toIntLinearEquiv = LinearEquiv.refl ℤ M","typeReferences":[["AddEquiv","toIntLinearEquiv"],["Module"],["AddCommGroup"],["LinearEquiv"],["Int"],["Semiring","toNonAssocSemiring"],["AddEquiv","refl"],["AddCommMonoid","toAddCommSemigroup"],["Int","instSemiring"],["RingHom","id"],["AddCommGroup","toAddCommMonoid"],["RingHomInvPair","ids"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Eq"],["LinearEquiv","refl"]],"valueReferences":[["rfl"],["AddEquiv","toIntLinearEquiv"],["LinearEquiv"],["Int"],["Semiring","toNonAssocSemiring"],["AddEquiv","refl"],["AddCommMonoid","toAddCommSemigroup"],["Int","instSemiring"],["RingHom","id"],["RingHomInvPair","ids"],["AddCommGroup","toAddCommMonoid"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"]]},{"isProp":false,"kind":"definition","name":["Units","mulLeftLinearEquiv"],"typeFallback":"forall (R : Type.{u_9}) (A : Type.{u_10}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 : Semiring.{u_9} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15 : Semiring.{u_10} A] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 : Module.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.22 : SMulCommClass.{u_9, u_10, u_10} R A A (SMulZeroClass.toSMul.{u_9, u_10} R A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_9, u_10} R A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))))) (DistribMulAction.toDistribSMul.{u_9, u_10} R A (MonoidWithZero.toMonoid.{u_9} R (Semiring.toMonoidWithZero.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))) (Module.toDistribMulAction.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18)))) (SMulZeroClass.toSMul.{u_10, u_10} A A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_10, u_10} A A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))))) (instDistribSMul.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))))], MonoidHom.{u_10, u_10} (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18) (MulOneClass.toMulOne.{u_10} (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (Units.instMulOneClass.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15)))) (MulOneClass.toMulOne.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18) (Monoid.toMulOneClass.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18) (DivInvMonoid.toMonoid.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18) (Group.toDivInvMonoid.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18) (LinearEquiv.automorphismGroup.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1636956180._hygCtx._hyg.18)))))","typeFull":"(R : Type u_9) →\n  (A : Type u_10) →\n    [inst : Semiring R] → [inst_1 : Semiring A] → [inst_2 : Module R A] → [SMulCommClass R A A] → Aˣ →* A ≃ₗ[R] A","typeReadable":"(R : Type u_9) →\n  (A : Type u_10) →\n    [inst : Semiring R] → [inst_1 : Semiring A] → [inst_2 : Module R A] → [SMulCommClass R A A] → Aˣ →* A ≃ₗ[R] 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{R₁' : Type.{u_1}} {M₁' : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59 : CommSemiring.{u_1} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 : AddCommMonoid.{u_2} M₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 : Module.{u_1, u_2} R₁' M₁' (CommSemiring.toSemiring.{u_1} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83], SMulCommClass.{u_1, u_1, u_2} R₁' R₁' M₁' (SemigroupAction.toSMul.{u_1, u_2} R₁' M₁' (Monoid.toSemigroup.{u_1} R₁' (CommMonoid.toMonoid.{u_1} R₁' (CommSemiring.toCommMonoid.{u_1} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59))) (MulAction.toSemigroupAction.{u_1, u_2} R₁' M₁' (CommMonoid.toMonoid.{u_1} R₁' (CommSemiring.toCommMonoid.{u_1} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59)) (DistribMulAction.toMulAction.{u_1, u_2} R₁' 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M₁'","typeReferences":[["CommMonoid","toMonoid"],["Module"],["CommSemiring"],["CommSemiring","toSemiring"],["SemigroupAction","toSMul"],["AddCommMonoid","toAddMonoid"],["CommSemiring","toCommMonoid"],["SMulCommClass"],["AddCommMonoid"],["Module","toDistribMulAction"],["DistribMulAction","toMulAction"],["Monoid","toSemigroup"],["MulAction","toSemigroupAction"]],"valueReferences":[["smulCommClass_self"],["Module","toDistribMulAction"],["CommMonoid","toMonoid"],["CommSemiring","toSemiring"],["DistribMulAction","toMulAction"],["AddCommMonoid","toAddMonoid"],["CommSemiring","toCommMonoid"]]},{"isProp":false,"kind":"definition","name":["DistribMulAction","toLinearEquiv"],"typeFallback":"forall (R : Type.{u_1}) {S : Type.{u_4}} (M : Type.{u_5}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.16 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.20 : Group.{u_4} S] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.23 : DistribMulAction.{u_4, u_5} S M (DivInvMonoid.toMonoid.{u_4} S (Group.toDivInvMonoid.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.20)) (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13)] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.27 : SMulCommClass.{u_4, u_1, u_5} S R M (SMulZeroClass.toSMul.{u_4, u_5} S M (AddZero.toZero.{u_5} M (AddZeroClass.toAddZero.{u_5} M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M 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Module R M] →\n            [inst_3 : Group S] → [inst_4 : DistribMulAction S M] → [SMulCommClass S R M] → S → M ≃ₗ[R] 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.4032173342._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4032173342._hygCtx._hyg.10 (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4032173342._hygCtx._hyg.10)) (m -> M) (m -> M) (Pi.addCommMonoid.{u_2, u_1} m (fun (a._@._internal._hyg.0 : m) => M) (fun (i : m) => inst._@.Mathlib.Algebra.Module.Equiv.Basic.4032173342._hygCtx._hyg.13)) (Pi.addCommMonoid.{u_2, u_1} m (fun (a._@._internal._hyg.0 : m) => M) (fun (i : m) => inst._@.Mathlib.Algebra.Module.Equiv.Basic.4032173342._hygCtx._hyg.13)) (Pi.Function.module.{u_2, u_3, u_1} m R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4032173342._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4032173342._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4032173342._hygCtx._hyg.16) (Pi.Function.module.{u_2, u_3, u_1} m R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4032173342._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4032173342._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4032173342._hygCtx._hyg.16)) (m -> M) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : m -> M) => m -> M) (LinearMap.instFunLike.{u_3, u_3, max u_1 u_2, max u_1 u_2} R R (m -> M) (m -> M) inst._@.Mathlib.Algebra.Module.Equiv.Basic.4032173342._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4032173342._hygCtx._hyg.10 (Pi.addCommMonoid.{u_2, u_1} m (fun (a._@._internal._hyg.0 : m) => M) (fun (i : m) => inst._@.Mathlib.Algebra.Module.Equiv.Basic.4032173342._hygCtx._hyg.13)) (Pi.addCommMonoid.{u_2, u_1} m (fun (a._@._internal._hyg.0 : m) => M) (fun (i : m) => inst._@.Mathlib.Algebra.Module.Equiv.Basic.4032173342._hygCtx._hyg.13)) (Pi.Function.module.{u_2, u_3, u_1} m R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4032173342._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4032173342._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4032173342._hygCtx._hyg.16) (Pi.Function.module.{u_2, u_3, u_1} m R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4032173342._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4032173342._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4032173342._hygCtx._hyg.16) (RingHom.id.{u_3} R (Semiring.toNonAssocSemiring.{u_3} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4032173342._hygCtx._hyg.10))) (LinearMap.id.{u_3, max u_1 u_2} R (m -> M) inst._@.Mathlib.Algebra.Module.Equiv.Basic.4032173342._hygCtx._hyg.10 (Pi.addCommMonoid.{u_2, u_1} m (fun (a._@._internal._hyg.0 : m) => M) (fun (i : m) => inst._@.Mathlib.Algebra.Module.Equiv.Basic.4032173342._hygCtx._hyg.13)) (Pi.Function.module.{u_2, u_3, u_1} m R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4032173342._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4032173342._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4032173342._hygCtx._hyg.16)) x i)","typeFull":"∀ (R : Type u_3) (M : Type u_1) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {m : Type u_2}\n  {n : Type u_4} (e : m ≃ n) (x : m → M) (i : m),\n  (LinearMap.funLeft R M ⇑e ∘ₗ LinearMap.funLeft R M ⇑e.symm) x i = LinearMap.id x i","typeReadable":"∀ (R : Type u_3) (M : Type u_1) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {m : Type u_2}\n  {n : Type u_4} (e : m ≃ n) (x : m → M) (i : m),\n  (LinearMap.funLeft R M ⇑e ∘ₗ LinearMap.funLeft R M ⇑e.symm) x i = LinearMap.id x i","typeReferences":[["RingHomInvPair","triples₂"],["Equiv","instEquivLike"],["LinearMap","instFunLike"],["Module"],["Pi","addCommMonoid"],["LinearMap","comp"],["LinearMap"],["LinearMap","id"],["DFunLike","coe"],["Equiv"],["Pi","Function","module"],["LinearMap","funLeft"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["EquivLike","toFunLike"],["RingHomInvPair","ids"],["Equiv","symm"],["Eq"],["Semiring"]],"valueReferences":[["RingHomInvPair","triples₂"],["Equiv","instEquivLike"],["LinearMap","instFunLike"],["RingHomCompTriple","ids"],["Pi","addCommMonoid"],["LinearMap","comp"],["DFunLike","coe"],["LinearMap","id"],["Equiv"],["Pi","Function","module"],["congrArg"],["LinearMap","funLeft_comp"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["EquivLike","toFunLike"],["Eq","symm"],["Equiv","symm"],["Eq"],["Function","comp"],["LinearMap"],["LinearMap","funLeft_id"],["LinearMap","funLeft"],["Equiv","symm_comp_self"],["Eq","refl"],["RingHomInvPair","ids"],["id"],["Eq","mpr"],["LinearMap","id_apply"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","apply_smulCommClass"],"typeFallback":"forall {R : Type.{u_1}} {S : Type.{u_4}} {M : Type.{u_5}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.19 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.25 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.29 : SMul.{u_4, u_1} S R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.33 : SMul.{u_4, u_5} S M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.37 : IsScalarTower.{u_4, u_1, u_5} S R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.29 (SMulZeroClass.toSMul.{u_1, u_5} R M (AddZero.toZero.{u_5} M (AddZeroClass.toAddZero.{u_5} M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.19)))) (DistribSMul.toSMulZeroClass.{u_1, u_5} R M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.19)) (DistribMulAction.toDistribSMul.{u_1, u_5} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.19) (Module.toDistribMulAction.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.25)))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.33], SMulCommClass.{u_4, u_5, u_5} S (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.25) M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.33 (SMulZeroClass.toSMul.{u_5, u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.25) M (AddZero.toZero.{u_5} M (AddZeroClass.toAddZero.{u_5} M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.19)))) (DistribSMul.toSMulZeroClass.{u_5, u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.25) M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.19)) (DistribMulAction.toDistribSMul.{u_5, u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.25) M (DivInvMonoid.toMonoid.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.25) (Group.toDivInvMonoid.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.25) (LinearEquiv.automorphismGroup.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.25))) (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.19) (LinearEquiv.applyDistribMulAction.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3489826275._hygCtx._hyg.25))))","typeFull":"∀ {R : Type u_1} {S : Type u_4} {M : Type u_5} [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 (M ≃ₗ[R] M) M","typeReadable":"∀ {R : Type u_1} {S : Type u_4} {M : Type u_5} [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 (M ≃ₗ[R] M) M","typeReferences":[["LinearEquiv","applyDistribMulAction"],["Module"],["IsScalarTower"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["AddZeroClass","toAddZero"],["LinearEquiv","automorphismGroup"],["SMulCommClass"],["Module","toDistribMulAction"],["AddCommMonoid"],["SMul"],["Semiring","toNonAssocSemiring"],["DivInvMonoid","toMonoid"],["RingHom","id"],["MonoidWithZero","toMonoid"],["RingHomInvPair","ids"],["Group","toDivInvMonoid"],["AddZero","toZero"],["Semiring"],["AddMonoid","toAddZeroClass"],["DistribSMul","toSMulZeroClass"]],"valueReferences":[["LinearMap","instFunLike"],["SMulCommClass","mk"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["DFunLike","coe"],["LinearEquiv","automorphismGroup"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Eq","symm"],["instHSMul"],["Group","toDivInvMonoid"],["DistribSMul","toSMulZeroClass"],["LinearEquiv","applyDistribMulAction"],["DistribMulAction","toDistribSMul"],["LinearEquiv","toLinearMap"],["AddZeroClass","toAddZero"],["LinearMap"],["DivInvMonoid","toMonoid"],["LinearMap","IsScalarTower","compatibleSMul"],["HSMul","hSMul"],["RingHomInvPair","ids"],["LinearMap","map_smul_of_tower"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["DistribMulAction","toModuleAut","_proof_1"],"typeFallback":"forall (R : Type.{u_2}) {S : Type.{u_3}} (M : Type.{u_1}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 : Semiring.{u_2} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13 : AddCommMonoid.{u_1} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.16 : Module.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.20 : Group.{u_3} S] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.23 : DistribMulAction.{u_3, u_1} S M (DivInvMonoid.toMonoid.{u_3} S (Group.toDivInvMonoid.{u_3} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.20)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13)] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._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.Equiv.Basic.4191798717._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.Equiv.Basic.4191798717._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_3, u_1} S M (DivInvMonoid.toMonoid.{u_3} S (Group.toDivInvMonoid.{u_3} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.20)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._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.Equiv.Basic.4191798717._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.Equiv.Basic.4191798717._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.Equiv.Basic.4191798717._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13) (Module.toDistribMulAction.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.16))))], Eq.{succ u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.16) (DistribMulAction.toLinearEquiv.{u_2, u_3, u_1} R S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._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 (DivInvMonoid.toMonoid.{u_3} S (Group.toDivInvMonoid.{u_3} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.20)))))))) (OfNat.ofNat.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R 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M] [inst_5 : SMulCommClass S R M],\n  DistribMulAction.toLinearEquiv 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 : Group S] [inst_4 : DistribMulAction S M] [inst_5 : SMulCommClass S R M],\n  DistribMulAction.toLinearEquiv R M 1 = 1","typeReferences":[["MulOneClass","toMulOne"],["Module"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["LinearEquiv","automorphismGroup"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Monoid","toMulOneClass"],["MonoidWithZero","toMonoid"],["Eq"],["Group","toDivInvMonoid"],["DistribMulAction"],["DistribSMul","toSMulZeroClass"],["Group"],["MulOne","toOne"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["DistribMulAction","toLinearEquiv"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["SMulCommClass"],["Module","toDistribMulAction"],["One","toOfNat1"],["DivInvMonoid","toMonoid"],["RingHomInvPair","ids"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["MulOneClass","toMulOne"],["MulOne","toOne"],["DistribMulAction","toLinearEquiv"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["OfNat","ofNat"],["LinearEquiv","automorphismGroup"],["LinearEquiv","ext"],["Semiring","toNonAssocSemiring"],["One","toOfNat1"],["DivInvMonoid","toMonoid"],["RingHom","id"],["one_smul"],["Monoid","toMulOneClass"],["DistribMulAction","toMulAction"],["RingHomInvPair","ids"],["Group","toDivInvMonoid"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","apply_smulCommClass'"],"typeFallback":"forall {R : Type.{u_1}} {S : Type.{u_4}} {M : Type.{u_5}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.19 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.25 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.29 : SMul.{u_4, u_1} S R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.33 : SMul.{u_4, u_5} S M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.37 : IsScalarTower.{u_4, u_1, u_5} S R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.29 (SMulZeroClass.toSMul.{u_1, u_5} R M (AddZero.toZero.{u_5} M (AddZeroClass.toAddZero.{u_5} M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.19)))) (DistribSMul.toSMulZeroClass.{u_1, u_5} R M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.19)) (DistribMulAction.toDistribSMul.{u_1, u_5} R M (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.19) (Module.toDistribMulAction.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.25)))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.33], SMulCommClass.{u_5, u_4, u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.25) S M (SMulZeroClass.toSMul.{u_5, u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.25) M (AddZero.toZero.{u_5} M (AddZeroClass.toAddZero.{u_5} M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.19)))) (DistribSMul.toSMulZeroClass.{u_5, u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.25) M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.19)) (DistribMulAction.toDistribSMul.{u_5, u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.25) M (DivInvMonoid.toMonoid.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.25) (Group.toDivInvMonoid.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.25) (LinearEquiv.automorphismGroup.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.25))) (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.19) (LinearEquiv.applyDistribMulAction.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.25)))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2418366657._hygCtx._hyg.33","typeFull":"∀ {R : Type u_1} {S : Type u_4} {M : Type u_5} [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 (M ≃ₗ[R] M) S M","typeReadable":"∀ {R : Type u_1} {S : Type u_4} {M : Type u_5} [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 (M ≃ₗ[R] M) S M","typeReferences":[["LinearEquiv","applyDistribMulAction"],["Module"],["IsScalarTower"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["AddZeroClass","toAddZero"],["LinearEquiv","automorphismGroup"],["SMulCommClass"],["Module","toDistribMulAction"],["AddCommMonoid"],["SMul"],["Semiring","toNonAssocSemiring"],["DivInvMonoid","toMonoid"],["RingHom","id"],["MonoidWithZero","toMonoid"],["RingHomInvPair","ids"],["Group","toDivInvMonoid"],["AddZero","toZero"],["Semiring"],["AddMonoid","toAddZeroClass"],["DistribSMul","toSMulZeroClass"]],"valueReferences":[["LinearEquiv","applyDistribMulAction"],["SMulCommClass","symm"],["DistribMulAction","toDistribSMul"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["AddZeroClass","toAddZero"],["LinearEquiv","automorphismGroup"],["Semiring","toNonAssocSemiring"],["DivInvMonoid","toMonoid"],["RingHom","id"],["RingHomInvPair","ids"],["LinearEquiv","apply_smulCommClass"],["Group","toDivInvMonoid"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["DistribSMul","toSMulZeroClass"]]},{"isProp":true,"kind":"theorem","name":["Units","mulLeftLinearEquiv_trans_mulLeftLinearEquiv"],"typeFallback":"forall {R : Type.{u_9}} {A : Type.{u_10}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12 : Semiring.{u_9} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.15 : Semiring.{u_10} A] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.18 : Module.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.15)))] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.22 : SMulCommClass.{u_9, u_10, u_10} R A A (SMulZeroClass.toSMul.{u_9, u_10} R A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_9, u_10} R A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.15))))) (DistribMulAction.toDistribSMul.{u_9, u_10} R A (MonoidWithZero.toMonoid.{u_9} R (Semiring.toMonoidWithZero.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12)) (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.15)))) (Module.toDistribMulAction.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.18)))) (SMulZeroClass.toSMul.{u_10, u_10} A A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_10, u_10} A A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.15))))) (instDistribSMul.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.15)))))] (a : Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.15))) (b : Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.15))), Eq.{succ u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.18) (LinearEquiv.trans.{u_9, u_9, u_9, u_10, u_10, u_10} R R R A A A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.18 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(RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.18) (Group.toDivInvMonoid.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R 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(Monoid.toMulOneClass.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.18) (DivInvMonoid.toMonoid.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.18) (Group.toDivInvMonoid.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.18) (LinearEquiv.automorphismGroup.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.18)))))) (Units.mulLeftLinearEquiv.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.15 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.22) (HMul.hMul.{u_10, u_10, u_10} (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.15))) (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.15))) (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.15))) (instHMul.{u_10} (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.15))) (Units.instMul.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.1474251121._hygCtx._hyg.15)))) b a))","typeFull":"∀ {R : Type u_9} {A : Type u_10} [inst : Semiring R] [inst_1 : Semiring A] [inst_2 : Module R A]\n  [inst_3 : SMulCommClass R A A] (a b : Aˣ),\n  (Units.mulLeftLinearEquiv R A) a ≪≫ₗ (Units.mulLeftLinearEquiv R A) b = (Units.mulLeftLinearEquiv R A) (b * a)","typeReadable":"∀ {R : Type u_9} {A : Type u_10} [inst : Semiring R] [inst_1 : Semiring A] [inst_2 : Module R A]\n  [inst_3 : SMulCommClass R A A] (a b : Aˣ),\n  (Units.mulLeftLinearEquiv R A) a ≪≫ₗ (Units.mulLeftLinearEquiv R A) b = (Units.mulLeftLinearEquiv R A) (b * a)","typeReferences":[["MulOneClass","toMulOne"],["Units","instMul"],["RingHomCompTriple","ids"],["Module"],["MonoidHom"],["MonoidHom","instFunLike"],["HMul","hMul"],["SMulZeroClass","toSMul"],["AddMonoidWithOne","toAddMonoid"],["instDistribSMul"],["LinearEquiv"],["DFunLike","coe"],["LinearEquiv","automorphismGroup"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Monoid","toMulOneClass"],["MonoidWithZero","toMonoid"],["Units","mulLeftLinearEquiv"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Eq"],["Group","toDivInvMonoid"],["NonAssocSemiring","toAddCommMonoidWithOne"],["Units"],["DistribSMul","toSMulZeroClass"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["Units","instMulOneClass"],["AddZeroClass","toAddZero"],["SMulCommClass"],["LinearEquiv","trans"],["Module","toDistribMulAction"],["DivInvMonoid","toMonoid"],["RingHomInvPair","ids"],["instHMul"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["MulOneClass","toMulOne"],["Units","instMul"],["MonoidHom"],["MonoidHom","instFunLike"],["HMul","hMul"],["LinearEquiv"],["DFunLike","coe"],["LinearEquiv","automorphismGroup"],["MulOne","toMul"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["Monoid","toMulOneClass"],["Eq","symm"],["Units","mulLeftLinearEquiv"],["Group","toDivInvMonoid"],["Units"],["MonoidHomClass","toMulHomClass"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["Semiring","toMonoidWithZero"],["Units","instMulOneClass"],["MonoidHom","instMonoidHomClass"],["DivInvMonoid","toMonoid"],["RingHomInvPair","ids"],["map_mul"],["instHMul"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","congrLeft","_proof_3"],"typeFallback":"forall (M : Type.{u_1}) {M₂ : Type.{u_2}} {M₃ : Type.{u_3}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 : AddCommMonoid.{u_1} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 : AddCommMonoid.{u_2} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.19 : AddCommMonoid.{u_3} M₃] {R : Type.{u_4}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 : Semiring.{u_4} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 : Module.{u_4, u_2} R M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.46 : Module.{u_4, u_3} R M₃ inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50 : Module.{u_4, u_1} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13] (e : LinearEquiv.{u_4, u_4, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHomInvPair.ids.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36) (RingHomInvPair.ids.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36) M₂ M₃ inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHomInvPair.ids.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36) (RingHomInvPair.ids.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36) (RingHomInvPair.ids.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36) (RingHomInvPair.ids.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36) (LinearEquiv.automorphismGroup._proof_7.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36) (LinearEquiv.automorphismGroup._proof_7.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36) (LinearEquiv.automorphismGroup._proof_7.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36) (LinearEquiv.automorphismGroup._proof_7.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36) e (LinearEquiv.refl.{u_4, u_1} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50)))) (Equiv.toFun.{succ (max u_1 u_2), succ (max u_1 u_3)} (LinearMap.{u_4, u_4, u_2, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50) (LinearMap.{u_4, u_4, u_3, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36))) (LinearMap.instAdd.{u_4, u_4, u_3, u_1} R R M₃ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36))) (LinearEquiv.arrowCongrAddEquiv.{u_4, u_4, u_4, u_4, u_2, u_3, u_1, u_1} R R R R M₂ M₃ M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50 (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHom.id.{u_4} R (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36)) (RingHomInvPair.ids.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36) (RingHomInvPair.ids.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36) (RingHomInvPair.ids.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36) (RingHomInvPair.ids.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36) (LinearEquiv.automorphismGroup._proof_7.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36) (LinearEquiv.automorphismGroup._proof_7.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36) (LinearEquiv.automorphismGroup._proof_7.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36) (LinearEquiv.automorphismGroup._proof_7.{u_4} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36) e (LinearEquiv.refl.{u_4, u_1} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.679963575._hygCtx._hyg.50))))","typeFull":"∀ (M : Type u_1) {M₂ : Type u_2} {M₃ : Type u_3} [inst : AddCommMonoid M] [inst_1 : AddCommMonoid M₂]\n  [inst_2 : AddCommMonoid M₃] {R : Type u_4} [inst_3 : Semiring R] [inst_4 : Module R M₂] [inst_5 : Module R M₃]\n  [inst_6 : Module R M] (e : M₂ ≃ₗ[R] M₃),\n  Function.LeftInverse (e.arrowCongrAddEquiv (LinearEquiv.refl R M)).invFun\n    (e.arrowCongrAddEquiv (LinearEquiv.refl R M)).toFun","typeReadable":"∀ (M : Type u_1) {M₂ : Type u_2} {M₃ : Type u_3} [inst : AddCommMonoid M] [inst_1 : AddCommMonoid M₂]\n  [inst_2 : AddCommMonoid M₃] {R : Type u_4} [inst_3 : Semiring R] [inst_4 : Module R M₂] [inst_5 : Module R M₃]\n  [inst_6 : Module R M] (e : M₂ ≃ₗ[R] M₃),\n  Function.LeftInverse (e.arrowCongrAddEquiv (LinearEquiv.refl R M)).invFun\n    (e.arrowCongrAddEquiv (LinearEquiv.refl R M)).toFun","typeReferences":[["Module"],["LinearEquiv","automorphismGroup","_proof_7"],["LinearEquiv"],["LinearMap"],["AddEquiv","toEquiv"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["LinearEquiv","arrowCongrAddEquiv"],["RingHom","id"],["Equiv","invFun"],["LinearMap","instAdd"],["RingHomInvPair","ids"],["Function","LeftInverse"],["Equiv","toFun"],["LinearEquiv","refl"],["Semiring"]],"valueReferences":[["Equiv","left_inv"],["Semiring","toNonAssocSemiring"],["LinearEquiv","arrowCongrAddEquiv"],["RingHom","id"],["LinearMap","instAdd"],["RingHomInvPair","ids"],["LinearEquiv","automorphismGroup","_proof_7"],["AddEquiv","toEquiv"],["LinearMap"],["LinearEquiv","refl"]]},{"isProp":false,"kind":"definition","name":["Units","mulRightLinearEquiv"],"typeFallback":"forall (R : Type.{u_9}) {A : Type.{u_10}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12 : Semiring.{u_9} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15 : Semiring.{u_10} A] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.18 : Module.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15)))] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.22 : IsScalarTower.{u_9, u_10, u_10} R A A (SMulZeroClass.toSMul.{u_9, u_10} R A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_9, u_10} R A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.18)))) (SMulZeroClass.toSMul.{u_10, u_10} A A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_10, u_10} A A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))))) (instDistribSMul.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))))) (SMulZeroClass.toSMul.{u_9, u_10} R A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_9, u_10} R A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))))) (DistribMulAction.toDistribSMul.{u_9, u_10} R A (MonoidWithZero.toMonoid.{u_9} R (Semiring.toMonoidWithZero.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12)) (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15)))) (Module.toDistribMulAction.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.18))))], (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))) -> (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.208021011._hygCtx._hyg.18)","typeFull":"(R : Type u_9) →\n  {A : Type u_10} →\n    [inst : Semiring R] → [inst_1 : Semiring A] → [inst_2 : Module R A] → [IsScalarTower R A A] → Aˣ → A ≃ₗ[R] A","typeReadable":"(R : Type u_9) →\n  {A : Type u_10} →\n    [inst : Semiring R] → [inst_1 : Semiring A] → [inst_2 : Module R A] → [IsScalarTower R A A] → Aˣ → A ≃ₗ[R] A","typeReferences":[["Module"],["IsScalarTower"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["SMulZeroClass","toSMul"],["LinearEquiv"],["instDistribSMul"],["AddZeroClass","toAddZero"],["AddMonoidWithOne","toAddMonoid"],["Module","toDistribMulAction"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["RingHomInvPair","ids"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["AddZero","toZero"],["NonAssocSemiring","toAddCommMonoidWithOne"],["Units"],["DistribSMul","toSMulZeroClass"],["Semiring"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["Equiv","left_inv"],["Units","mulRightLinearEquiv","_proof_2"],["LinearMap","mk"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["AddHom","mk"],["Semiring","toMonoidWithZero"],["Units","mulRightLinearEquiv","_proof_1"],["Units","mulRight"],["Semiring","toNonAssocSemiring"],["AddCommMonoid","toAddCommSemigroup"],["Equiv","invFun"],["Units","val"],["RingHom","id"],["Equiv","right_inv"],["MonoidWithZero","toMonoid"],["RingHomInvPair","ids"],["LinearEquiv","mk"],["Equiv","toFun"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["LinearMap","mulRight"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","automorphismGroup","toLinearMapMonoidHom","_proof_1"],"typeFallback":"forall {R : Type.{u_2}} {M : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 : Semiring.{u_2} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 : AddCommMonoid.{u_1} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 : Module.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19], Eq.{succ u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (LinearEquiv.toLinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 (OfNat.ofNat.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) 1 (One.toOfNat1.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (MulOne.toOne.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (MulOneClass.toMulOne.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (Monoid.toMulOneClass.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (DivInvMonoid.toMonoid.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (Group.toDivInvMonoid.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) (LinearEquiv.automorphismGroup.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25))))))))) (LinearEquiv.toLinearMap.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 (OfNat.ofNat.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.25) 1 (One.toOfNat1.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2725838365._hygCtx._hyg.19 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21)} {σ₂₁ : RingHom.{u_2, u_4} R₂ R₁ (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21) (Semiring.toNonAssocSemiring.{u_4} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18)} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.98 : RingHomInvPair.{u_4, u_2} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 σ₁₂ σ₂₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.102 : RingHomInvPair.{u_2, u_4} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 σ₂₁ σ₁₂] (e : LinearEquiv.{u_4, u_2, u_3, u_1} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.102 M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46) (x._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.165 : Module.End.{u_4, u_3} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42) (x._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.167 : Module.End.{u_4, u_3} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42), Eq.{succ u_1} (Module.End.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46) (Equiv.toFun.{succ u_3, succ u_1} (LinearMap.{u_4, u_4, u_3, u_3} R₁ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 (RingHom.id.{u_4} R₁ (Semiring.toNonAssocSemiring.{u_4} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18)) M₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42) (LinearMap.{u_2, u_2, u_1, u_1} R₂ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 (RingHom.id.{u_2} R₂ (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21)) M₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46) (AddEquiv.toEquiv.{u_3, u_1} (LinearMap.{u_4, u_4, u_3, u_3} R₁ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 (RingHom.id.{u_4} R₁ (Semiring.toNonAssocSemiring.{u_4} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18)) M₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42) (LinearMap.{u_2, u_2, u_1, u_1} R₂ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 (RingHom.id.{u_2} R₂ (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21)) M₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46) (LinearMap.instAdd.{u_4, u_4, u_3, u_3} R₁ R₁ M₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 (RingHom.id.{u_4} R₁ (Semiring.toNonAssocSemiring.{u_4} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18))) (LinearMap.instAdd.{u_2, u_2, u_1, u_1} R₂ R₂ M₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 (RingHom.id.{u_2} R₂ (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21))) (LinearEquiv.arrowCongrAddEquiv.{u_4, u_2, u_4, u_2, u_3, u_1, u_3, u_1} R₁ R₂ R₁ R₂ M₁ M₂ M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 σ₁₂ σ₂₁ σ₁₂ σ₂₁ (RingHom.id.{u_4} R₁ (Semiring.toNonAssocSemiring.{u_4} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18)) (RingHom.id.{u_2} R₂ (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21)) σ₂₁ σ₁₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.102 (RingHomCompTriple.ids.{u_4, u_2} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 σ₁₂) (RingHomInvPair.triples₂.{u_4, u_2} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.98) (RingHomCompTriple.ids.{u_2, u_4} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 σ₂₁) (RingHomInvPair.triples₂.{u_2, u_4} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 σ₂₁ σ₁₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.102) e e)) (HMul.hMul.{u_3, u_3, u_3} (Module.End.{u_4, u_3} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42) (Module.End.{u_4, u_3} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42) (Module.End.{u_4, u_3} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42) (instHMul.{u_3} (Module.End.{u_4, u_3} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42) (Module.End.instMul.{u_4, u_3} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42)) x._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.165 x._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.167)) (HMul.hMul.{u_1, u_1, u_1} (Module.End.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46) (Module.End.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46) (Module.End.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46) (instHMul.{u_1} (Module.End.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46) (Module.End.instMul.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46)) (Equiv.toFun.{succ u_3, succ u_1} (LinearMap.{u_4, u_4, u_3, u_3} R₁ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 (RingHom.id.{u_4} R₁ (Semiring.toNonAssocSemiring.{u_4} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18)) M₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42) (LinearMap.{u_2, u_2, u_1, u_1} R₂ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 (RingHom.id.{u_2} R₂ (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21)) M₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46) (AddEquiv.toEquiv.{u_3, u_1} (LinearMap.{u_4, u_4, u_3, u_3} R₁ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 (RingHom.id.{u_4} R₁ (Semiring.toNonAssocSemiring.{u_4} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18)) M₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42) (LinearMap.{u_2, u_2, u_1, u_1} R₂ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 (RingHom.id.{u_2} R₂ (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21)) M₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46) (LinearMap.instAdd.{u_4, u_4, u_3, u_3} R₁ R₁ M₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 (RingHom.id.{u_4} R₁ (Semiring.toNonAssocSemiring.{u_4} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18))) (LinearMap.instAdd.{u_2, u_2, u_1, u_1} R₂ R₂ M₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 (RingHom.id.{u_2} R₂ (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21))) (LinearEquiv.arrowCongrAddEquiv.{u_4, u_2, u_4, u_2, u_3, u_1, u_3, u_1} R₁ R₂ R₁ R₂ M₁ M₂ M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.46 σ₁₂ σ₂₁ σ₁₂ σ₂₁ (RingHom.id.{u_4} R₁ (Semiring.toNonAssocSemiring.{u_4} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18)) (RingHom.id.{u_2} R₂ (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21)) σ₂₁ σ₁₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.102 (RingHomCompTriple.ids.{u_4, u_2} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 σ₁₂) (RingHomInvPair.triples₂.{u_4, u_2} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.98) (RingHomCompTriple.ids.{u_2, u_4} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 σ₂₁) 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σ₂₁ σ₁₂ σ₂₁ (RingHom.id.{u_4} R₁ (Semiring.toNonAssocSemiring.{u_4} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18)) (RingHom.id.{u_2} R₂ (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21)) σ₂₁ σ₁₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.102 (RingHomCompTriple.ids.{u_4, u_2} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 σ₁₂) (RingHomInvPair.triples₂.{u_4, u_2} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.98) (RingHomCompTriple.ids.{u_2, u_4} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 σ₂₁) (RingHomInvPair.triples₂.{u_2, u_4} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.18 σ₂₁ σ₁₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.102) e e)) x._@.Mathlib.Algebra.Module.Equiv.Basic.700455265._hygCtx._hyg.167))","typeFull":"∀ {R₁ : Type u_4} {R₂ : Type u_2} {M₁ : Type u_3} {M₂ : Type u_1} [inst : Semiring R₁] [inst_1 : Semiring R₂]\n  [inst_2 : AddCommMonoid M₁] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R₁ M₁] [inst_5 : Module R₂ M₂]\n  {σ₁₂ : R₁ →+* R₂} {σ₂₁ : R₂ →+* R₁} [inst_6 : RingHomInvPair σ₁₂ σ₂₁] [inst_7 : RingHomInvPair σ₂₁ σ₁₂]\n  (e : M₁ ≃ₛₗ[σ₁₂] M₂) (x x_1 : Module.End R₁ M₁),\n  (e.arrowCongrAddEquiv e).toFun (x * x_1) = (e.arrowCongrAddEquiv e).toFun x * (e.arrowCongrAddEquiv e).toFun x_1","typeReadable":"∀ {R₁ : Type u_4} {R₂ : Type u_2} {M₁ : Type u_3} {M₂ : Type u_1} [inst : Semiring R₁] [inst_1 : Semiring R₂]\n  [inst_2 : AddCommMonoid M₁] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R₁ M₁] [inst_5 : Module R₂ M₂]\n  {σ₁₂ : R₁ →+* R₂} {σ₂₁ : R₂ →+* R₁} [inst_6 : RingHomInvPair σ₁₂ σ₂₁] [inst_7 : RingHomInvPair σ₂₁ σ₁₂]\n  (e : M₁ ≃ₛₗ[σ₁₂] M₂) (x x_1 : Module.End R₁ M₁),\n  (e.arrowCongrAddEquiv e).toFun (x * x_1) = (e.arrowCongrAddEquiv e).toFun x * (e.arrowCongrAddEquiv e).toFun x_1","typeReferences":[["RingHomInvPair","triples₂"],["RingHom"],["Module","End"],["RingHomCompTriple","ids"],["Module"],["HMul","hMul"],["LinearEquiv"],["LinearMap"],["AddEquiv","toEquiv"],["Module","End","instMul"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["LinearEquiv","arrowCongrAddEquiv"],["RingHom","id"],["LinearMap","instAdd"],["instHMul"],["Equiv","toFun"],["RingHomInvPair"],["Eq"],["Semiring"]],"valueReferences":[["RingHomInvPair","triples₂"],["LinearEquiv","symm_apply_apply"],["LinearMap","instFunLike"],["Eq","trans"],["RingHomCompTriple","ids"],["HMul","hMul"],["LinearEquiv"],["DFunLike","coe"],["congrArg"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["LinearMap","ext"],["LinearMap","instAdd"],["EquivLike","toFunLike"],["Equiv","toFun"],["Eq"],["LinearEquiv","instEquivLike"],["Module","End"],["True"],["Function","comp"],["AddEquiv","toEquiv"],["LinearMap"],["LinearEquiv","symm"],["Module","End","instMul"],["eq_self"],["LinearEquiv","arrowCongrAddEquiv"],["of_eq_true"],["instHMul"]]},{"isProp":true,"kind":"theorem","name":["Module","compHom","toLinearEquiv_symm_apply"],"typeFallback":"forall 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{R : Type.{u_1}} {R₂ : Type.{u_2}} {M : Type.{u_5}} {M₂ : Type.{u_7}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 : Semiring.{u_2} R₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.16 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19 : AddCommMonoid.{u_7} M₂] {module_M : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.16} {module_M₂ : Module.{u_2, u_7} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19} {σ₁₂ : RingHom.{u_1, u_2} R R₂ (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10) (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13)} {σ₂₁ : RingHom.{u_2, u_1} R₂ R (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13) (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10)} {re₁₂ : RingHomInvPair.{u_1, u_2} R R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 σ₁₂ σ₂₁} {re₂₁ : RingHomInvPair.{u_2, u_1} R₂ R inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10 σ₂₁ σ₁₂} (f : LinearMap.{u_1, u_2, u_5, u_7} R R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 σ₁₂ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19 module_M module_M₂) (g : LinearMap.{u_2, u_1, u_7, u_5} R₂ R inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10 σ₂₁ M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.16 module_M₂ module_M), (Eq.{succ u_7} (LinearMap.{u_2, u_2, u_7, u_7} R₂ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 (RingHom.id.{u_2} R₂ (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13)) M₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19 module_M₂ module_M₂) (LinearMap.comp.{u_2, u_1, u_2, u_7, u_5, u_7} R₂ R R₂ M₂ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19 module_M₂ module_M module_M₂ σ₂₁ σ₁₂ (RingHom.id.{u_2} R₂ (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13)) (RingHomInvPair.triples₂.{u_1, u_2} R R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 σ₁₂ σ₂₁ re₁₂) f g) (LinearMap.id.{u_2, u_7} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19 module_M₂)) -> (Eq.{succ u_5} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10)) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.16 module_M module_M) (LinearMap.comp.{u_1, u_2, u_1, u_5, u_7, u_5} R R₂ R M M₂ M inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.16 module_M module_M₂ module_M σ₁₂ σ₂₁ (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10)) (RingHomInvPair.triples₂.{u_2, u_1} R₂ R inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10 σ₂₁ σ₁₂ re₂₁) g f) (LinearMap.id.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.16 module_M)) -> (LinearEquiv.{u_1, u_2, u_5, u_7} R R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.13 σ₁₂ σ₂₁ re₁₂ re₂₁ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.748591541._hygCtx._hyg.19 module_M module_M₂)","typeFull":"{R : Type u_1} →\n  {R₂ : Type u_2} →\n    {M : Type u_5} →\n      {M₂ : Type u_7} →\n        [inst : Semiring R] →\n          [inst_1 : Semiring R₂] →\n            [inst_2 : AddCommMonoid M] →\n              [inst_3 : AddCommMonoid M₂] →\n                {module_M : Module R M} →\n                  {module_M₂ : Module R₂ M₂} →\n                    {σ₁₂ : R →+* R₂} →\n                      {σ₂₁ : R₂ →+* R} →\n                        {re₁₂ : RingHomInvPair σ₁₂ σ₂₁} →\n                          {re₂₁ : RingHomInvPair σ₂₁ σ₁₂} →\n                            (f : M →ₛₗ[σ₁₂] M₂) →\n                              (g : M₂ →ₛₗ[σ₂₁] M) → f ∘ₛₗ g = LinearMap.id → g ∘ₛₗ f = LinearMap.id → M ≃ₛₗ[σ₁₂] M₂","typeReadable":"{R : Type u_1} →\n  {R₂ : Type u_2} →\n    {M : Type u_5} →\n      {M₂ : Type u_7} →\n        [inst : Semiring R] →\n          [inst_1 : Semiring R₂] →\n            [inst_2 : AddCommMonoid M] →\n              [inst_3 : AddCommMonoid M₂] →\n                {module_M : Module R M} →\n                  {module_M₂ : Module R₂ M₂} →\n                    {σ₁₂ : R →+* R₂} →\n                      {σ₂₁ : R₂ →+* R} →\n                        {re₁₂ : RingHomInvPair σ₁₂ σ₂₁} →\n                          {re₂₁ : RingHomInvPair σ₂₁ σ₁₂} →\n                            (f : M →ₛₗ[σ₁₂] M₂) →\n                              (g : M₂ →ₛₗ[σ₂₁] M) → f ∘ₛₗ g = LinearMap.id → g ∘ₛₗ f = LinearMap.id → M ≃ₛₗ[σ₁₂] M₂","typeReferences":[["RingHomInvPair","triples₂"],["RingHom"],["Module"],["LinearMap","comp"],["LinearMap"],["LinearEquiv"],["LinearMap","id"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["RingHomInvPair"],["Eq"],["Semiring"]],"valueReferences":[["LinearEquiv","ofLinear","_proof_2"],["LinearEquiv","ofLinear","_proof_1"],["LinearMap","instFunLike"],["LinearEquiv","mk"],["LinearMap"],["DFunLike","coe"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","piApply","_proof_3"],"typeFallback":"forall {R : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13 : CommSemiring.{u_1} R], SMulCommClass.{u_1, u_1, u_1} R R R (SemigroupAction.toSMul.{u_1, u_1} R R (Monoid.toSemigroup.{u_1} R (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))) (MulAction.toSemigroupAction.{u_1, u_1} R R (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)) (DistribMulAction.toMulAction.{u_1, u_1} R R (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)) (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.Equiv.Basic.1550793534._hygCtx._hyg.13))))) (Module.toDistribMulAction.{u_1, u_1} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))))) (Module.toDistribMulAction.{u_1, u_1} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13)))) (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1550793534._hygCtx._hyg.13))))))","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"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","arrowCongr_symm_apply"],"typeFallback":"forall {R₁ : Type.{u_9}} {R₂ : Type.{u_10}} {R₁' : Type.{u_12}} {R₂' : Type.{u_13}} {M₁ : Type.{u_17}} {M₂ : Type.{u_18}} {M₁' : Type.{u_20}} {M₂' : Type.{u_21}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.50 : Semiring.{u_9} R₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.53 : Semiring.{u_10} R₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59 : CommSemiring.{u_12} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62 : CommSemiring.{u_13} R₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.74 : AddCommMonoid.{u_17} M₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.77 : AddCommMonoid.{u_18} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.83 : AddCommMonoid.{u_20} M₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.86 : AddCommMonoid.{u_21} M₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.98 : Module.{u_9, u_17} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.74] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.102 : Module.{u_10, u_18} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.77] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.110 : Module.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.83] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.114 : Module.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.86] {σ₁₂ : RingHom.{u_9, u_10} R₁ R₂ (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.53)} {σ₂₁ : RingHom.{u_10, u_9} R₂ R₁ (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.53) (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.50)} {σ₁'₂' : RingHom.{u_12, u_13} R₁' R₂' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59)) (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62))} {σ₂'₁' : RingHom.{u_13, u_12} R₂' R₁' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62)) (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59))} {σ₁₁' : RingHom.{u_9, u_12} R₁ R₁' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59))} {σ₂₂' : RingHom.{u_10, u_13} R₂ R₂' (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.53) (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62))} {σ₂₁' : RingHom.{u_10, u_12} R₂ R₁' (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.53) (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59))} {σ₁₂' : RingHom.{u_9, u_13} R₁ R₂' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62))} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.285 : RingHomInvPair.{u_9, u_10} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.53 σ₁₂ σ₂₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.289 : RingHomInvPair.{u_10, u_9} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.50 σ₂₁ σ₁₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.293 : RingHomInvPair.{u_12, u_13} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62) σ₁'₂' σ₂'₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.297 : RingHomInvPair.{u_13, u_12} R₂' R₁' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59) σ₂'₁' σ₁'₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.351 : RingHomCompTriple.{u_9, u_12, u_13} R₁ R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62) σ₁₁' σ₁'₂' σ₁₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.356 : RingHomCompTriple.{u_10, u_9, u_13} R₂ R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62) σ₂₁ σ₁₂' σ₂₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.361 : RingHomCompTriple.{u_10, u_13, u_12} R₂ R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59) σ₂₂' σ₂'₁' σ₂₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.366 : RingHomCompTriple.{u_9, u_10, u_12} R₁ R₂ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59) σ₁₂ σ₂₁' σ₁₁'] (e₁ : LinearEquiv.{u_9, u_10, u_17, u_18} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.53 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.285 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.289 M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.102) (e₂ : LinearEquiv.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.297 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.114) (f : LinearMap.{u_10, u_13, u_18, u_21} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.114) (x : M₁), Eq.{succ u_20} M₁' (DFunLike.coe.{max (succ u_17) (succ u_20), succ u_17, succ u_20} (LinearMap.{u_9, u_12, u_17, u_20} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.110) M₁ (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M₁) => M₁') (LinearMap.instFunLike.{u_9, u_12, u_17, u_20} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.110 σ₁₁') (DFunLike.coe.{max (max (max (succ u_17) (succ u_18)) (succ u_20)) (succ u_21), max (succ u_18) (succ u_21), max (succ u_17) (succ u_20)} (LinearEquiv.{u_13, u_12, max u_18 u_21, max u_17 u_20} R₂' R₁' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59) σ₂'₁' σ₁'₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.297 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.293 (LinearMap.{u_10, u_13, u_18, u_21} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.53 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.110))))) (LinearMap.{u_10, u_13, u_18, u_21} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.114) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : LinearMap.{u_10, u_13, u_18, u_21} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.114) => LinearMap.{u_9, u_12, u_17, u_20} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.110) (EquivLike.toFunLike.{max (max (max (succ u_17) (succ u_18)) (succ u_20)) (succ u_21), max (succ u_18) (succ u_21), max (succ u_17) (succ u_20)} (LinearEquiv.{u_13, u_12, max u_18 u_21, max u_17 u_20} R₂' R₁' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59) σ₂'₁' σ₁'₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.297 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.293 (LinearMap.{u_10, u_13, u_18, u_21} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.114) (LinearMap.{u_9, u_12, u_17, u_20} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.110) (LinearMap.addCommMonoid.{u_10, u_13, u_18, u_21} R₂ R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.114 σ₂₂') (LinearMap.addCommMonoid.{u_9, u_12, u_17, u_20} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.110 σ₁₁') (LinearMap.module.{u_10, u_13, u_13, u_18, u_21} R₂ R₂' R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.114 σ₂₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.114)))) (LinearMap.module.{u_9, u_12, u_12, u_17, u_20} R₁ R₁' R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.110 σ₁₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.110))))) (LinearMap.{u_10, u_13, u_18, u_21} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.114) (LinearMap.{u_9, u_12, u_17, u_20} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.110) (LinearEquiv.instEquivLike.{u_13, u_12, max u_18 u_21, max u_17 u_20} R₂' R₁' (LinearMap.{u_10, u_13, u_18, u_21} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.114) (LinearMap.{u_9, u_12, u_17, u_20} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.110) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59) (LinearMap.addCommMonoid.{u_10, u_13, u_18, u_21} R₂ R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.114 σ₂₂') (LinearMap.addCommMonoid.{u_9, u_12, u_17, u_20} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.110 σ₁₁') (LinearMap.module.{u_10, u_13, u_13, u_18, u_21} R₂ R₂' R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.114 σ₂₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.114)))) (LinearMap.module.{u_9, u_12, u_12, u_17, u_20} R₁ R₁' R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.110 σ₁₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.110)))) σ₂'₁' σ₁'₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.297 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.293)) (LinearEquiv.symm.{u_12, u_13, max u_17 u_20, max u_18 u_21} R₁' R₂' (LinearMap.{u_9, u_12, u_17, u_20} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.110) (LinearMap.{u_10, u_13, u_18, u_21} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.114) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62) (LinearMap.addCommMonoid.{u_9, u_12, u_17, u_20} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.110 σ₁₁') (LinearMap.addCommMonoid.{u_10, u_13, u_18, u_21} R₂ R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.114 σ₂₂') (LinearMap.module.{u_9, u_12, u_12, u_17, u_20} R₁ R₁' R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.98 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.59 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.62 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.114 σ₁₂ σ₂₁ σ₁'₂' σ₂'₁' σ₁₁' σ₂₂' σ₂₁' σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.285 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.289 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2311912846._hygCtx._hyg.293 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{R₂' : Type u_13} {M₁ : Type u_17} {M₂ : Type u_18}\n  {M₁' : Type u_20} {M₂' : Type u_21} [inst : Semiring R₁] [inst_1 : Semiring R₂] [inst_2 : CommSemiring R₁']\n  [inst_3 : CommSemiring R₂'] [inst_4 : AddCommMonoid M₁] [inst_5 : AddCommMonoid M₂] [inst_6 : AddCommMonoid M₁']\n  [inst_7 : AddCommMonoid M₂'] [inst_8 : Module R₁ M₁] [inst_9 : Module R₂ M₂] [inst_10 : Module R₁' M₁']\n  [inst_11 : Module R₂' M₂'] {σ₁₂ : R₁ →+* R₂} {σ₂₁ : R₂ →+* R₁} {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'}\n  {σ₁₁' : R₁ →+* R₁'} {σ₂₂' : R₂ →+* R₂'} {σ₂₁' : R₂ →+* R₁'} {σ₁₂' : R₁ →+* R₂'} [inst_12 : RingHomInvPair σ₁₂ σ₂₁]\n  [inst_13 : RingHomInvPair σ₂₁ σ₁₂] [inst_14 : RingHomInvPair σ₁'₂' σ₂'₁'] [inst_15 : RingHomInvPair σ₂'₁' σ₁'₂']\n  [inst_16 : RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_17 : RingHomCompTriple σ₂₁ σ₁₂' σ₂₂']\n  [inst_18 : RingHomCompTriple σ₂₂' σ₂'₁' σ₂₁'] [inst_19 : RingHomCompTriple σ₁₂ σ₂₁' σ₁₁'] (e₁ : M₁ ≃ₛₗ[σ₁₂] M₂)\n  (e₂ : M₁' ≃ₛₗ[σ₁'₂'] M₂') (f : M₂ →ₛₗ[σ₂₂'] M₂') (x : M₁), 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[inst_19 : RingHomCompTriple σ₁₂ σ₂₁' σ₁₁'] (e₁ : M₁ ≃ₛₗ[σ₁₂] M₂)\n  (e₂ : M₁' ≃ₛₗ[σ₁'₂'] M₂') (f : M₂ →ₛₗ[σ₂₂'] M₂') (x : M₁), ((e₁.arrowCongr e₂).symm f) x = e₂.symm (f (e₁ x))","typeReferences":[["RingHom"],["smulCommClass_self"],["LinearMap","instFunLike"],["CommMonoid","toMonoid"],["Module"],["CommSemiring"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["DFunLike","coe"],["RingHomCompTriple"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["EquivLike","toFunLike"],["DistribMulAction","toMulAction"],["Eq"],["LinearEquiv","instEquivLike"],["CommSemiring","toSemiring"],["LinearMap","module"],["LinearMap"],["LinearEquiv","symm"],["LinearEquiv","arrowCongr"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["RingHomInvPair"],["Semiring"]],"valueReferences":[["rfl"],["smulCommClass_self"],["LinearMap","instFunLike"],["CommMonoid","toMonoid"],["CommSemiring","toSemiring"],["LinearMap","module"],["AddCommMonoid","toAddMonoid"],["LinearMap"],["LinearEquiv"],["LinearEquiv","symm"],["DFunLike","coe"],["LinearEquiv","arrowCongr"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["EquivLike","toFunLike"],["DistribMulAction","toMulAction"],["LinearEquiv","instEquivLike"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","sumPiEquivProdPi","_proof_3"],"typeFallback":"forall (S : Type.{u_3}) (T : Type.{u_2}) (A : (Sum.{u_3, u_2} S T) -> Type.{u_1}), Function.LeftInverse.{max (max (succ u_1) (succ u_2)) (succ u_3), max (succ (max u_1 u_2)) (succ (max u_1 u_3))} (forall (i : Sum.{u_3, u_2} S T), A i) (Prod.{max u_1 u_3, max u_1 u_2} (forall (i : S), A (Sum.inl.{u_3, u_2} S T i)) (forall (i' : T), A (Sum.inr.{u_3, u_2} S T i'))) (Equiv.invFun.{max (max (succ u_1) (succ u_2)) (succ u_3), max (succ (max u_1 u_2)) (succ (max u_1 u_3))} (forall (i : Sum.{u_3, u_2} S T), A i) (Prod.{max u_1 u_3, max u_1 u_2} (forall (i : S), A (Sum.inl.{u_3, u_2} S T i)) (forall (i' : T), A (Sum.inr.{u_3, u_2} S T i'))) (Equiv.sumPiEquivProdPi.{u_1, u_3, u_2} S T A)) (Equiv.toFun.{max (max (succ u_1) (succ u_2)) (succ u_3), max (succ (max u_1 u_2)) (succ (max u_1 u_3))} (forall (i : Sum.{u_3, u_2} S T), A i) (Prod.{max u_1 u_3, max u_1 u_2} (forall (i : S), A (Sum.inl.{u_3, u_2} S T i)) (forall (i' : T), A (Sum.inr.{u_3, u_2} S T i'))) (Equiv.sumPiEquivProdPi.{u_1, u_3, u_2} S T A))","typeFull":"∀ (S : Type u_3) (T : Type u_2) (A : S ⊕ T → Type u_1),\n  Function.LeftInverse (Equiv.sumPiEquivProdPi A).invFun (Equiv.sumPiEquivProdPi A).toFun","typeReadable":"∀ (S : Type u_3) (T : Type u_2) (A : S ⊕ T → Type u_1),\n  Function.LeftInverse (Equiv.sumPiEquivProdPi A).invFun (Equiv.sumPiEquivProdPi A).toFun","typeReferences":[["Prod"],["Equiv","sumPiEquivProdPi"],["Sum","inl"],["Equiv","invFun"],["Function","LeftInverse"],["Equiv","toFun"],["Sum","inr"],["Sum"]],"valueReferences":[["Prod"],["Equiv","sumPiEquivProdPi"],["Equiv","left_inv"],["Sum","inl"],["Sum","inr"],["Sum"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","arrowCongrAddEquiv","_proof_1"],"typeFallback":"forall {R₁ : Type.{u_3}} {R₂ : Type.{u_5}} {R₁' : Type.{u_4}} {R₂' : Type.{u_6}} {M₁ : Type.{u_1}} {M₂ : Type.{u_7}} {M₁' : Type.{u_2}} {M₂' : Type.{u_8}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 : Semiring.{u_3} R₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 : Semiring.{u_5} R₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 : Semiring.{u_4} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 : Semiring.{u_6} R₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 : AddCommMonoid.{u_1} M₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 : AddCommMonoid.{u_7} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 : AddCommMonoid.{u_2} M₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 : AddCommMonoid.{u_8} M₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 : Module.{u_3, u_1} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 : Module.{u_5, u_7} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 : Module.{u_4, u_2} R₁' M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 : Module.{u_6, u_8} R₂' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39] {σ₁₂ : RingHom.{u_3, u_5} R₁ R₂ (Semiring.toNonAssocSemiring.{u_3} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_5} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21)} {σ₂₁ : RingHom.{u_5, u_3} R₂ R₁ (Semiring.toNonAssocSemiring.{u_5} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21) (Semiring.toNonAssocSemiring.{u_3} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18)} {σ₁'₂' : RingHom.{u_4, u_6} R₁' R₂' (Semiring.toNonAssocSemiring.{u_4} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24) (Semiring.toNonAssocSemiring.{u_6} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27)} {σ₂'₁' : RingHom.{u_6, u_4} R₂' R₁' (Semiring.toNonAssocSemiring.{u_6} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27) (Semiring.toNonAssocSemiring.{u_4} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24)} {σ₁₁' : RingHom.{u_3, u_4} R₁ R₁' (Semiring.toNonAssocSemiring.{u_3} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_4} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24)} {σ₂₂' : RingHom.{u_5, u_6} R₂ R₂' (Semiring.toNonAssocSemiring.{u_5} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21) (Semiring.toNonAssocSemiring.{u_6} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27)} {σ₂₁' : RingHom.{u_5, u_4} R₂ R₁' (Semiring.toNonAssocSemiring.{u_5} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21) (Semiring.toNonAssocSemiring.{u_4} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24)} {σ₁₂' : RingHom.{u_3, u_6} R₁ R₂' (Semiring.toNonAssocSemiring.{u_3} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_6} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27)} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 : RingHomInvPair.{u_3, u_5} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 σ₁₂ σ₂₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 : RingHomInvPair.{u_5, u_3} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 σ₂₁ σ₁₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 : RingHomInvPair.{u_4, u_6} R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₁'₂' σ₂'₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 : RingHomInvPair.{u_6, u_4} R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₂'₁' σ₁'₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.114 : RingHomCompTriple.{u_3, u_4, u_6} R₁ R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₁₁' σ₁'₂' σ₁₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.119 : RingHomCompTriple.{u_5, u_3, u_6} R₂ R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₂₁ σ₁₂' σ₂₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.124 : RingHomCompTriple.{u_5, u_6, u_4} R₂ R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₂₂' σ₂'₁' σ₂₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.129 : RingHomCompTriple.{u_3, u_5, u_4} R₁ R₂ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₂ σ₂₁' σ₁₁'] (e₁ : LinearEquiv.{u_3, u_5, u_1, u_7} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46) (e₂ : LinearEquiv.{u_4, u_6, u_2, u_8} R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54) (f : LinearMap.{u_3, u_4, u_1, u_2} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50), Eq.{succ (max u_1 u_2)} (LinearMap.{u_3, u_4, u_1, u_2} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50) ((fun (f : LinearMap.{u_5, u_6, u_7, u_8} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54) => LinearMap.comp.{u_3, u_5, u_4, u_1, u_7, u_2} R₁ R₂ R₁' M₁ M₂ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 σ₁₂ σ₂₁' σ₁₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.129 (LinearMap.comp.{u_5, u_6, u_4, u_7, u_8, u_2} R₂ R₂' R₁' M₂ M₂' M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 σ₂₂' σ₂'₁' σ₂₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.124 (LinearEquiv.toLinearMap.{u_6, u_4, u_8, u_2} R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₂'₁' σ₁'₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 M₂' M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 (LinearEquiv.symm.{u_4, u_6, u_2, u_8} R₁' R₂' M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 e₂)) f) (LinearEquiv.toLinearMap.{u_3, u_5, u_1, u_7} R₁ R₂ 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.25) (n : Nat) (m : M), Eq.{succ u_5} M (DFunLike.coe.{succ u_5, succ u_5, succ u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.25) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (EquivLike.toFunLike.{succ u_5, succ u_5, succ u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.25) M M (LinearEquiv.instEquivLike.{u_1, u_1, u_5, u_5} R R M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10))) (HPow.hPow.{u_5, 0, u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.25) Nat (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.25) (instHPow.{u_5, 0} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.25) Nat (Monoid.toPow.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.25) (DivInvMonoid.toMonoid.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.25) (Group.toDivInvMonoid.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.25) (LinearEquiv.automorphismGroup.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.25))))) e n) m) (Nat.iterate.{succ u_5} M (DFunLike.coe.{succ u_5, succ u_5, succ u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.25) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (EquivLike.toFunLike.{succ u_5, succ u_5, succ u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.25) M M (LinearEquiv.instEquivLike.{u_1, u_1, u_5, u_5} R R M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.262892056._hygCtx._hyg.10))) e) n m)","typeFull":"∀ {R : Type u_1} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (e : M ≃ₗ[R] M)\n  (n : ℕ) (m : M), (e ^ n) m = (⇑e)^[n] m","typeReadable":"∀ {R : Type u_1} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (e : M ≃ₗ[R] M)\n  (n : ℕ) (m : M), (e ^ n) m = (⇑e)^[n] m","typeReferences":[["instHPow"],["Module"],["LinearEquiv"],["HPow","hPow"],["DFunLike","coe"],["LinearEquiv","automorphismGroup"],["AddCommMonoid"],["Nat"],["Nat","iterate"],["Semiring","toNonAssocSemiring"],["DivInvMonoid","toMonoid"],["Monoid","toPow"],["RingHom","id"],["EquivLike","toFunLike"],["RingHomInvPair","ids"],["Eq"],["LinearEquiv","instEquivLike"],["Group","toDivInvMonoid"],["Semiring"]],"valueReferences":[["instHPow"],["congr_fun"],["LinearEquiv","coe_pow"],["LinearEquiv"],["HPow","hPow"],["DFunLike","coe"],["LinearEquiv","automorphismGroup"],["Nat"],["Nat","iterate"],["Semiring","toNonAssocSemiring"],["Monoid","toPow"],["DivInvMonoid","toMonoid"],["RingHom","id"],["EquivLike","toFunLike"],["RingHomInvPair","ids"],["LinearEquiv","instEquivLike"],["Group","toDivInvMonoid"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","mk","congr_simp"],"typeFallback":"forall {R : Type.{u_14}} {S : Type.{u_15}} [inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.30 : Semiring.{u_14} R] [inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.33 : Semiring.{u_15} S] {σ : RingHom.{u_14, u_15} R S (Semiring.toNonAssocSemiring.{u_14} R inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.30) (Semiring.toNonAssocSemiring.{u_15} S inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.33)} {σ' : RingHom.{u_15, u_14} S R (Semiring.toNonAssocSemiring.{u_15} S inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.33) (Semiring.toNonAssocSemiring.{u_14} R inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.30)} [inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.46 : RingHomInvPair.{u_14, u_15} R S inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.33 σ σ'] [inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.50 : RingHomInvPair.{u_15, u_14} S R inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.30 σ' σ] {M : Type.{u_16}} {M₂ : Type.{u_17}} [inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.56 : AddCommMonoid.{u_16} M] [inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.59 : AddCommMonoid.{u_17} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.62 : Module.{u_14, u_16} R M inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.56] [inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.66 : Module.{u_15, u_17} S M₂ inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.59] (toLinearMap : LinearMap.{u_14, u_15, u_16, u_17} R S inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.33 σ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.56 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.59 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.62 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.66) (toLinearMap_1 : LinearMap.{u_14, u_15, u_16, u_17} R S inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.33 σ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.56 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.59 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.62 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.66) (e_toLinearMap : Eq.{max (succ u_16) (succ u_17)} (LinearMap.{u_14, u_15, u_16, u_17} R S inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.33 σ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.56 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.59 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.62 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.66) toLinearMap toLinearMap_1) (invFun : M₂ -> M) (invFun_1 : M₂ -> M) (e_invFun : Eq.{max (succ u_16) (succ u_17)} (M₂ -> M) invFun invFun_1) (left_inv : Function.LeftInverse.{succ u_16, succ u_17} M M₂ invFun (AddHom.toFun.{u_16, u_17} M M₂ (AddCommMagma.toAdd.{u_16} M (AddCommSemigroup.toAddCommMagma.{u_16} M (AddCommMonoid.toAddCommSemigroup.{u_16} M inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.56))) (AddCommMagma.toAdd.{u_17} M₂ (AddCommSemigroup.toAddCommMagma.{u_17} M₂ (AddCommMonoid.toAddCommSemigroup.{u_17} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.59))) (LinearMap.toAddHom.{u_14, u_15, u_16, u_17} R S inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.33 σ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.56 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.59 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.62 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.66 toLinearMap))) (right_inv : Function.RightInverse.{succ u_16, succ u_17} M M₂ invFun (AddHom.toFun.{u_16, u_17} M M₂ (AddCommMagma.toAdd.{u_16} M (AddCommSemigroup.toAddCommMagma.{u_16} M (AddCommMonoid.toAddCommSemigroup.{u_16} M inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.56))) (AddCommMagma.toAdd.{u_17} M₂ (AddCommSemigroup.toAddCommMagma.{u_17} M₂ (AddCommMonoid.toAddCommSemigroup.{u_17} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.59))) (LinearMap.toAddHom.{u_14, u_15, u_16, u_17} R S inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.33 σ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.56 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.59 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.62 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.66 toLinearMap))), Eq.{max (succ u_16) (succ u_17)} (LinearEquiv.{u_14, u_15, u_16, u_17} R S inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.33 σ σ' inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.50 M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.56 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.59 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.62 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.66) (LinearEquiv.mk.{u_14, u_15, u_16, u_17} R S inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.33 σ σ' inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.50 M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.56 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.59 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.62 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.66 toLinearMap invFun left_inv right_inv) (LinearEquiv.mk.{u_14, u_15, u_16, u_17} R S inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.33 σ σ' inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.50 M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.56 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.59 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.62 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.66 toLinearMap_1 invFun_1 (Eq.ndrec.{0, max (succ u_16) (succ u_17)} (LinearMap.{u_14, u_15, u_16, u_17} R S inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.33 σ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.56 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.59 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.62 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.66) toLinearMap (fun (toLinearMap : LinearMap.{u_14, u_15, u_16, u_17} R S inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.33 σ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.56 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.59 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.62 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.66) => Function.LeftInverse.{succ u_16, succ u_17} M M₂ invFun_1 (AddHom.toFun.{u_16, u_17} M M₂ (AddCommMagma.toAdd.{u_16} M (AddCommSemigroup.toAddCommMagma.{u_16} M (AddCommMonoid.toAddCommSemigroup.{u_16} M inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.56))) (AddCommMagma.toAdd.{u_17} M₂ (AddCommSemigroup.toAddCommMagma.{u_17} M₂ (AddCommMonoid.toAddCommSemigroup.{u_17} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.59))) (LinearMap.toAddHom.{u_14, u_15, u_16, u_17} R S inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.33 σ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.56 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.59 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.62 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.66 toLinearMap))) (Eq.ndrec.{0, max (succ u_16) (succ u_17)} (M₂ -> M) invFun (fun (invFun : M₂ -> M) => Function.LeftInverse.{succ u_16, succ u_17} M M₂ invFun (AddHom.toFun.{u_16, u_17} M M₂ (AddCommMagma.toAdd.{u_16} M (AddCommSemigroup.toAddCommMagma.{u_16} M (AddCommMonoid.toAddCommSemigroup.{u_16} M inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.56))) (AddCommMagma.toAdd.{u_17} M₂ (AddCommSemigroup.toAddCommMagma.{u_17} M₂ (AddCommMonoid.toAddCommSemigroup.{u_17} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.59))) (LinearMap.toAddHom.{u_14, u_15, u_16, u_17} R S inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.33 σ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.56 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.59 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.62 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.66 toLinearMap))) left_inv invFun_1 e_invFun) toLinearMap_1 e_toLinearMap) (Eq.ndrec.{0, max (succ u_16) (succ u_17)} (LinearMap.{u_14, u_15, u_16, u_17} R S inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.33 σ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.56 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.59 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.62 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.66) toLinearMap (fun (toLinearMap : LinearMap.{u_14, u_15, u_16, u_17} R S inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.33 σ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.56 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.59 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.62 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.66) => Function.RightInverse.{succ u_16, succ u_17} M M₂ invFun_1 (AddHom.toFun.{u_16, u_17} M M₂ (AddCommMagma.toAdd.{u_16} M (AddCommSemigroup.toAddCommMagma.{u_16} M (AddCommMonoid.toAddCommSemigroup.{u_16} M inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.56))) (AddCommMagma.toAdd.{u_17} M₂ (AddCommSemigroup.toAddCommMagma.{u_17} M₂ (AddCommMonoid.toAddCommSemigroup.{u_17} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.59))) (LinearMap.toAddHom.{u_14, u_15, u_16, u_17} R S inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.33 σ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.56 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.59 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.62 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.66 toLinearMap))) (Eq.ndrec.{0, max (succ u_16) (succ u_17)} (M₂ -> M) invFun (fun (invFun : M₂ -> M) => Function.RightInverse.{succ u_16, succ u_17} M M₂ invFun (AddHom.toFun.{u_16, u_17} M M₂ (AddCommMagma.toAdd.{u_16} M (AddCommSemigroup.toAddCommMagma.{u_16} M (AddCommMonoid.toAddCommSemigroup.{u_16} M inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.56))) (AddCommMagma.toAdd.{u_17} M₂ (AddCommSemigroup.toAddCommMagma.{u_17} M₂ (AddCommMonoid.toAddCommSemigroup.{u_17} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.59))) (LinearMap.toAddHom.{u_14, u_15, u_16, u_17} R S inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.33 σ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.56 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.59 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.62 inst._@.Mathlib.Algebra.Module.Equiv.Defs.2398389480._hygCtx._hyg.66 toLinearMap))) right_inv invFun_1 e_invFun) toLinearMap_1 e_toLinearMap))","typeFull":"∀ {R : Type u_14} {S : Type u_15} [inst : Semiring R] [inst_1 : Semiring S] {σ : R →+* S} {σ' : S →+* R}\n  [inst_2 : RingHomInvPair σ σ'] [inst_3 : RingHomInvPair σ' σ] {M : Type u_16} {M₂ : Type u_17}\n  [inst_4 : AddCommMonoid M] [inst_5 : AddCommMonoid M₂] [inst_6 : Module R M] [inst_7 : Module S M₂]\n  (toLinearMap toLinearMap_1 : M →ₛₗ[σ] M₂) (e_toLinearMap : toLinearMap = toLinearMap_1) (invFun invFun_1 : M₂ → M)\n  (e_invFun : invFun = invFun_1) (left_inv : Function.LeftInverse invFun toLinearMap.toFun)\n  (right_inv : Function.RightInverse invFun toLinearMap.toFun),\n  { toLinearMap := toLinearMap, invFun := invFun, left_inv := left_inv, right_inv := right_inv } =\n    { toLinearMap := toLinearMap_1, invFun := invFun_1, left_inv := ⋯, right_inv := ⋯ }","typeReadable":"∀ {R : Type u_14} {S : Type u_15} [inst : Semiring R] [inst_1 : Semiring S] {σ : R →+* S} {σ' : S →+* R}\n  [inst_2 : RingHomInvPair σ σ'] [inst_3 : RingHomInvPair σ' σ] {M : Type u_16} {M₂ : Type u_17}\n  [inst_4 : AddCommMonoid M] [inst_5 : AddCommMonoid M₂] [inst_6 : Module R M] [inst_7 : Module S M₂]\n  (toLinearMap toLinearMap_1 : M →ₛₗ[σ] M₂) (e_toLinearMap : toLinearMap = toLinearMap_1) (invFun invFun_1 : M₂ → M)\n  (e_invFun : invFun = invFun_1) (left_inv : Function.LeftInverse invFun toLinearMap.toFun)\n  (right_inv : Function.RightInverse invFun toLinearMap.toFun),\n  { toLinearMap := toLinearMap, invFun := invFun, left_inv := left_inv, right_inv := right_inv } =\n    { toLinearMap := toLinearMap_1, invFun := invFun_1, left_inv := ⋯, right_inv := ⋯ }","typeReferences":[["RingHom"],["Module"],["LinearMap","toAddHom"],["LinearEquiv"],["LinearMap"],["Function","RightInverse"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["AddCommMonoid","toAddCommSemigroup"],["Function","LeftInverse"],["LinearEquiv","mk"],["AddHom","toFun"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Eq","ndrec"],["RingHomInvPair"],["Eq"],["Semiring"]],"valueReferences":[["LinearMap","toAddHom"],["LinearMap"],["LinearEquiv"],["Function","RightInverse"],["AddCommMonoid","toAddCommSemigroup"],["Eq","refl"],["Function","LeftInverse"],["LinearEquiv","mk"],["AddHom","toFun"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Eq","rec"],["Eq"],["Eq","ndrec"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","arrowCongrAddEquiv","_proof_3"],"typeFallback":"forall {R₁ : Type.{u_5}} {R₂ : Type.{u_3}} {R₁' : Type.{u_7}} {R₂' : Type.{u_4}} {M₁ : Type.{u_6}} {M₂ : Type.{u_1}} {M₁' : Type.{u_8}} {M₂' : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 : Semiring.{u_5} R₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 : Semiring.{u_3} R₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 : Semiring.{u_7} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 : Semiring.{u_4} R₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 : AddCommMonoid.{u_6} M₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 : AddCommMonoid.{u_1} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 : AddCommMonoid.{u_8} M₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 : AddCommMonoid.{u_2} M₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 : Module.{u_5, u_6} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 : Module.{u_3, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 : Module.{u_7, u_8} R₁' M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 : Module.{u_4, u_2} R₂' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39] {σ₁₂ : RingHom.{u_5, u_3} R₁ R₂ (Semiring.toNonAssocSemiring.{u_5} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_3} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21)} {σ₂₁ : RingHom.{u_3, u_5} R₂ R₁ (Semiring.toNonAssocSemiring.{u_3} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21) (Semiring.toNonAssocSemiring.{u_5} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18)} {σ₁'₂' : RingHom.{u_7, u_4} R₁' R₂' (Semiring.toNonAssocSemiring.{u_7} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24) (Semiring.toNonAssocSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27)} {σ₂'₁' : RingHom.{u_4, u_7} R₂' R₁' (Semiring.toNonAssocSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27) (Semiring.toNonAssocSemiring.{u_7} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24)} {σ₁₁' : RingHom.{u_5, u_7} R₁ R₁' (Semiring.toNonAssocSemiring.{u_5} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_7} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24)} {σ₂₂' : RingHom.{u_3, u_4} R₂ R₂' (Semiring.toNonAssocSemiring.{u_3} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21) (Semiring.toNonAssocSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27)} {σ₁₂' : RingHom.{u_5, u_4} R₁ R₂' (Semiring.toNonAssocSemiring.{u_5} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_4} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27)} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 : RingHomInvPair.{u_5, u_3} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 σ₁₂ σ₂₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 : RingHomInvPair.{u_3, u_5} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 σ₂₁ σ₁₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 : RingHomInvPair.{u_7, u_4} R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₁'₂' σ₂'₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 : RingHomInvPair.{u_4, u_7} R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₂'₁' σ₁'₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.114 : RingHomCompTriple.{u_5, u_7, u_4} R₁ R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₁₁' σ₁'₂' σ₁₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.119 : RingHomCompTriple.{u_3, u_5, u_4} R₂ R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₂₁ σ₁₂' σ₂₂'] (e₁ : LinearEquiv.{u_5, u_3, u_6, u_1} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46) (e₂ : LinearEquiv.{u_7, u_4, u_8, u_2} R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54) (f : LinearMap.{u_5, u_7, u_6, u_8} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50) (g : LinearMap.{u_5, u_7, u_6, u_8} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50), Eq.{succ (max u_1 u_2)} (LinearMap.{u_3, u_4, u_1, u_2} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54) (LinearMap.comp.{u_3, u_5, u_4, u_1, u_6, u_2} R₂ R₁ R₂' M₂ M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 σ₂₁ σ₁₂' σ₂₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.119 (LinearMap.comp.{u_5, u_7, u_4, u_6, u_8, u_2} R₁ R₁' R₂' M₁ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 σ₁₁' σ₁'₂' σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.114 (LinearEquiv.toLinearMap.{u_7, u_4, u_8, u_2} R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 e₂) (HAdd.hAdd.{max u_6 u_8, max u_6 u_8, max u_6 u_8} (LinearMap.{u_5, u_7, u_6, u_8} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50) (LinearMap.{u_5, u_7, u_6, u_8} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50) (LinearMap.{u_5, u_7, u_6, u_8} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50) (instHAdd.{max u_6 u_8} (LinearMap.{u_5, u_7, u_6, u_8} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50) (LinearMap.instAdd.{u_5, u_7, u_6, u_8} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 σ₁₁')) f g)) (LinearEquiv.toLinearMap.{u_3, u_5, u_1, u_6} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 σ₂₁ σ₁₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 M₂ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 (LinearEquiv.symm.{u_5, u_3, u_6, u_1} R₁ R₂ M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 e₁))) (HAdd.hAdd.{max u_1 u_2, max u_1 u_2, max u_1 u_2} (LinearMap.{u_3, u_4, u_1, u_2} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54) (LinearMap.{u_3, u_4, u_1, u_2} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 M₂ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 (LinearEquiv.symm.{u_5, u_3, u_6, u_1} R₁ R₂ M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 e₁))))","typeFull":"∀ {R₁ : Type u_5} {R₂ : Type u_3} {R₁' : Type u_7} {R₂' : Type u_4} {M₁ : Type u_6} {M₂ : Type u_1} {M₁' : Type u_8}\n  {M₂' : Type u_2} [inst : Semiring R₁] [inst_1 : Semiring R₂] [inst_2 : Semiring R₁'] [inst_3 : Semiring R₂']\n  [inst_4 : AddCommMonoid M₁] [inst_5 : AddCommMonoid M₂] [inst_6 : AddCommMonoid M₁'] [inst_7 : AddCommMonoid M₂']\n  [inst_8 : Module R₁ M₁] [inst_9 : Module R₂ M₂] [inst_10 : Module R₁' M₁'] [inst_11 : Module R₂' M₂']\n  {σ₁₂ : R₁ →+* R₂} {σ₂₁ : R₂ →+* R₁} {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} {σ₁₁' : R₁ →+* R₁'}\n  {σ₂₂' : R₂ →+* R₂'} {σ₁₂' : R₁ →+* R₂'} [inst_12 : RingHomInvPair σ₁₂ σ₂₁] [inst_13 : RingHomInvPair σ₂₁ σ₁₂]\n  [inst_14 : RingHomInvPair σ₁'₂' σ₂'₁'] [inst_15 : RingHomInvPair σ₂'₁' σ₁'₂']\n  [inst_16 : RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_17 : RingHomCompTriple σ₂₁ σ₁₂' σ₂₂'] (e₁ : M₁ ≃ₛₗ[σ₁₂] M₂)\n  (e₂ : M₁' ≃ₛₗ[σ₁'₂'] M₂') (f g : M₁ →ₛₗ[σ₁₁'] M₁'),\n  (↑e₂ ∘ₛₗ (f + g)) ∘ₛₗ ↑e₁.symm = (↑e₂ ∘ₛₗ f) ∘ₛₗ ↑e₁.symm + (↑e₂ ∘ₛₗ g) ∘ₛₗ ↑e₁.symm","typeReadable":"∀ {R₁ : Type u_5} {R₂ : Type u_3} {R₁' : Type u_7} {R₂' : Type u_4} {M₁ : Type u_6} {M₂ : Type u_1} {M₁' : Type u_8}\n  {M₂' : Type u_2} [inst : Semiring R₁] [inst_1 : Semiring R₂] [inst_2 : Semiring R₁'] [inst_3 : Semiring R₂']\n  [inst_4 : AddCommMonoid M₁] [inst_5 : AddCommMonoid M₂] [inst_6 : AddCommMonoid M₁'] [inst_7 : AddCommMonoid M₂']\n  [inst_8 : Module R₁ M₁] [inst_9 : Module R₂ M₂] [inst_10 : Module R₁' M₁'] [inst_11 : Module R₂' M₂']\n  {σ₁₂ : R₁ →+* R₂} {σ₂₁ : R₂ →+* R₁} {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} {σ₁₁' : R₁ →+* R₁'}\n  {σ₂₂' : R₂ →+* R₂'} {σ₁₂' : R₁ →+* R₂'} [inst_12 : RingHomInvPair σ₁₂ σ₂₁] [inst_13 : RingHomInvPair σ₂₁ σ₁₂]\n  [inst_14 : RingHomInvPair σ₁'₂' σ₂'₁'] [inst_15 : RingHomInvPair σ₂'₁' σ₁'₂']\n  [inst_16 : RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_17 : RingHomCompTriple σ₂₁ σ₁₂' σ₂₂'] (e₁ : M₁ ≃ₛₗ[σ₁₂] M₂)\n  (e₂ : M₁' ≃ₛₗ[σ₁'₂'] M₂') (f g : M₁ ���ₛₗ[σ₁₁'] M₁'),\n  (↑e₂ ∘ₛₗ (f + g)) ∘ₛₗ ↑e₁.symm = (↑e₂ ∘ₛₗ f) ∘ₛₗ ↑e₁.symm + (↑e₂ ∘ₛₗ g) ∘ₛₗ ↑e₁.symm","typeReferences":[["RingHom"],["instHAdd"],["Module"],["LinearMap","comp"],["LinearEquiv","toLinearMap"],["LinearEquiv"],["LinearMap"],["LinearEquiv","symm"],["RingHomCompTriple"],["HAdd","hAdd"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["LinearMap","instAdd"],["RingHomInvPair"],["Eq"],["Semiring"]],"valueReferences":[["LinearMap","instFunLike"],["Eq","trans"],["LinearMap","comp"],["LinearEquiv"],["DFunLike","coe"],["congrArg"],["SemilinearEquivClass","instSemilinearMapClass"],["LinearMap","ext"],["LinearMap","instAdd"],["EquivLike","toFunLike"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["congrFun'"],["Eq"],["LinearEquiv","instEquivLike"],["True"],["instHAdd"],["LinearEquiv","toLinearMap"],["SemilinearMapClass","toAddHomClass"],["LinearMap"],["LinearEquiv","symm"],["HAdd","hAdd"],["map_add"],["eq_self"],["LinearEquiv","instSemilinearEquivClass"],["of_eq_true"],["AddCommMonoid","toAddCommSemigroup"]]},{"isProp":true,"kind":"theorem","name":["addMonoidEndRingEquivInt","_proof_1"],"typeFallback":"forall (A : Type.{u_1}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11 : AddCommGroup.{u_1} A], SMulCommClass.{0, 0, u_1} Int Int A (SubNegMonoid.toZSMul.{u_1} A (AddGroup.toSubNegMonoid.{u_1} A (AddCommGroup.toAddGroup.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11))) (SMulZeroClass.toSMul.{0, u_1} Int A (AddZero.toZero.{u_1} A (AddZeroClass.toAddZero.{u_1} A (AddMonoid.toAddZeroClass.{u_1} A (SubNegMonoid.toAddMonoid.{u_1} A (AddGroup.toSubNegMonoid.{u_1} A (AddCommGroup.toAddGroup.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11)))))) (DistribSMul.toSMulZeroClass.{0, u_1} Int A (AddMonoid.toAddZeroClass.{u_1} A (SubNegMonoid.toAddMonoid.{u_1} A (AddGroup.toSubNegMonoid.{u_1} A (AddCommGroup.toAddGroup.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11)))) (DistribMulAction.toDistribSMul.{0, u_1} Int A (MonoidWithZero.toMonoid.{0} Int (Semiring.toMonoidWithZero.{0} Int Int.instSemiring)) (SubNegMonoid.toAddMonoid.{u_1} A (AddGroup.toSubNegMonoid.{u_1} A (AddCommGroup.toAddGroup.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11))) (Module.toDistribMulAction.{0, u_1} Int A Int.instSemiring (AddCommGroup.toAddCommMonoid.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11) (AddCommGroup.toIntModule.{u_1} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3003806223._hygCtx._hyg.11)))))","typeFull":"∀ (A : Type u_1) [inst : AddCommGroup A], SMulCommClass ℤ ℤ A","typeReadable":"∀ (A : Type u_1) [inst : AddCommGroup A], SMulCommClass ℤ ℤ A","typeReferences":[["AddCommGroup","toAddGroup"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddCommGroup"],["SMulZeroClass","toSMul"],["AddZeroClass","toAddZero"],["AddCommGroup","toIntModule"],["Int"],["SMulCommClass"],["Module","toDistribMulAction"],["SubNegMonoid","toAddMonoid"],["Int","instSemiring"],["MonoidWithZero","toMonoid"],["AddCommGroup","toAddCommMonoid"],["AddGroup","toSubNegMonoid"],["SubNegMonoid","toZSMul"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["DistribSMul","toSMulZeroClass"]],"valueReferences":[["Module","toDistribMulAction"],["SubNegMonoid","toAddMonoid"],["Int","instSemiring"],["AddCommGroup","toAddGroup"],["MonoidWithZero","toMonoid"],["AddCommGroup","toAddCommMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddGroup","toSubNegMonoid"],["AddGroup","int_smulCommClass"],["AddCommGroup","toIntModule"],["Int"]]},{"isProp":true,"kind":"theorem","name":["AddEquiv","toIntLinearEquiv_symm"],"typeFallback":"forall 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RingHomCompTriple.{u_1, u_1, u_1} R R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._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":true,"kind":"theorem","name":["LinearEquiv","arrowCongr_trans"],"typeFallback":"forall {R₁ : Type.{u_9}} {R₂ : Type.{u_10}} {R₃ : Type.{u_11}} {R₁' : Type.{u_12}} {R₂' : Type.{u_13}} {R₃' : Type.{u_14}} {M₁ : Type.{u_17}} {M₂ : Type.{u_18}} {M₃ : Type.{u_19}} {M₁' : Type.{u_20}} {M₂' : Type.{u_21}} {M₃' : Type.{u_22}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.50 : Semiring.{u_9} R₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.53 : Semiring.{u_10} R₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.56 : Semiring.{u_11} R₃] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59 : CommSemiring.{u_12} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.62 : CommSemiring.{u_13} R₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65 : CommSemiring.{u_14} R₃'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.74 : AddCommMonoid.{u_17} M₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.77 : AddCommMonoid.{u_18} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.80 : AddCommMonoid.{u_19} M₃] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.83 : AddCommMonoid.{u_20} M₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.86 : AddCommMonoid.{u_21} M₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.89 : AddCommMonoid.{u_22} M₃'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.98 : Module.{u_9, u_17} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.74] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.102 : Module.{u_10, u_18} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.77] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.106 : Module.{u_11, u_19} R₃ M₃ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.56 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.80] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.110 : Module.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.83] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.114 : Module.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.86] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.118 : Module.{u_14, u_22} R₃' M₃' (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.89] {σ₁₂ : RingHom.{u_9, u_10} R₁ R₂ (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.53)} {σ₂₁ : RingHom.{u_10, u_9} R₂ R₁ (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.53) (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.50)} {σ₂₃ : RingHom.{u_10, u_11} R₂ R₃ (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.53) (Semiring.toNonAssocSemiring.{u_11} R₃ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.56)} {σ₃₂ : RingHom.{u_11, u_10} R₃ R₂ (Semiring.toNonAssocSemiring.{u_11} R₃ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.56) (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.53)} {σ₁₃ : RingHom.{u_9, u_11} R₁ R₃ (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_11} R₃ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.56)} {σ₃₁ : RingHom.{u_11, u_9} R₃ R₁ (Semiring.toNonAssocSemiring.{u_11} R₃ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.56) (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.50)} {σ₁'₂' : RingHom.{u_12, u_13} R₁' R₂' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59)) (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.62))} {σ₂'₁' : RingHom.{u_13, u_12} R₂' R₁' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.62)) (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59))} {σ₂'₃' : RingHom.{u_13, u_14} R₂' R₃' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.62)) (Semiring.toNonAssocSemiring.{u_14} R₃' (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65))} {σ₃'₂' : RingHom.{u_14, u_13} R₃' R₂' (Semiring.toNonAssocSemiring.{u_14} R₃' (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65)) (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.62))} {σ₁'₃' : RingHom.{u_12, u_14} R₁' R₃' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59)) (Semiring.toNonAssocSemiring.{u_14} R₃' (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65))} {σ₃'₁' : RingHom.{u_14, u_12} R₃' R₁' (Semiring.toNonAssocSemiring.{u_14} R₃' (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65)) (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59))} {σ₁₁' : RingHom.{u_9, u_12} R₁ R₁' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59))} {σ₂₂' : RingHom.{u_10, u_13} R₂ R₂' (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.53) (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.62))} {σ₃₃' : RingHom.{u_11, u_14} R₃ R₃' (Semiring.toNonAssocSemiring.{u_11} R₃ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.56) (Semiring.toNonAssocSemiring.{u_14} R₃' (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65))} {σ₂₁' : RingHom.{u_10, u_12} R₂ R₁' (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.53) (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59))} {σ₁₂' : RingHom.{u_9, u_13} R₁ R₂' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.62))} {σ₃₂' : RingHom.{u_11, u_13} R₃ R₂' (Semiring.toNonAssocSemiring.{u_11} R₃ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.56) (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.62))} {σ₂₃' : RingHom.{u_10, u_14} R₂ R₃' (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.53) (Semiring.toNonAssocSemiring.{u_14} R₃' (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65))} {σ₃₁' : RingHom.{u_11, u_12} R₃ R₁' (Semiring.toNonAssocSemiring.{u_11} R₃ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.56) (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59))} {σ₁₃' : RingHom.{u_9, u_14} R₁ R₃' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_14} R₃' (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65))} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.285 : RingHomInvPair.{u_9, u_10} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.53 σ₁₂ σ₂₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.289 : RingHomInvPair.{u_10, u_9} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.50 σ₂₁ σ₁₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.293 : RingHomInvPair.{u_12, u_13} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.62) σ₁'₂' σ₂'₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.297 : RingHomInvPair.{u_13, u_12} R₂' R₁' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59) σ₂'₁' σ₁'₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.301 : RingHomInvPair.{u_10, u_11} R₂ R₃ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.56 σ₂₃ σ₃₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.305 : RingHomInvPair.{u_11, u_10} R₃ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.56 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.53 σ₃₂ σ₂₃] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.309 : RingHomInvPair.{u_13, u_14} R₂' R₃' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65) σ₂'₃' σ₃'₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.313 : RingHomInvPair.{u_14, u_13} R₃' R₂' (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.62) σ₃'₂' σ₂'₃'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.317 : RingHomInvPair.{u_9, u_11} R₁ R₃ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.56 σ₁₃ σ₃₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.321 : RingHomInvPair.{u_11, u_9} R₃ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.56 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.50 σ₃₁ σ₁₃] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.325 : RingHomInvPair.{u_12, u_14} R₁' R₃' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65) σ₁'₃' σ₃'₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.329 : RingHomInvPair.{u_14, u_12} R₃' R₁' (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59) σ₃'₁' σ₁'₃'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.351 : RingHomCompTriple.{u_9, u_12, u_13} R₁ R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.62) σ₁₁' σ₁'₂' σ₁₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.356 : RingHomCompTriple.{u_10, u_9, u_13} R₂ R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.62) σ₂₁ σ₁₂' σ₂₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.361 : RingHomCompTriple.{u_10, u_13, u_12} R₂ R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59) σ₂₂' σ₂'₁' σ₂₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.366 : RingHomCompTriple.{u_9, u_10, u_12} R₁ R₂ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59) σ₁₂ σ₂₁' σ₁₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.371 : RingHomCompTriple.{u_9, u_12, u_14} R₁ R₁' R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65) σ₁₁' σ₁'₃' σ₁₃'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.376 : RingHomCompTriple.{u_11, u_9, u_14} R₃ R₁ R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.56 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65) σ₃₁ σ₁₃' σ₃₃'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.381 : RingHomCompTriple.{u_11, u_14, u_12} R₃ R₃' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.56 (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59) σ₃₃' σ₃'₁' σ₃₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.386 : RingHomCompTriple.{u_9, u_11, u_12} R₁ R₃ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.56 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59) σ₁₃ σ₃₁' σ₁₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.391 : RingHomCompTriple.{u_10, u_13, u_14} R₂ R₂' R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65) σ₂₂' σ₂'₃' σ₂₃'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.396 : RingHomCompTriple.{u_11, u_10, u_14} R₃ R₂ R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.56 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65) σ₃₂ σ₂₃' σ₃₃'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.401 : RingHomCompTriple.{u_11, u_14, u_13} R₃ R₃' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.56 (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.62) σ₃₃' σ₃'₂' σ₃₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.406 : RingHomCompTriple.{u_10, u_11, u_13} R₂ R₃ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.56 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.62) σ₂₃ σ₃₂' σ₂₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.451 : RingHomCompTriple.{u_9, u_10, u_11} R₁ R₂ R₃ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.56 σ₁₂ σ₂₃ σ₁₃] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.456 : RingHomCompTriple.{u_11, u_10, u_9} R₃ R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.56 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.50 σ₃₂ σ₂₁ σ₃₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.461 : RingHomCompTriple.{u_12, u_13, u_14} R₁' R₂' R₃' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65) σ₁'₂' σ₂'₃' σ₁'₃'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.466 : RingHomCompTriple.{u_14, u_13, u_12} R₃' R₂' R₁' (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59) σ₃'₂' σ₂'₁' σ₃'₁'] (e₁ : LinearEquiv.{u_9, u_10, u_17, u_18} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.53 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.285 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.289 M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.102) (e₁' : LinearEquiv.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.297 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.114) (e₂ : LinearEquiv.{u_10, u_11, u_18, u_19} R₂ R₃ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.56 σ₂₃ σ₃₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.301 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.305 M₂ M₃ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.80 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.106) (e₂' : LinearEquiv.{u_13, u_14, u_21, u_22} R₂' R₃' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65) σ₂'₃' σ₃'₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.309 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.313 M₂' M₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.89 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.118), Eq.{max (max (max (succ u_17) (succ u_19)) (succ u_20)) (succ u_22)} (LinearEquiv.{u_12, u_14, max u_17 u_20, max u_19 u_22} R₁' R₃' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65) σ₁'₃' σ₃'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.325 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.329 (LinearMap.{u_9, u_12, u_17, u_20} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.110) (LinearMap.{u_11, u_14, u_19, u_22} R₃ R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.56 (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65) σ₃₃' M₃ M₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.80 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.89 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.118) (LinearMap.addCommMonoid.{u_9, u_12, u_17, u_20} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.110 σ₁₁') (LinearMap.addCommMonoid.{u_11, u_14, u_19, u_22} R₃ R₃' M₃ M₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.56 (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.80 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.89 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.118 σ₃₃') (LinearMap.module.{u_9, u_12, u_12, u_17, u_20} R₁ R₁' R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.110 σ₁₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.110)))) (LinearMap.module.{u_11, u_14, u_14, u_19, u_22} R₃ R₃' R₃' M₃ M₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.56 (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.80 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.89 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.118 σ₃₃' (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.118 (smulCommClass_self.{u_14, u_22} R₃' M₃' (CommSemiring.toCommMonoid.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65) (DistribMulAction.toMulAction.{u_14, u_22} R₃' M₃' (CommMonoid.toMonoid.{u_14} R₃' (CommSemiring.toCommMonoid.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65)) (AddCommMonoid.toAddMonoid.{u_22} M₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.89) (Module.toDistribMulAction.{u_14, u_22} R₃' M₃' (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.89 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.118))))) (LinearEquiv.trans.{u_12, u_13, u_14, max u_17 u_20, max u_18 u_21, max u_19 u_22} R₁' R₂' R₃' (LinearMap.{u_9, u_12, u_17, u_20} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.110) (LinearMap.{u_10, u_13, u_18, u_21} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.114) (LinearMap.{u_11, u_14, u_19, u_22} R₃ R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.56 (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65) σ₃₃' M₃ M₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.80 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.89 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.118) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65) (LinearMap.addCommMonoid.{u_9, u_12, u_17, u_20} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.110 σ₁₁') (LinearMap.addCommMonoid.{u_10, u_13, u_18, u_21} R₂ R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.114 σ₂₂') (LinearMap.addCommMonoid.{u_11, u_14, u_19, u_22} R₃ R₃' M₃ M₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.56 (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.80 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.89 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.118 σ₃₃') (LinearMap.module.{u_9, u_12, u_12, u_17, u_20} R₁ R₁' R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.110 σ₁₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.110)))) (LinearMap.module.{u_10, u_13, u_13, u_18, u_21} R₂ R₂' R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.114 σ₂₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.114)))) (LinearMap.module.{u_11, u_14, u_14, u_19, u_22} R₃ R₃' R₃' M₃ M₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.56 (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.80 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.89 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.118 σ₃₃' (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.118 (smulCommClass_self.{u_14, u_22} R₃' M₃' (CommSemiring.toCommMonoid.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65) (DistribMulAction.toMulAction.{u_14, u_22} R₃' M₃' (CommMonoid.toMonoid.{u_14} R₃' (CommSemiring.toCommMonoid.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65)) (AddCommMonoid.toAddMonoid.{u_22} M₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.89) (Module.toDistribMulAction.{u_14, u_22} R₃' M₃' (CommSemiring.toSemiring.{u_14} R₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.89 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.118)))) σ₁'₂' σ₂'₁' σ₁'₃' σ₃'₁' σ₂'₃' σ₃'₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.461 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.466 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.309 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.325 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.297 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.313 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.329 (LinearEquiv.arrowCongr.{u_9, u_10, u_12, u_13, u_17, u_18, u_20, u_21} R₁ R₂ R₁' R₂' M₁ M₂ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.59 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.62 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.114 σ₁₂ σ₂₁ σ₁'₂' σ₂'₁' σ₁₁' σ₂₂' σ₂₁' σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.285 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.289 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.297 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.351 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.356 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.361 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.366 e₁ e₁') (LinearEquiv.arrowCongr.{u_10, u_11, u_13, u_14, u_18, u_19, u_21, u_22} R₂ R₃ R₂' R₃' M₂ M₃ M₂' M₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.56 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.62 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.65 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.80 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.89 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.118 σ₂₃ σ₃₂ σ₂'₃' σ₃'₂' σ₂₂' σ₃₃' σ₃₂' σ₂₃' inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.301 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.305 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.309 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.313 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.391 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.396 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.56 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.80 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.106 σ₁₂ σ₂₁ σ₁₃ σ₃₁ σ₂₃ σ₃₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.451 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.456 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.285 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.301 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.317 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1251365987._hygCtx._hyg.289 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⋯","typeReferences":[["smulCommClass_self"],["RingHom"],["CommMonoid","toMonoid"],["Module"],["LinearMap","module"],["CommSemiring"],["CommSemiring","toSemiring"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["LinearMap"],["LinearEquiv","arrowCongr"],["CommSemiring","toCommMonoid"],["RingHomCompTriple"],["LinearMap","addCommMonoid"],["LinearEquiv","trans"],["Module","toDistribMulAction"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["DistribMulAction","toMulAction"],["RingHomInvPair"],["Eq"],["Semiring"]],"valueReferences":[["rfl"],["smulCommClass_self"],["CommMonoid","toMonoid"],["CommSemiring","toSemiring"],["LinearMap","module"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["LinearMap"],["LinearEquiv","arrowCongr"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["LinearEquiv","trans"],["Module","toDistribMulAction"],["DistribMulAction","toMulAction"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","arrowCongrAddEquiv","eq_1"],"typeFallback":"forall {R₁ : Type.{u_9}} {R₂ : Type.{u_10}} {R₁' : Type.{u_11}} {R₂' : Type.{u_12}} {M₁ : Type.{u_13}} {M₂ : Type.{u_14}} {M₁' : Type.{u_15}} {M₂' : Type.{u_16}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 : Semiring.{u_9} R₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 : Semiring.{u_10} R₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 : Semiring.{u_11} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 : Semiring.{u_12} R₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 : AddCommMonoid.{u_13} M₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 : AddCommMonoid.{u_14} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 : AddCommMonoid.{u_15} M₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 : AddCommMonoid.{u_16} M₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 : Module.{u_9, u_13} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 : Module.{u_10, u_14} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 : Module.{u_11, u_15} R₁' M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 : Module.{u_12, u_16} R₂' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39] {σ₁₂ : RingHom.{u_9, u_10} R₁ R₂ (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21)} {σ₂₁ : RingHom.{u_10, u_9} R₂ R₁ (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21) (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18)} {σ₁'₂' : RingHom.{u_11, u_12} R₁' R₂' (Semiring.toNonAssocSemiring.{u_11} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24) (Semiring.toNonAssocSemiring.{u_12} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27)} {σ₂'₁' : RingHom.{u_12, u_11} R₂' R₁' (Semiring.toNonAssocSemiring.{u_12} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27) (Semiring.toNonAssocSemiring.{u_11} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24)} {σ₁₁' : RingHom.{u_9, u_11} R₁ R₁' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_11} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24)} {σ₂₂' : RingHom.{u_10, u_12} R₂ R₂' (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21) (Semiring.toNonAssocSemiring.{u_12} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27)} {σ₂₁' : RingHom.{u_10, u_11} R₂ R₁' (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21) (Semiring.toNonAssocSemiring.{u_11} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24)} {σ₁₂' : RingHom.{u_9, u_12} R₁ R₂' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18) (Semiring.toNonAssocSemiring.{u_12} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27)} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 : RingHomInvPair.{u_9, u_10} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 σ₁₂ σ₂₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 : RingHomInvPair.{u_10, u_9} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 σ₂₁ σ₁₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 : RingHomInvPair.{u_11, u_12} R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₁'₂' σ₂'₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 : RingHomInvPair.{u_12, u_11} R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₂'₁' σ₁'₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.114 : RingHomCompTriple.{u_9, u_11, u_12} R₁ R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₁₁' σ₁'₂' σ₁₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.119 : RingHomCompTriple.{u_10, u_9, u_12} R₂ R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₂₁ σ₁₂' σ₂₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.124 : RingHomCompTriple.{u_10, u_12, u_11} R₂ R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₂₂' σ₂'₁' σ₂₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.129 : RingHomCompTriple.{u_9, u_10, u_11} R₁ R₂ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₂ σ₂₁' σ₁₁'] (e₁ : LinearEquiv.{u_9, u_10, u_13, u_14} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46) (e₂ : LinearEquiv.{u_11, u_12, u_15, u_16} R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54), Eq.{max (succ (max u_16 u_14)) (succ (max u_15 u_13))} (AddEquiv.{max u_15 u_13, max u_16 u_14} (LinearMap.{u_9, u_11, u_13, u_15} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50) (LinearMap.{u_10, u_12, u_14, u_16} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54) (LinearMap.instAdd.{u_9, u_11, u_13, u_15} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 σ₁₁') (LinearMap.instAdd.{u_10, u_12, u_14, u_16} R₂ R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 σ₂₂')) (LinearEquiv.arrowCongrAddEquiv.{u_9, u_10, u_11, u_12, u_13, u_14, u_15, u_16} R₁ R₂ R₁' R₂' M₁ M₂ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 σ₁₂ σ₂₁ σ₁'₂' σ₂'₁' σ₁₁' σ₂₂' σ₂₁' σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.119 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.124 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.129 e₁ e₂) (AddEquiv.mk.{max u_13 u_15, max u_14 u_16} (LinearMap.{u_9, u_11, u_13, u_15} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50) (LinearMap.{u_10, u_12, u_14, u_16} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54) (LinearMap.instAdd.{u_9, u_11, u_13, u_15} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 σ₁₁') (LinearMap.instAdd.{u_10, u_12, u_14, u_16} R��� R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 σ₂₂') (Equiv.mk.{succ (max u_13 u_15), succ (max u_14 u_16)} (LinearMap.{u_9, u_11, u_13, u_15} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50) (LinearMap.{u_10, u_12, u_14, u_16} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54) (fun (f : LinearMap.{u_9, u_11, u_13, u_15} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50) => LinearMap.comp.{u_10, u_9, u_12, u_14, u_13, u_16} R₂ R₁ R₂' M₂ M₁ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 σ₂₁ σ₁₂' σ₂₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.119 (LinearMap.comp.{u_9, u_11, u_12, u_13, u_15, u_16} R₁ R₁' R₂' M₁ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 σ₁₁' σ₁'₂' σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.114 (LinearEquiv.toLinearMap.{u_11, u_12, u_15, u_16} R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 e₂) f) (LinearEquiv.toLinearMap.{u_10, u_9, u_14, u_13} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 σ₂₁ σ₁₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 M₂ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 (LinearEquiv.symm.{u_9, u_10, u_13, u_14} R₁ R₂ M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 e₁))) (fun (f : LinearMap.{u_10, u_12, u_14, u_16} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54) => LinearMap.comp.{u_9, u_10, u_11, u_13, u_14, u_15} R₁ R₂ R₁' M₁ M₂ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 σ₁₂ σ₂₁' σ₁₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.129 (LinearMap.comp.{u_10, u_12, u_11, u_14, u_16, u_15} R₂ R₂' R₁' M₂ M₂' M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 σ₂₂' σ₂'₁' σ₂₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.124 (LinearEquiv.toLinearMap.{u_12, u_11, u_16, u_15} R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₂'₁' σ₁'₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 M₂' M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 (LinearEquiv.symm.{u_11, u_12, u_15, u_16} R₁' R₂' M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 e₂)) f) (LinearEquiv.toLinearMap.{u_9, u_10, u_13, u_14} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 e₁)) (fun (f : LinearMap.{u_9, u_11, u_13, u_15} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50) => LinearEquiv.arrowCongrAddEquiv._proof_1.{u_13, u_15, u_9, u_11, u_10, u_12, u_14, u_16} R₁ R₂ R₁' R₂' M₁ M₂ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 σ₁₂ σ₂₁ σ₁'₂' σ₂'₁' σ₁₁' σ₂₂' σ₂₁' σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.119 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.124 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.129 e₁ e₂ f) (fun (f : LinearMap.{u_10, u_12, u_14, u_16} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54) => LinearEquiv.arrowCongrAddEquiv._proof_2.{u_14, u_16, u_10, u_12, u_9, u_11, u_13, u_15} R₁ R₂ R₁' R₂' M₁ M₂ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 σ₁₂ σ₂₁ σ₁'₂' σ₂'₁' σ₁₁' σ₂₂' σ₂₁' σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.119 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.124 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.129 e₁ e₂ f)) (fun (f : LinearMap.{u_9, u_11, u_13, u_15} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50) (g : LinearMap.{u_9, u_11, u_13, u_15} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50) => LinearEquiv.arrowCongrAddEquiv._proof_3.{u_14, u_16, u_10, u_12, u_9, u_13, u_11, u_15} R₁ R₂ R₁' R₂' M₁ M₂ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.24 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.27 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.33 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.36 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.46 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.54 σ₁₂ σ₂₁ σ₁'₂' σ₂'₁' σ₁₁' σ₂₂' σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.106 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4284637387._hygCtx._hyg.119 e₁ e₂ f g))","typeFull":"∀ {R₁ : Type u_9} {R₂ : Type u_10} {R₁' : Type u_11} {R₂' : Type u_12} {M₁ : Type u_13} {M₂ : Type u_14}\n  {M₁' : Type u_15} {M₂' : Type u_16} [inst : Semiring R₁] [inst_1 : Semiring R₂] [inst_2 : Semiring R₁']\n  [inst_3 : Semiring R₂'] [inst_4 : AddCommMonoid M₁] [inst_5 : AddCommMonoid M₂] [inst_6 : AddCommMonoid M₁']\n  [inst_7 : AddCommMonoid M₂'] [inst_8 : Module R₁ M₁] [inst_9 : Module R₂ M₂] [inst_10 : Module R₁' M₁']\n  [inst_11 : Module R₂' M₂'] {σ₁₂ : R₁ →+* R₂} {σ₂₁ : R₂ →+* R₁} {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'}\n  {σ₁₁' : R₁ →+* R₁'} {σ₂₂' : R₂ →+* R₂'} {σ₂₁' : R₂ →+* R₁'} {σ₁₂' : R₁ →+* R₂'} [inst_12 : RingHomInvPair σ₁₂ σ₂₁]\n  [inst_13 : RingHomInvPair σ₂₁ σ₁₂] [inst_14 : RingHomInvPair σ₁'₂' σ₂'₁'] [inst_15 : RingHomInvPair σ₂'₁' σ₁'₂']\n  [inst_16 : RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_17 : RingHomCompTriple σ₂₁ σ₁₂' σ₂₂']\n  [inst_18 : RingHomCompTriple σ₂₂' σ₂'₁' σ₂₁'] [inst_19 : RingHomCompTriple σ₁₂ σ₂₁' σ₁₁'] (e₁ : M₁ ≃ₛₗ[σ₁₂] M₂)\n  (e₂ : M₁' ≃ₛₗ[σ₁'₂'] M₂'),\n  e₁.arrowCongrAddEquiv e₂ =\n    { toFun := fun f => (↑e₂ ∘ₛₗ f) ∘ₛₗ ↑e₁.symm, invFun := fun f => (↑e₂.symm ∘ₛₗ f) ∘ₛₗ ↑e₁, left_inv := ⋯,\n      right_inv := ⋯, map_add' := ⋯ }","typeReadable":"∀ {R₁ : Type u_9} {R₂ : Type u_10} {R₁' : Type u_11} {R₂' : Type u_12} {M₁ : Type u_13} {M₂ : Type u_14}\n  {M₁' : Type u_15} {M₂' : Type u_16} [inst : Semiring R₁] [inst_1 : Semiring R₂] [inst_2 : Semiring R₁']\n  [inst_3 : Semiring R₂'] [inst_4 : AddCommMonoid M₁] [inst_5 : AddCommMonoid M₂] [inst_6 : AddCommMonoid M₁']\n  [inst_7 : AddCommMonoid M₂'] [inst_8 : Module R₁ M₁] [inst_9 : Module R₂ M₂] [inst_10 : Module R₁' M₁']\n  [inst_11 : Module R₂' M₂'] {σ₁₂ : R₁ →+* R₂} {σ₂₁ : R₂ →+* R₁} {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'}\n  {σ₁₁' : R₁ →+* R₁'} {σ₂₂' : R₂ →+* R₂'} {σ₂₁' : R₂ →+* R₁'} {σ₁₂' : R₁ →+* R₂'} [inst_12 : RingHomInvPair σ₁₂ σ₂₁]\n  [inst_13 : RingHomInvPair σ₂₁ σ₁₂] [inst_14 : RingHomInvPair σ₁'₂' σ₂'₁'] [inst_15 : RingHomInvPair σ₂'₁' σ₁'₂']\n  [inst_16 : RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_17 : RingHomCompTriple σ₂₁ σ₁₂' σ₂₂']\n  [inst_18 : RingHomCompTriple σ₂₂' σ₂'₁' σ₂₁'] [inst_19 : RingHomCompTriple σ₁₂ σ₂₁' σ₁₁'] (e₁ : M₁ ≃ₛₗ[σ₁₂] M₂)\n  (e₂ : M₁' ≃ₛₗ[σ₁'₂'] M₂'),\n  e₁.arrowCongrAddEquiv e₂ =\n    { toFun := fun f => (↑e₂ ∘ₛₗ f) ∘ₛₗ ↑e₁.symm, invFun := fun f => (↑e₂.symm ∘ₛₗ f) ∘ₛₗ ↑e₁, left_inv := ⋯,\n      right_inv := ⋯, map_add' := ⋯ }","typeReferences":[["RingHom"],["AddEquiv","mk"],["LinearEquiv","arrowCongrAddEquiv","_proof_2"],["Equiv","mk"],["Module"],["LinearMap","comp"],["LinearEquiv","toLinearMap"],["LinearEquiv"],["LinearMap"],["LinearEquiv","symm"],["AddEquiv"],["LinearEquiv","arrowCongrAddEquiv","_proof_1"],["RingHomCompTriple"],["LinearEquiv","arrowCongrAddEquiv","_proof_3"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["LinearEquiv","arrowCongrAddEquiv"],["LinearMap","instAdd"],["RingHomInvPair"],["Eq"],["Semiring"]],"valueReferences":[["LinearEquiv","arrowCongrAddEquiv"],["Eq","refl"],["LinearMap","instAdd"],["LinearMap"],["AddEquiv"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","piUnique","_proof_4"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1979755013._hygCtx._hyg.11 : Unique.{succ u_1} α] (f : α -> Type.{u_2}), Function.RightInverse.{max (succ u_1) (succ u_2), succ u_2} (forall (i : α), f i) (f (Inhabited.default.{succ u_1} α (Unique.instInhabited.{succ u_1} α inst._@.Mathlib.Algebra.Module.Equiv.Basic.1979755013._hygCtx._hyg.11))) (Equiv.invFun.{max (succ u_1) (succ u_2), succ u_2} (forall (i : α), f i) (f (Inhabited.default.{succ u_1} α (Unique.instInhabited.{succ u_1} α inst._@.Mathlib.Algebra.Module.Equiv.Basic.1979755013._hygCtx._hyg.11))) (Equiv.piUnique.{succ u_1, succ u_2} α inst._@.Mathlib.Algebra.Module.Equiv.Basic.1979755013._hygCtx._hyg.11 f)) (Equiv.toFun.{max (succ u_1) (succ u_2), succ u_2} (forall (i : α), f i) (f (Inhabited.default.{succ u_1} α (Unique.instInhabited.{succ u_1} α inst._@.Mathlib.Algebra.Module.Equiv.Basic.1979755013._hygCtx._hyg.11))) (Equiv.piUnique.{succ u_1, succ u_2} α inst._@.Mathlib.Algebra.Module.Equiv.Basic.1979755013._hygCtx._hyg.11 f))","typeFull":"∀ {α : Type u_1} [inst : Unique α] (f : α → Type u_2),\n  Function.RightInverse (Equiv.piUnique f).invFun (Equiv.piUnique f).toFun","typeReadable":"∀ {α : Type u_1} [inst : Unique α] (f : α → Type u_2),\n  Function.RightInverse (Equiv.piUnique f).invFun (Equiv.piUnique f).toFun","typeReferences":[["Equiv","piUnique"],["Unique"],["Function","RightInverse"],["Equiv","invFun"],["Equiv","toFun"],["Unique","instInhabited"],["Inhabited","default"]],"valueReferences":[["Equiv","piUnique"],["Equiv","right_inv"],["Unique","instInhabited"],["Inhabited","default"]]},{"isProp":true,"kind":"theorem","name":["DistribMulAction","toLinearEquiv_symm_apply"],"typeFallback":"forall (R : Type.{u_1}) {S : Type.{u_4}} (M : Type.{u_5}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.16 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.20 : Group.{u_4} S] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.23 : DistribMulAction.{u_4, u_5} S M (DivInvMonoid.toMonoid.{u_4} S (Group.toDivInvMonoid.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.20)) (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13)] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.27 : SMulCommClass.{u_4, u_1, u_5} S R M (SMulZeroClass.toSMul.{u_4, u_5} S M (AddZero.toZero.{u_5} M (AddZeroClass.toAddZero.{u_5} M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u_4, u_5} S M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u_4, 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13) (Module.toDistribMulAction.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.16))))] (s : S) (a._@._internal._hyg.0 : M), Eq.{succ u_5} M (DFunLike.coe.{succ u_5, succ u_5, succ u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.16) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (EquivLike.toFunLike.{succ u_5, succ u_5, succ u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.16) M M (LinearEquiv.instEquivLike.{u_1, u_1, u_5, u_5} R R M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.16 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10))) (LinearEquiv.symm.{u_1, u_1, u_5, u_5} R R M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.16 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10) (DistribMulAction.toLinearEquiv.{u_1, u_4, u_5} R S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.27 s)) a._@._internal._hyg.0) (HSMul.hSMul.{u_4, u_5, u_5} S M M (instHSMul.{u_4, u_5} S M (SemigroupAction.toSMul.{u_4, u_5} S M (Monoid.toSemigroup.{u_4} S (DivInvMonoid.toMonoid.{u_4} S (Group.toDivInvMonoid.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.20))) (MulAction.toSemigroupAction.{u_4, u_5} S M (DivInvMonoid.toMonoid.{u_4} S (Group.toDivInvMonoid.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.20)) (DistribMulAction.toMulAction.{u_4, u_5} S M (DivInvMonoid.toMonoid.{u_4} S (Group.toDivInvMonoid.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.20)) (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.23)))) (Inv.inv.{u_4} S (InvOneClass.toInv.{u_4} S (DivInvOneMonoid.toInvOneClass.{u_4} S (DivisionMonoid.toDivInvOneMonoid.{u_4} S (Group.toDivisionMonoid.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.20)))) s) a._@._internal._hyg.0)","typeFull":"∀ (R : Type u_1) {S : Type u_4} (M : Type u_5) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  [inst_3 : Group S] [inst_4 : DistribMulAction S M] [inst_5 : SMulCommClass S R M] (s : S) (a : M),\n  (DistribMulAction.toLinearEquiv R M s).symm a = s⁻¹ • a","typeReadable":"∀ (R : Type u_1) {S : Type u_4} (M : Type u_5) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n  [inst_3 : Group S] [inst_4 : DistribMulAction S M] [inst_5 : SMulCommClass S R M] (s : S) (a : M),\n  (DistribMulAction.toLinearEquiv R M s).symm a = s⁻¹ • a","typeReferences":[["Module"],["SemigroupAction","toSMul"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["DFunLike","coe"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["EquivLike","toFunLike"],["DistribMulAction","toMulAction"],["instHSMul"],["Monoid","toSemigroup"],["LinearEquiv","instEquivLike"],["Eq"],["Group","toDivInvMonoid"],["DistribMulAction"],["DistribSMul","toSMulZeroClass"],["Group"],["Group","toDivisionMonoid"],["Inv","inv"],["InvOneClass","toInv"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["DistribMulAction","toLinearEquiv"],["AddZeroClass","toAddZero"],["LinearEquiv","symm"],["SMulCommClass"],["Module","toDistribMulAction"],["DivInvOneMonoid","toInvOneClass"],["DivInvMonoid","toMonoid"],["HSMul","hSMul"],["RingHomInvPair","ids"],["MulAction","toSemigroupAction"],["AddZero","toZero"],["DivisionMonoid","toDivInvOneMonoid"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["Semiring","toNonAssocSemiring"],["RingHom","id"],["Eq","refl"],["EquivLike","toFunLike"],["RingHomInvPair","ids"],["DistribMulAction","toLinearEquiv"],["LinearEquiv","instEquivLike"],["LinearEquiv"],["LinearEquiv","symm"],["DFunLike","coe"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","conj_symm_conj"],"typeFallback":"forall {R₁' : Type.{u_12}} {R₂' : Type.{u_13}} {M₁' : Type.{u_20}} {M₂' : Type.{u_21}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59 : CommSemiring.{u_12} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62 : CommSemiring.{u_13} R₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 : AddCommMonoid.{u_20} M₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 : AddCommMonoid.{u_21} M₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 : Module.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 : Module.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86] {σ₁'₂' : RingHom.{u_12, u_13} R₁' R₂' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59)) (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62))} {σ₂'₁' : RingHom.{u_13, u_12} R₂' R₁' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62)) (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59))} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.293 : RingHomInvPair.{u_12, u_13} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) σ₁'₂' σ₂'₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.297 : RingHomInvPair.{u_13, u_12} R₂' R₁' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) σ₂'₁' σ₁'₂'] (e : LinearEquiv.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.297 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114) (f : Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110), Eq.{succ u_20} (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110) (DFunLike.coe.{max (succ u_20) (succ u_21), succ u_21, succ u_20} (LinearEquiv.{u_13, u_12, u_21, u_20} R₂' R₁' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) σ₂'₁' σ₁'₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.297 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.293 (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114) (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62)))) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62))) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114)))) (LinearMap.module.{u_12, u_12, u_12, u_20, u_20} R₁' R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110))))) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114) => Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110) (EquivLike.toFunLike.{max (succ u_20) (succ u_21), succ u_21, succ u_20} (LinearEquiv.{u_13, u_12, u_21, u_20} R₂' R₁' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) σ₂'₁' σ₁'₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.297 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.293 (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114) (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62)))) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62))) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114)))) (LinearMap.module.{u_12, u_12, u_12, u_20, u_20} R₁' R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110))))) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114) (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110) (LinearEquiv.instEquivLike.{u_13, u_12, u_21, u_20} R₂' R₁' (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114) (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62)))) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62))) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114)))) (LinearMap.module.{u_12, u_12, u_12, u_20, u_20} R₁' R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110)))) σ₂'₁' σ₁'₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.297 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.293)) (LinearEquiv.conj.{u_13, u_12, u_21, u_20} R₂' R₁' M₂' M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 σ₂'₁' σ₁'₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.297 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.293 (LinearEquiv.symm.{u_12, u_13, u_20, u_21} R₁' R₂' M₁' M₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.297 e)) (DFunLike.coe.{max (succ u_20) (succ u_21), succ u_20, succ u_21} (LinearEquiv.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.297 (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59)))) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62)))) (LinearMap.module.{u_12, u_12, u_12, u_20, u_20} R₁' R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62))) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114))))) (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110) => Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114) (EquivLike.toFunLike.{max (succ u_20) (succ u_21), succ u_20, succ u_21} (LinearEquiv.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.297 (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59)))) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62)))) (LinearMap.module.{u_12, u_12, u_12, u_20, u_20} R₁' R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62))) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114))))) (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114) (LinearEquiv.instEquivLike.{u_12, u_13, u_20, u_21} R₁' R₂' (Module.End.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110) (Module.End.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) (LinearMap.addCommMonoid.{u_12, u_12, u_20, u_20} R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59)))) (LinearMap.addCommMonoid.{u_13, u_13, u_21, u_21} R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62)))) (LinearMap.module.{u_12, u_12, u_12, u_20, u_20} R₁' R₁' R₁' M₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 (RingHom.id.{u_12} R₁' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59))) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110)))) (LinearMap.module.{u_13, u_13, u_13, u_21, u_21} R₂' R₂' R₂' M₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 (RingHom.id.{u_13} R₂' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62))) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114)))) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.297)) (LinearEquiv.conj.{u_12, u_13, u_20, u_21} R₁' R₂' M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.59 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.62 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.114 σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2098416930._hygCtx._hyg.297 e) f)) f","typeFull":"∀ {R₁' : Type u_12} {R₂' : Type u_13} {M₁' : Type u_20} {M₂' : Type u_21} [inst : CommSemiring R₁']\n  [inst_1 : CommSemiring R₂'] [inst_2 : AddCommMonoid M₁'] [inst_3 : AddCommMonoid M₂'] [inst_4 : Module R₁' M₁']\n  [inst_5 : Module R₂' M₂'] {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} [inst_6 : RingHomInvPair σ₁'₂' σ₂'₁']\n  [inst_7 : RingHomInvPair σ₂'₁' σ₁'₂'] (e : M₁' ≃ₛₗ[σ₁'₂'] M₂') (f : Module.End R₁' M₁'), e.symm.conj (e.conj f) = f","typeReadable":"∀ {R₁' : Type u_12} {R₂' : Type u_13} {M₁' : Type u_20} {M₂' : Type u_21} [inst : CommSemiring R₁']\n  [inst_1 : CommSemiring R₂'] [inst_2 : AddCommMonoid M₁'] [inst_3 : AddCommMonoid M₂'] [inst_4 : Module R₁' M₁']\n  [inst_5 : Module R₂' M₂'] {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'} [inst_6 : RingHomInvPair σ₁'₂' σ₂'₁']\n  [inst_7 : RingHomInvPair σ₂'₁' σ₁'₂'] (e : M₁' ≃ₛₗ[σ₁'₂'] M₂') (f : Module.End R₁' M₁'), e.symm.conj (e.conj f) = f","typeReferences":[["smulCommClass_self"],["RingHom"],["Module","End"],["CommMonoid","toMonoid"],["Module"],["LinearMap","module"],["CommSemiring"],["CommSemiring","toSemiring"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["LinearEquiv","symm"],["DFunLike","coe"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["LinearEquiv","conj"],["Module","toDistribMulAction"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["EquivLike","toFunLike"],["DistribMulAction","toMulAction"],["LinearEquiv","instEquivLike"],["RingHomInvPair"],["Eq"]],"valueReferences":[["smulCommClass_self"],["LinearEquiv","symm_apply_apply"],["CommMonoid","toMonoid"],["LinearMap","instFunLike"],["Eq","trans"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["DFunLike","coe"],["congrArg"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["LinearMap","ext"],["EquivLike","toFunLike"],["DistribMulAction","toMulAction"],["congrFun'"],["LinearEquiv","instEquivLike"],["Eq"],["Module","End"],["True"],["LinearMap","module"],["CommSemiring","toSemiring"],["LinearMap"],["LinearEquiv","symm"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["eq_self"],["Module","toDistribMulAction"],["LinearEquiv","conj"],["of_eq_true"]]},{"isProp":false,"kind":"definition","name":["LinearEquiv","congrRight"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_5}} {M₂ : Type.{u_7}} {M₃ : Type.{u_8}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10 : CommSemiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.13 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.16 : AddCommMonoid.{u_7} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.19 : AddCommMonoid.{u_8} M₃] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.22 : Module.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.26 : Module.{u_1, u_7} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.30 : Module.{u_1, u_8} R M₃ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.19], (LinearEquiv.{u_1, u_1, u_7, u_8} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10))) (RingHomInvPair.ids.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10)) M₂ M₃ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.30) -> (LinearEquiv.{u_1, u_1, max u_7 u_5, max u_8 u_5} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10))) (RingHomInvPair.ids.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10)) (LinearMap.{u_1, u_1, u_5, u_7} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10))) M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.26) (LinearMap.{u_1, u_1, u_5, u_8} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10))) M M₃ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.30) (LinearMap.addCommMonoid.{u_1, u_1, u_5, u_7} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10)))) (LinearMap.addCommMonoid.{u_1, u_1, u_5, u_8} R R M M₃ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.30 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10)))) (LinearMap.module.{u_1, u_1, u_1, u_5, u_7} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.26 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.26 (smulCommClass_self.{u_1, u_7} R M₂ (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_7} R M₂ (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_7} M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.16) (Module.toDistribMulAction.{u_1, u_7} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.26)))) (LinearMap.module.{u_1, u_1, u_1, u_5, u_8} R R R M M₃ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.30 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.30 (smulCommClass_self.{u_1, u_8} R M₃ (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10) (DistribMulAction.toMulAction.{u_1, u_8} R M₃ (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{u_8} M₃ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.19) (Module.toDistribMulAction.{u_1, u_8} R M₃ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1962554192._hygCtx._hyg.30)))))","typeFull":"{R : Type u_1} →\n  {M : Type u_5} →\n    {M₂ : Type u_7} →\n      {M₃ : Type u_8} →\n        [inst : CommSemiring R] →\n          [inst_1 : AddCommMonoid M] →\n            [inst_2 : AddCommMonoid M₂] →\n              [inst_3 : AddCommMonoid M₃] →\n                [inst_4 : Module R M] →\n                  [inst_5 : Module R M₂] → [inst_6 : Module R M₃] → (M₂ ≃ₗ[R] M₃) → (M →ₗ[R] M₂) ≃ₗ[R] M →ₗ[R] M₃","typeReadable":"{R : Type u_1} →\n  {M : Type u_5} →\n    {M₂ : Type u_7} →\n      {M₃ : Type u_8} →\n        [inst : CommSemiring R] →\n          [inst_1 : AddCommMonoid M] →\n            [inst_2 : AddCommMonoid M₂] →\n              [inst_3 : AddCommMonoid M₃] →\n                [inst_4 : Module R M] →\n                  [inst_5 : Module R M₂] → [inst_6 : Module R M₃] → (M₂ ≃ₗ[R] M₃) → (M →ₗ[R] M₂) ≃ₗ[R] M →ₗ[R] M₃","typeReferences":[["smulCommClass_self"],["CommMonoid","toMonoid"],["Module"],["CommSemiring"],["CommSemiring","toSemiring"],["LinearMap","module"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["LinearMap"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["DistribMulAction","toMulAction"],["RingHomInvPair","ids"]],"valueReferences":[["LinearEquiv","congrRight","_proof_2"],["LinearEquiv","congrRight","_proof_1"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["CommSemiring","toSemiring"],["LinearEquiv","arrowCongr"],["LinearEquiv","refl"]]},{"isProp":true,"kind":"theorem","name":["addMonoidHomLequivNat_symm_apply"],"typeFallback":"forall {A : Type.{u_9}} {B : Type.{u_10}} (R : Type.{u_11}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.13 : Semiring.{u_11} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.16 : AddCommMonoid.{u_9} A] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19 : AddCommMonoid.{u_10} B] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.22 : Module.{u_11, u_10} R B inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19] (f : LinearMap.{0, 0, u_9, u_10} Nat Nat Nat.instSemiring Nat.instSemiring (RingHom.id.{0} Nat Nat.instNonAssocSemiring) A B inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19 (AddCommMonoid.toNatModule.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.16) (AddCommMonoid.toNatModule.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19)), Eq.{max (succ u_9) (succ u_10)} (AddMonoidHom.{u_9, u_10} A B (AddZeroClass.toAddZero.{u_9} A (AddMonoid.toAddZeroClass.{u_9} A (AddCommMonoid.toAddMonoid.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.16))) (AddZeroClass.toAddZero.{u_10} B (AddMonoid.toAddZeroClass.{u_10} B (AddCommMonoid.toAddMonoid.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19)))) (DFunLike.coe.{succ (max u_10 u_9), succ (max u_10 u_9), succ (max u_10 u_9)} (LinearEquiv.{u_11, u_11, max u_10 u_9, max u_10 u_9} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.13 (RingHom.id.{u_11} R (Semiring.toNonAssocSemiring.{u_11} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.13)) (RingHom.id.{u_11} R (Semiring.toNonAssocSemiring.{u_11} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.13)) (RingHomInvPair.ids.{u_11} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.13) (RingHomInvPair.ids.{u_11} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.13) 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19 (AddCommMonoid.toNatModule.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.16) (AddCommMonoid.toNatModule.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19) (RingHom.id.{0} Nat Nat.instNonAssocSemiring)) (AddMonoidHom.instAddCommMonoid.{u_9, u_10} A B (AddMonoid.toAddZeroClass.{u_9} A (AddCommMonoid.toAddMonoid.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.16)) inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19) (LinearMap.module.{0, 0, u_11, u_9, u_10} Nat Nat R A B Nat.instSemiring Nat.instSemiring inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19 (AddCommMonoid.toNatModule.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.16) 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[inst_1 : AddCommMonoid M₂] (e : M ≃+ M₂),\n  e.symm.toNatLinearEquiv = e.toNatLinearEquiv.symm","typeReferences":[["AddEquiv","symm"],["LinearEquiv"],["LinearEquiv","symm"],["AddEquiv"],["AddEquiv","toNatLinearEquiv"],["AddCommMonoid"],["Nat"],["Semiring","toNonAssocSemiring"],["AddCommMonoid","toAddCommSemigroup"],["Nat","instSemiring"],["Nat","instNonAssocSemiring"],["RingHom","id"],["RingHomInvPair","ids"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["AddCommMonoid","toNatModule"],["Eq"]],"valueReferences":[["rfl"],["AddEquiv","symm"],["LinearEquiv"],["Nat"],["AddEquiv","toNatLinearEquiv"],["Semiring","toNonAssocSemiring"],["AddCommMonoid","toAddCommSemigroup"],["Nat","instSemiring"],["Nat","instNonAssocSemiring"],["RingHom","id"],["RingHomInvPair","ids"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["AddCommMonoid","toNatModule"]]},{"isProp":true,"kind":"theorem","name":["addMonoidHomLequivNat_apply"],"typeFallback":"forall {A : Type.{u_9}} {B : Type.{u_10}} (R : Type.{u_11}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.13 : Semiring.{u_11} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.16 : AddCommMonoid.{u_9} A] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19 : AddCommMonoid.{u_10} B] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.22 : Module.{u_11, u_10} R B inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19] (f : AddMonoidHom.{u_9, u_10} A B (AddZeroClass.toAddZero.{u_9} A (AddMonoid.toAddZeroClass.{u_9} A (AddCommMonoid.toAddMonoid.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.16))) (AddZeroClass.toAddZero.{u_10} B (AddMonoid.toAddZeroClass.{u_10} B (AddCommMonoid.toAddMonoid.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19)))), Eq.{max (succ u_9) (succ u_10)} (LinearMap.{0, 0, u_9, 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(DistribMulAction.toDistribSMul.{u_11, u_10} R B (MonoidWithZero.toMonoid.{u_11} R (Semiring.toMonoidWithZero.{u_11} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.13)) (AddCommMonoid.toAddMonoid.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19) (Module.toDistribMulAction.{u_11, u_10} R B inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.22))))) (AddMonoidHom.{u_9, u_10} A B (AddZeroClass.toAddZero.{u_9} A (AddMonoid.toAddZeroClass.{u_9} A (AddCommMonoid.toAddMonoid.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.16))) (AddZeroClass.toAddZero.{u_10} B (AddMonoid.toAddZeroClass.{u_10} B (AddCommMonoid.toAddMonoid.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19)))) (fun 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19 (AddCommMonoid.toNatModule.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.16) (AddCommMonoid.toNatModule.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19) (RingHom.id.{0} Nat Nat.instNonAssocSemiring)) (AddMonoidHom.instModule.{u_11, u_9, u_10} R A B inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.13 (AddCommMonoid.toAddMonoid.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.22) (LinearMap.module.{0, 0, u_11, u_9, u_10} Nat Nat R A B Nat.instSemiring Nat.instSemiring inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19 (AddCommMonoid.toNatModule.{u_9} A 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.22))))) (AddMonoidHom.{u_9, u_10} A B (AddZeroClass.toAddZero.{u_9} A (AddMonoid.toAddZeroClass.{u_9} A (AddCommMonoid.toAddMonoid.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.16))) (AddZeroClass.toAddZero.{u_10} B (AddMonoid.toAddZeroClass.{u_10} B (AddCommMonoid.toAddMonoid.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19)))) (LinearMap.{0, 0, u_9, u_10} Nat Nat Nat.instSemiring Nat.instSemiring (RingHom.id.{0} Nat Nat.instNonAssocSemiring) A B inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19 (AddCommMonoid.toNatModule.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.16) (AddCommMonoid.toNatModule.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19)) (LinearEquiv.instEquivLike.{u_11, u_11, max u_10 u_9, max u_10 u_9} 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(AddMonoidHom.instAddCommMonoid.{u_9, u_10} A B (AddMonoid.toAddZeroClass.{u_9} A (AddCommMonoid.toAddMonoid.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.16)) inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19) (LinearMap.addCommMonoid.{0, 0, u_9, u_10} Nat Nat A B Nat.instSemiring Nat.instSemiring inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19 (AddCommMonoid.toNatModule.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.16) (AddCommMonoid.toNatModule.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.19) (RingHom.id.{0} Nat Nat.instNonAssocSemiring)) (AddMonoidHom.instModule.{u_11, u_9, u_10} R A B inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.13 (AddCommMonoid.toAddMonoid.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.4208518450._hygCtx._hyg.16) 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→ₛₗ[σ₂₁] M) {h₁ : f ∘ₛₗ g = LinearMap.id} {h₂ : g ∘ₛₗ f = LinearMap.id}, ↑(LinearEquiv.ofLinear f g h₁ h₂) = f","typeReadable":"∀ {R : Type u_1} {R₂ : Type u_2} {M : Type u_5} {M₂ : Type u_7} [inst : Semiring R] [inst_1 : Semiring R₂]\n  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] {module_M : Module R M} {module_M₂ : Module R₂ M₂}\n  {σ₁₂ : R →+* R₂} {σ₂₁ : R₂ →+* R} {re₁₂ : RingHomInvPair σ₁₂ σ₂₁} {re₂₁ : RingHomInvPair σ₂₁ σ₁₂} (f : M →ₛₗ[σ₁₂] M₂)\n  (g : M₂ →ₛₗ[σ₂₁] M) {h₁ : f ∘ₛₗ g = LinearMap.id} {h₂ : g ∘ₛₗ f = LinearMap.id}, ↑(LinearEquiv.ofLinear f g h₁ h₂) = 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.18) (DivInvMonoid.toMonoid.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.18) (Group.toDivInvMonoid.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.18) (LinearEquiv.automorphismGroup.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.18)))))) (Units.mulLeftLinearEquiv.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.15 inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.22) u)) (LinearMap.mulLeft.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.12 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.15)) inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.22 (Units.val.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.38275726._hygCtx._hyg.15)) u))","typeFull":"∀ {R : Type u_9} {A : Type u_10} [inst : Semiring R] [inst_1 : Semiring A] [inst_2 : Module R A]\n  [inst_3 : SMulCommClass R A A] (u : Aˣ), ↑((Units.mulLeftLinearEquiv R A) u) = LinearMap.mulLeft R ↑u","typeReadable":"∀ {R : Type u_9} {A : Type u_10} [inst : Semiring R] [inst_1 : Semiring A] [inst_2 : Module R A]\n  [inst_3 : SMulCommClass R A A] (u : Aˣ), ↑((Units.mulLeftLinearEquiv R A) u) = LinearMap.mulLeft R ↑u","typeReferences":[["MulOneClass","toMulOne"],["Module"],["MonoidHom"],["MonoidHom","instFunLike"],["SMulZeroClass","toSMul"],["LinearEquiv"],["AddMonoidWithOne","toAddMonoid"],["instDistribSMul"],["DFunLike","coe"],["LinearEquiv","automorphismGroup"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Monoid","toMulOneClass"],["MonoidWithZero","toMonoid"],["Units","mulLeftLinearEquiv"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["LinearMap","mulLeft"],["Eq"],["Group","toDivInvMonoid"],["NonAssocSemiring","toAddCommMonoidWithOne"],["Units"],["DistribSMul","toSMulZeroClass"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["Units","instMulOneClass"],["LinearEquiv","toLinearMap"],["AddZeroClass","toAddZero"],["LinearMap"],["SMulCommClass"],["Module","toDistribMulAction"],["DivInvMonoid","toMonoid"],["Units","val"],["RingHomInvPair","ids"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["MulOneClass","toMulOne"],["rfl"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["MonoidHom"],["MonoidHom","instFunLike"],["Semiring","toMonoidWithZero"],["Units","instMulOneClass"],["LinearEquiv","toLinearMap"],["LinearEquiv"],["LinearMap"],["DFunLike","coe"],["LinearEquiv","automorphismGroup"],["Semiring","toNonAssocSemiring"],["DivInvMonoid","toMonoid"],["RingHom","id"],["Monoid","toMulOneClass"],["MonoidWithZero","toMonoid"],["RingHomInvPair","ids"],["Units","mulLeftLinearEquiv"],["Group","toDivInvMonoid"],["Units"]]},{"isProp":true,"kind":"theorem","name":["DistribMulAction","toLinearEquiv","_proof_1"],"typeFallback":"forall {S : Type.{u_2}} (M : Type.{u_1}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13 : AddCommMonoid.{u_1} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.20 : Group.{u_2} S] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.23 : DistribMulAction.{u_2, u_1} S M (DivInvMonoid.toMonoid.{u_2} S (Group.toDivInvMonoid.{u_2} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.20)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13)] (s : S) (x : M) (y : M), Eq.{succ u_1} M (Equiv.toFun.{succ u_1, succ u_1} M M (AddEquiv.toEquiv.{u_1, u_1} M M (AddSemigroup.toAdd.{u_1} M (AddMonoid.toAddSemigroup.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13))) (AddSemigroup.toAdd.{u_1} M (AddMonoid.toAddSemigroup.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13))) (DistribMulAction.toAddEquiv.{u_2, u_1} S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.20 (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.23 s)) (HAdd.hAdd.{u_1, u_1, u_1} M M M (instHAdd.{u_1} M (AddSemigroup.toAdd.{u_1} M (AddMonoid.toAddSemigroup.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13)))) x y)) (HAdd.hAdd.{u_1, u_1, u_1} M M M (instHAdd.{u_1} M (AddSemigroup.toAdd.{u_1} M (AddMonoid.toAddSemigroup.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13)))) (Equiv.toFun.{succ u_1, succ u_1} M M (AddEquiv.toEquiv.{u_1, u_1} M M (AddSemigroup.toAdd.{u_1} M (AddMonoid.toAddSemigroup.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13))) (AddSemigroup.toAdd.{u_1} M (AddMonoid.toAddSemigroup.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13))) (DistribMulAction.toAddEquiv.{u_2, u_1} S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.20 (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.23 s)) x) (Equiv.toFun.{succ u_1, succ u_1} M M (AddEquiv.toEquiv.{u_1, u_1} M M (AddSemigroup.toAdd.{u_1} M (AddMonoid.toAddSemigroup.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13))) (AddSemigroup.toAdd.{u_1} M (AddMonoid.toAddSemigroup.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13))) (DistribMulAction.toAddEquiv.{u_2, u_1} S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.20 (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.23 s)) y))","typeFull":"∀ {S : Type u_2} (M : Type u_1) [inst : AddCommMonoid M] [inst_1 : Group S] [inst_2 : DistribMulAction S M] (s : S)\n  (x y : M),\n  (DistribMulAction.toAddEquiv M s).toFun (x + y) =\n    (DistribMulAction.toAddEquiv M s).toFun x + (DistribMulAction.toAddEquiv M s).toFun y","typeReadable":"∀ {S : Type u_2} (M : Type u_1) [inst : AddCommMonoid M] [inst_1 : Group S] [inst_2 : DistribMulAction S M] (s : S)\n  (x y : M),\n  (DistribMulAction.toAddEquiv M s).toFun (x + y) =\n    (DistribMulAction.toAddEquiv M s).toFun x + (DistribMulAction.toAddEquiv M s).toFun y","typeReferences":[["Group"],["instHAdd"],["AddCommMonoid","toAddMonoid"],["AddEquiv","toEquiv"],["HAdd","hAdd"],["AddCommMonoid"],["DistribMulAction","toAddEquiv"],["DivInvMonoid","toMonoid"],["AddMonoid","toAddSemigroup"],["Equiv","toFun"],["Eq"],["Group","toDivInvMonoid"],["DistribMulAction"],["AddSemigroup","toAdd"]],"valueReferences":[["DistribMulAction","toAddEquiv"],["AddMonoid","toAddSemigroup"],["AddCommMonoid","toAddMonoid"],["AddEquiv","map_add'"],["AddSemigroup","toAdd"]]},{"isProp":true,"kind":"theorem","name":["Module","compHom","toLinearEquiv","_proof_1"],"typeFallback":"forall {R : Type.{u_2}} {S : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.12 : Semiring.{u_2} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.15 : Semiring.{u_1} S], RingHomClass.{max u_1 u_2, u_2, u_1} (RingEquiv.{u_2, u_1} R S (Distrib.toMul.{u_2} R (NonUnitalNonAssocSemiring.toDistrib.{u_2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.12)))) (Distrib.toMul.{u_1} S (NonUnitalNonAssocSemiring.toDistrib.{u_1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} S (Semiring.toNonAssocSemiring.{u_1} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.15)))) (Distrib.toAdd.{u_2} R (NonUnitalNonAssocSemiring.toDistrib.{u_2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.12)))) (Distrib.toAdd.{u_1} S (NonUnitalNonAssocSemiring.toDistrib.{u_1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} S (Semiring.toNonAssocSemiring.{u_1} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.15))))) R S (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.12) (Semiring.toNonAssocSemiring.{u_1} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.15) (EquivLike.toFunLike.{succ (max u_1 u_2), succ u_2, succ u_1} (RingEquiv.{u_2, u_1} R S (Distrib.toMul.{u_2} R (NonUnitalNonAssocSemiring.toDistrib.{u_2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.12)))) (Distrib.toMul.{u_1} S (NonUnitalNonAssocSemiring.toDistrib.{u_1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} S (Semiring.toNonAssocSemiring.{u_1} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.15)))) (Distrib.toAdd.{u_2} R (NonUnitalNonAssocSemiring.toDistrib.{u_2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.12)))) (Distrib.toAdd.{u_1} S (NonUnitalNonAssocSemiring.toDistrib.{u_1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} S (Semiring.toNonAssocSemiring.{u_1} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.15))))) R S (RingEquiv.instEquivLike.{u_2, u_1} R S (Distrib.toMul.{u_2} R (NonUnitalNonAssocSemiring.toDistrib.{u_2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.12)))) (Distrib.toMul.{u_1} S (NonUnitalNonAssocSemiring.toDistrib.{u_1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} S (Semiring.toNonAssocSemiring.{u_1} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.15)))) (Distrib.toAdd.{u_2} R (NonUnitalNonAssocSemiring.toDistrib.{u_2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.12)))) (Distrib.toAdd.{u_1} S (NonUnitalNonAssocSemiring.toDistrib.{u_1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} S (Semiring.toNonAssocSemiring.{u_1} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.15))))))","typeFull":"∀ {R : Type u_2} {S : Type u_1} [inst : Semiring R] [inst_1 : Semiring S], RingHomClass (R ≃+* S) R S","typeReadable":"∀ {R : Type u_2} {S : Type u_1} [inst : Semiring R] [inst_1 : Semiring S], RingHomClass (R ≃+* S) R S","typeReferences":[["Distrib","toAdd"],["Semiring","toNonAssocSemiring"],["NonUnitalNonAssocSemiring","toDistrib"],["RingEquiv","instEquivLike"],["EquivLike","toFunLike"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["Distrib","toMul"],["RingEquiv"],["RingHomClass"],["Semiring"]],"valueReferences":[["Distrib","toAdd"],["Semiring","toNonAssocSemiring"],["NonUnitalNonAssocSemiring","toDistrib"],["RingEquivClass","toRingHomClass"],["RingEquiv","instRingEquivClass"],["RingEquiv","instEquivLike"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["Distrib","toMul"],["RingEquiv"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","funCongrLeft","_proof_4"],"typeFallback":"forall (R : Type.{u_3}) (M : Type.{u_2}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4032173342._hygCtx._hyg.10 : Semiring.{u_3} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4032173342._hygCtx._hyg.13 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4032173342._hygCtx._hyg.16 : 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.25), Eq.{succ u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.25) (HMul.hMul.{u_5, u_5, u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10) M M 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.25) (MulOne.toMul.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.19 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.25) (DivInvMonoid.toMonoid.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.25) (Group.toDivInvMonoid.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.25) (LinearEquiv.automorphismGroup.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.25))))))) f g) (LinearEquiv.trans.{u_1, u_1, u_1, u_5, u_5, u_5} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1579910002._hygCtx._hyg.25 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Module S M] [inst_5 : SMulCommClass R S M] (m : S) (x : R →ₗ[R] M),\n  ((LinearMap.applyₗ' S) 1).toFun (m • x) = (RingHom.id S) m • ((LinearMap.applyₗ' S) 1).toFun x","typeReferences":[["RingHom"],["Module"],["RingHom","instFunLike"],["LinearMap","toAddHom"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["AddMonoidHom"],["MonoidWithZero","toMonoid"],["instHSMul"],["AddMonoidHom","instFunLike"],["AddHom","toFun"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Semiring","toModule"],["Eq"],["NonAssocSemiring","toAddCommMonoidWithOne"],["DistribSMul","toSMulZeroClass"],["LinearMap","applyₗ'"],["LinearMap","module"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["LinearMap"],["OfNat","ofNat"],["LinearMap","addCommMonoid"],["SMulCommClass"],["Module","toDistribMulAction"],["One","toOfNat1"],["AddCommMonoid","toAddCommSemigroup"],["HSMul","hSMul"],["AddMonoidWithOne","toOne"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["LinearMap","applyₗ'"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["LinearMap","module"],["AddCommMonoid","toAddMonoid"],["LinearMap"],["AddZeroClass","toAddZero"],["DFunLike","coe"],["OfNat","ofNat"],["LinearMap","addCommMonoid"],["Semiring","toNonAssocSemiring"],["One","toOfNat1"],["RingHom","id"],["AddMonoidHom"],["AddMonoidWithOne","toOne"],["AddMonoidHom","instFunLike"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["LinearMap","map_smul'"],["Semiring","toModule"],["NonAssocSemiring","toAddCommMonoidWithOne"],["AddMonoid","toAddZeroClass"]]},{"isProp":false,"kind":"definition","name":["Module","compHom","toLinearEquiv"],"typeFallback":"forall {R : Type.{u_9}} {S : Type.{u_10}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.12 : Semiring.{u_9} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.15 : Semiring.{u_10} S] (g : RingEquiv.{u_9, u_10} R S (Distrib.toMul.{u_9} R (NonUnitalNonAssocSemiring.toDistrib.{u_9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.12)))) (Distrib.toMul.{u_10} S (NonUnitalNonAssocSemiring.toDistrib.{u_10} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} S (Semiring.toNonAssocSemiring.{u_10} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.15)))) (Distrib.toAdd.{u_9} R (NonUnitalNonAssocSemiring.toDistrib.{u_9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.12)))) (Distrib.toAdd.{u_10} S 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(NonUnitalNonAssocSemiring.toDistrib.{u_9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.12)))) (Distrib.toMul.{u_10} S (NonUnitalNonAssocSemiring.toDistrib.{u_10} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} S (Semiring.toNonAssocSemiring.{u_10} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.15)))) (Distrib.toAdd.{u_9} R (NonUnitalNonAssocSemiring.toDistrib.{u_9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.12)))) (Distrib.toAdd.{u_10} S (NonUnitalNonAssocSemiring.toDistrib.{u_10} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} S (Semiring.toNonAssocSemiring.{u_10} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.15))))) R S (EquivLike.toFunLike.{max (succ u_10) (succ u_9), succ u_9, succ u_10} 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(RingEquiv.instEquivLike.{u_9, u_10} R S (Distrib.toMul.{u_9} R (NonUnitalNonAssocSemiring.toDistrib.{u_9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.12)))) (Distrib.toMul.{u_10} S (NonUnitalNonAssocSemiring.toDistrib.{u_10} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} S (Semiring.toNonAssocSemiring.{u_10} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.15)))) (Distrib.toAdd.{u_9} R (NonUnitalNonAssocSemiring.toDistrib.{u_9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.12)))) (Distrib.toAdd.{u_10} S (NonUnitalNonAssocSemiring.toDistrib.{u_10} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} S (Semiring.toNonAssocSemiring.{u_10} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.15)))))) (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.12) (Semiring.toNonAssocSemiring.{u_10} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.15) (RingEquivClass.toRingHomClass.{max u_10 u_9, u_9, u_10} (RingEquiv.{u_9, u_10} R S (Distrib.toMul.{u_9} R (NonUnitalNonAssocSemiring.toDistrib.{u_9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.12)))) (Distrib.toMul.{u_10} S (NonUnitalNonAssocSemiring.toDistrib.{u_10} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} S (Semiring.toNonAssocSemiring.{u_10} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.15)))) (Distrib.toAdd.{u_9} R (NonUnitalNonAssocSemiring.toDistrib.{u_9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.12)))) (Distrib.toAdd.{u_10} S (NonUnitalNonAssocSemiring.toDistrib.{u_10} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} S (Semiring.toNonAssocSemiring.{u_10} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.15))))) R S (RingEquiv.instEquivLike.{u_9, u_10} R S (Distrib.toMul.{u_9} R (NonUnitalNonAssocSemiring.toDistrib.{u_9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.12)))) (Distrib.toMul.{u_10} S (NonUnitalNonAssocSemiring.toDistrib.{u_10} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} S (Semiring.toNonAssocSemiring.{u_10} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.15)))) (Distrib.toAdd.{u_9} R (NonUnitalNonAssocSemiring.toDistrib.{u_9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.12)))) (Distrib.toAdd.{u_10} S (NonUnitalNonAssocSemiring.toDistrib.{u_10} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} S (Semiring.toNonAssocSemiring.{u_10} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.15))))) (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.12) (Semiring.toNonAssocSemiring.{u_10} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.15) (RingEquiv.instRingEquivClass.{u_9, u_10} R S (Distrib.toMul.{u_9} R (NonUnitalNonAssocSemiring.toDistrib.{u_9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.12)))) (Distrib.toMul.{u_10} S (NonUnitalNonAssocSemiring.toDistrib.{u_10} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} S (Semiring.toNonAssocSemiring.{u_10} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.15)))) (Distrib.toAdd.{u_9} R (NonUnitalNonAssocSemiring.toDistrib.{u_9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.12)))) (Distrib.toAdd.{u_10} S (NonUnitalNonAssocSemiring.toDistrib.{u_10} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} S (Semiring.toNonAssocSemiring.{u_10} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555650._hygCtx._hyg.15)))))) g))","typeFull":"{R : Type u_9} → {S : Type u_10} → [inst : Semiring R] → [inst_1 : Semiring S] → (g : R ≃+* S) → R ≃ₗ[R] S","typeReadable":"{R : Type u_9} → {S : Type u_10} → [inst : Semiring R] → [inst_1 : Semiring S] → (g : R ≃+* S) → R ≃ₗ[R] S","typeReferences":[["Distrib","toAdd"],["NonUnitalNonAssocSemiring","toDistrib"],["RingEquiv","instRingEquivClass"],["RingEquiv","instEquivLike"],["Distrib","toMul"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["LinearEquiv"],["Semiring","toNonAssocSemiring"],["RingEquivClass","toRingHomClass"],["RingHom","id"],["EquivLike","toFunLike"],["RingEquiv"],["RingHomInvPair","ids"],["Semiring","toModule"],["RingHomClass","toRingHom"],["Semiring"],["Module","compHom"]],"valueReferences":[["LinearMap","mk"],["AddHom","mk"],["DFunLike","coe"],["Module","compHom","toLinearEquiv","_proof_2"],["Semiring","toNonAssocSemiring"],["RingEquiv","symm"],["RingHom","id"],["EquivLike","toFunLike"],["Module","compHom","toLinearEquiv","_proof_5"],["LinearEquiv","mk"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Semiring","toModule"],["RingHomClass","toRingHom"],["Distrib","toAdd"],["NonUnitalNonAssocSemiring","toDistrib"],["RingEquiv","instEquivLike"],["Distrib","toMul"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["Module","compHom","toLinearEquiv","_proof_3"],["Module","compHom","toLinearEquiv","_proof_4"],["AddCommMonoid","toAddCommSemigroup"],["RingEquiv"],["RingHomInvPair","ids"],["Module","compHom"],["Module","compHom","toLinearEquiv","_proof_1"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","coe_one"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_5}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.19 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.25 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.19], Eq.{succ u_5} (M -> M) (DFunLike.coe.{succ u_5, succ u_5, succ u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.25) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (EquivLike.toFunLike.{succ u_5, succ u_5, succ u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.25) M M (LinearEquiv.instEquivLike.{u_1, u_1, u_5, u_5} R R M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10))) (OfNat.ofNat.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.25) 1 (One.toOfNat1.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.25) (InvOneClass.toOne.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.25) (DivInvOneMonoid.toInvOneClass.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.25) (DivisionMonoid.toDivInvOneMonoid.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.25) (LinearEquiv.automorphismGroup.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2552065102._hygCtx._hyg.25)))))))) (id.{succ u_5} M)","typeFull":"∀ {R : Type u_1} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M], ⇑1 = id","typeReadable":"∀ {R : Type u_1} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M], ⇑1 = id","typeReferences":[["Group","toDivisionMonoid"],["Module"],["InvOneClass","toOne"],["LinearEquiv"],["DFunLike","coe"],["OfNat","ofNat"],["LinearEquiv","automorphismGroup"],["AddCommMonoid"],["DivInvOneMonoid","toInvOneClass"],["Semiring","toNonAssocSemiring"],["One","toOfNat1"],["RingHom","id"],["EquivLike","toFunLike"],["id"],["RingHomInvPair","ids"],["Eq"],["LinearEquiv","instEquivLike"],["DivisionMonoid","toDivInvOneMonoid"],["Semiring"]],"valueReferences":[["rfl"],["Group","toDivisionMonoid"],["InvOneClass","toOne"],["LinearEquiv"],["DFunLike","coe"],["OfNat","ofNat"],["LinearEquiv","automorphismGroup"],["Semiring","toNonAssocSemiring"],["DivInvOneMonoid","toInvOneClass"],["One","toOfNat1"],["RingHom","id"],["EquivLike","toFunLike"],["RingHomInvPair","ids"],["LinearEquiv","instEquivLike"],["DivisionMonoid","toDivInvOneMonoid"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","mk","congr_simp"],"typeFallback":"forall {R : Type.{u_14}} {S : Type.{u_15}} [inst._@.Mathlib.Algebra.Module.LinearMap.Defs.2302359325._hygCtx._hyg.30 : Semiring.{u_14} R] [inst._@.Mathlib.Algebra.Module.LinearMap.Defs.2302359325._hygCtx._hyg.33 : Semiring.{u_15} S] {σ : RingHom.{u_14, u_15} R S (Semiring.toNonAssocSemiring.{u_14} R inst._@.Mathlib.Algebra.Module.LinearMap.Defs.2302359325._hygCtx._hyg.30) (Semiring.toNonAssocSemiring.{u_15} S inst._@.Mathlib.Algebra.Module.LinearMap.Defs.2302359325._hygCtx._hyg.33)} {M : Type.{u_16}} {M₂ : Type.{u_17}} [inst._@.Mathlib.Algebra.Module.LinearMap.Defs.2302359325._hygCtx._hyg.43 : AddCommMonoid.{u_16} M] [inst._@.Mathlib.Algebra.Module.LinearMap.Defs.2302359325._hygCtx._hyg.46 : AddCommMonoid.{u_17} M₂] [inst._@.Mathlib.Algebra.Module.LinearMap.Defs.2302359325._hygCtx._hyg.49 : Module.{u_14, u_16} R M inst._@.Mathlib.Algebra.Module.LinearMap.Defs.2302359325._hygCtx._hyg.30 inst._@.Mathlib.Algebra.Module.LinearMap.Defs.2302359325._hygCtx._hyg.43] 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(AddCommGroup.toAddGroup.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19)))))) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : AddMonoidHom.{u_9, u_10} A B (AddZeroClass.toAddZero.{u_9} A (AddMonoid.toAddZeroClass.{u_9} A (SubNegMonoid.toAddMonoid.{u_9} A (AddGroup.toSubNegMonoid.{u_9} A (AddCommGroup.toAddGroup.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16))))) (AddZeroClass.toAddZero.{u_10} B (AddMonoid.toAddZeroClass.{u_10} B (SubNegMonoid.toAddMonoid.{u_10} B (AddGroup.toSubNegMonoid.{u_10} B (AddCommGroup.toAddGroup.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19)))))) => LinearMap.{0, 0, u_9, u_10} Int Int Int.instSemiring Int.instSemiring (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int Int.instSemiring)) A B (AddCommGroup.toAddCommMonoid.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_10} B 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16) (AddCommGroup.toIntModule.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19) (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int Int.instSemiring)) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.22 (AddGroup.int_smulCommClass.{u_11, u_10} R B (AddCommGroup.toAddGroup.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19) (DistribMulAction.toDistribSMul.{u_11, u_10} R B (MonoidWithZero.toMonoid.{u_11} R (Semiring.toMonoidWithZero.{u_11} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.13)) (SubNegMonoid.toAddMonoid.{u_10} B (AddGroup.toSubNegMonoid.{u_10} B (AddCommGroup.toAddGroup.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19))) (Module.toDistribMulAction.{u_11, u_10} R B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.13 (AddCommGroup.toAddCommMonoid.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.22))))) (AddMonoidHom.{u_9, u_10} A B (AddZeroClass.toAddZero.{u_9} A (AddMonoid.toAddZeroClass.{u_9} A (SubNegMonoid.toAddMonoid.{u_9} A (AddGroup.toSubNegMonoid.{u_9} A (AddCommGroup.toAddGroup.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16))))) (AddZeroClass.toAddZero.{u_10} B (AddMonoid.toAddZeroClass.{u_10} B (SubNegMonoid.toAddMonoid.{u_10} B (AddGroup.toSubNegMonoid.{u_10} B (AddCommGroup.toAddGroup.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19)))))) (LinearMap.{0, 0, u_9, u_10} Int Int Int.instSemiring Int.instSemiring (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int Int.instSemiring)) A B (AddCommGroup.toAddCommMonoid.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19) (AddCommGroup.toIntModule.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16) (AddCommGroup.toIntModule.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19)) (LinearEquiv.instEquivLike.{u_11, u_11, max u_10 u_9, max u_10 u_9} R R (AddMonoidHom.{u_9, u_10} A B (AddZeroClass.toAddZero.{u_9} A (AddMonoid.toAddZeroClass.{u_9} A (SubNegMonoid.toAddMonoid.{u_9} A (AddGroup.toSubNegMonoid.{u_9} A (AddCommGroup.toAddGroup.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16))))) (AddZeroClass.toAddZero.{u_10} B (AddMonoid.toAddZeroClass.{u_10} B (SubNegMonoid.toAddMonoid.{u_10} B (AddGroup.toSubNegMonoid.{u_10} B (AddCommGroup.toAddGroup.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19)))))) (LinearMap.{0, 0, u_9, u_10} Int Int Int.instSemiring Int.instSemiring (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int Int.instSemiring)) A B (AddCommGroup.toAddCommMonoid.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19) (AddCommGroup.toIntModule.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16) (AddCommGroup.toIntModule.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19)) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.13 (AddMonoidHom.instAddCommMonoid.{u_9, u_10} A B (AddMonoid.toAddZeroClass.{u_9} A (SubNegMonoid.toAddMonoid.{u_9} A (AddGroup.toSubNegMonoid.{u_9} A (AddCommGroup.toAddGroup.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16)))) (AddCommGroup.toAddCommMonoid.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19)) (LinearMap.addCommMonoid.{0, 0, u_9, u_10} Int Int A B Int.instSemiring Int.instSemiring (AddCommGroup.toAddCommMonoid.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19) (AddCommGroup.toIntModule.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16) (AddCommGroup.toIntModule.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19) (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int Int.instSemiring))) (AddMonoidHom.instModule.{u_11, u_9, u_10} R A B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.13 (SubNegMonoid.toAddMonoid.{u_9} A (AddGroup.toSubNegMonoid.{u_9} A (AddCommGroup.toAddGroup.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16))) (AddCommGroup.toAddCommMonoid.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.22) (LinearMap.module.{0, 0, u_11, u_9, u_10} Int Int R A B Int.instSemiring Int.instSemiring (AddCommGroup.toAddCommMonoid.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16) (AddCommGroup.toAddCommMonoid.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19) (AddCommGroup.toIntModule.{u_9} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16) (AddCommGroup.toIntModule.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19) (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int Int.instSemiring)) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.22 (AddGroup.int_smulCommClass.{u_11, u_10} R B (AddCommGroup.toAddGroup.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19) (DistribMulAction.toDistribSMul.{u_11, u_10} R B (MonoidWithZero.toMonoid.{u_11} R (Semiring.toMonoidWithZero.{u_11} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.13)) (SubNegMonoid.toAddMonoid.{u_10} B (AddGroup.toSubNegMonoid.{u_10} B (AddCommGroup.toAddGroup.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19))) (Module.toDistribMulAction.{u_11, u_10} R B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.13 (AddCommGroup.toAddCommMonoid.{u_10} B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19) inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.22)))) (RingHom.id.{u_11} R (Semiring.toNonAssocSemiring.{u_11} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.13)) (RingHom.id.{u_11} R (Semiring.toNonAssocSemiring.{u_11} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.13)) (RingHomInvPair.ids.{u_11} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.13) (RingHomInvPair.ids.{u_11} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.13))) (addMonoidHomLequivInt.{u_9, u_10, u_11} A B R inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.22) f) (AddMonoidHom.toIntLinearMap.{u_9, u_10} A B inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.3685785899._hygCtx._hyg.19 f)","typeFull":"∀ {A : Type u_9} {B : Type u_10} (R : Type u_11) [inst : Semiring R] [inst_1 : AddCommGroup A] [inst_2 : AddCommGroup B]\n  [inst_3 : Module R B] (f : A →+ B), (addMonoidHomLequivInt R) f = f.toIntLinearMap","typeReadable":"∀ {A : Type u_9} {B : Type u_10} (R : Type u_11) [inst : Semiring R] [inst_1 : AddCommGroup A] [inst_2 : AddCommGroup B]\n  [inst_3 : Module R B] (f : A →+ B), (addMonoidHomLequivInt R) f = f.toIntLinearMap","typeReferences":[["Module"],["AddCommGroup","toAddGroup"],["LinearEquiv"],["DFunLike","coe"],["AddMonoidHom","instModule"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["AddMonoidHom"],["EquivLike","toFunLike"],["MonoidWithZero","toMonoid"],["addMonoidHomLequivInt"],["AddGroup","toSubNegMonoid"],["LinearEquiv","instEquivLike"],["Eq"],["AddGroup","int_smulCommClass"],["LinearMap","module"],["DistribMulAction","toDistribSMul"],["AddMonoidHom","toIntLinearMap"],["Semiring","toMonoidWithZero"],["AddCommGroup"],["LinearMap"],["AddZeroClass","toAddZero"],["AddCommGroup","toIntModule"],["Int"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["SubNegMonoid","toAddMonoid"],["Int","instSemiring"],["AddCommGroup","toAddCommMonoid"],["RingHomInvPair","ids"],["AddMonoidHom","instAddCommMonoid"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["AddCommGroup","toAddGroup"],["LinearEquiv"],["DFunLike","coe"],["AddMonoidHom","instModule"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["AddMonoidHom"],["EquivLike","toFunLike"],["MonoidWithZero","toMonoid"],["addMonoidHomLequivInt"],["AddGroup","toSubNegMonoid"],["LinearEquiv","instEquivLike"],["AddGroup","int_smulCommClass"],["LinearMap","module"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["LinearMap"],["AddCommGroup","toIntModule"],["Int"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["SubNegMonoid","toAddMonoid"],["Int","instSemiring"],["Eq","refl"],["RingHomInvPair","ids"],["AddCommGroup","toAddCommMonoid"],["AddMonoidHom","instAddCommMonoid"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","arrowCongr","congr_simp"],"typeFallback":"forall {R₁ : Type.{u_9}} {R₂ : Type.{u_10}} {R₁' : Type.{u_12}} {R₂' : Type.{u_13}} {M₁ : Type.{u_17}} {M₂ : Type.{u_18}} {M₁' : Type.{u_20}} {M₂' : Type.{u_21}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 : Semiring.{u_9} R₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 : Semiring.{u_10} R₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59 : CommSemiring.{u_12} R₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62 : CommSemiring.{u_13} R₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 : AddCommMonoid.{u_17} M₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 : AddCommMonoid.{u_18} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 : AddCommMonoid.{u_20} M₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 : AddCommMonoid.{u_21} M₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 : Module.{u_9, u_17} R₁ M₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 : Module.{u_10, u_18} R₂ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 : Module.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 : Module.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86] {σ₁₂ : RingHom.{u_9, u_10} R₁ R₂ (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53)} {σ₂₁ : RingHom.{u_10, u_9} R₂ R₁ (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53) (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50)} {σ₁'₂' : RingHom.{u_12, u_13} R₁' R₂' (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59)) (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62))} {σ₂'₁' : RingHom.{u_13, u_12} R₂' R₁' (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62)) 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59))} {σ₂₁'_1 : RingHom.{u_10, u_12} R₂ R₁' (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53) (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59))} (e_σ₂₁' : Eq.{max (succ u_10) (succ u_12)} (RingHom.{u_10, u_12} R₂ R₁' (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53) (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59))) σ₂₁' σ₂₁'_1) {σ₁₂' : RingHom.{u_9, u_13} R₁ R₂' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62))} {σ₁₂'_1 : RingHom.{u_9, u_13} R₁ R₂' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62))} (e_σ₁₂' : Eq.{max (succ u_9) (succ u_13)} (RingHom.{u_9, u_13} R₁ R₂' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62))) σ₁₂' σ₁₂'_1) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.285 : RingHomInvPair.{u_9, u_10} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 σ₁₂ σ₂₁] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.289 : RingHomInvPair.{u_10, u_9} R₂ R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 σ₂₁ σ₁₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.293 : RingHomInvPair.{u_12, u_13} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₁'₂' σ₂'₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.297 : RingHomInvPair.{u_13, u_12} R₂' R₁' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₂'₁' σ₁'₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.351 : RingHomCompTriple.{u_9, u_12, u_13} R₁ R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₁₁' σ₁'₂' σ₁₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.356 : RingHomCompTriple.{u_10, u_9, u_13} R₂ R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₁ σ₁₂' σ₂₂'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.361 : RingHomCompTriple.{u_10, u_13, u_12} R₂ R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₂₂' σ₂'₁' σ₂₁'] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.366 : RingHomCompTriple.{u_9, u_10, u_12} R₁ R₂ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₂ σ₂₁' σ₁₁'] (e₁ : LinearEquiv.{u_9, u_10, u_17, u_18} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.285 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.289 M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102) (e₁_1 : LinearEquiv.{u_9, u_10, u_17, u_18} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.285 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.289 M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102), (Eq.{max (succ u_17) (succ u_18)} (LinearEquiv.{u_9, u_10, u_17, u_18} R₁ R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 σ₁₂ σ₂₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.285 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.289 M₁ M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102) e₁ e₁_1) -> (forall (e₂ : LinearEquiv.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.297 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (e₂_1 : LinearEquiv.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.297 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114), (Eq.{max (succ u_20) (succ u_21)} (LinearEquiv.{u_12, u_13, u_20, u_21} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.297 M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) e₂ e₂_1) -> (Eq.{max (succ (max u_20 u_17)) (succ (max u_21 u_18))} (LinearEquiv.{u_12, u_13, max u_20 u_17, max u_21 u_18} R₁' R₂' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₁'₂' σ₂'₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.297 (LinearMap.{u_9, u_12, u_17, u_20} R₁ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110) (LinearMap.{u_10, u_13, u_18, u_21} R₂ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114) (LinearMap.addCommMonoid.{u_9, u_12, u_17, u_20} R₁ R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 σ₁₁') (LinearMap.addCommMonoid.{u_10, u_13, u_18, u_21} R₂ R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 σ₂₂') (LinearMap.module.{u_9, u_12, u_12, u_17, u_20} R₁ R₁' R₁' M₁ M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 σ₁₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 (smulCommClass_self.{u_12, u_20} R₁' M₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (DistribMulAction.toMulAction.{u_12, u_20} R₁' M₁' (CommMonoid.toMonoid.{u_12} R₁' (CommSemiring.toCommMonoid.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59)) (AddCommMonoid.toAddMonoid.{u_20} M₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83) (Module.toDistribMulAction.{u_12, u_20} R₁' M₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110)))) (LinearMap.module.{u_10, u_13, u_13, u_18, u_21} R₂ R₂' R₂' M₂ M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 σ₂₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 (smulCommClass_self.{u_13, u_21} R₂' M₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) (DistribMulAction.toMulAction.{u_13, u_21} R₂' M₂' (CommMonoid.toMonoid.{u_13} R₂' (CommSemiring.toCommMonoid.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62)) (AddCommMonoid.toAddMonoid.{u_21} M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86) (Module.toDistribMulAction.{u_13, u_21} R₂' M₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114))))) (LinearEquiv.arrowCongr.{u_9, u_10, u_12, u_13, u_17, u_18, u_20, u_21} R₁ R₂ R₁' R₂' M₁ M₂ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 σ₁₂ σ₂₁ σ₁'₂' σ₂'₁' σ₁₁' σ₂₂' σ₂₁' σ₁₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.285 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.289 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.297 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.351 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.356 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.361 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.366 e₁ e₂) (LinearEquiv.arrowCongr.{u_9, u_10, u_12, u_13, u_17, u_18, u_20, u_21} R₁ R₂ R₁' R₂' M₁ M₂ M₁' M₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.77 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.86 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.98 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.102 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.110 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.114 σ₁₂ σ₂₁ σ₁'₂' σ₂'₁' σ₁₁' σ₂₂' σ₂₁'_1 σ₁₂'_1 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.285 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.289 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.293 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.297 (Eq.ndrec.{0, max (succ u_9) (succ u_13)} (RingHom.{u_9, u_13} R₁ R₂' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62))) σ₁₂' (fun {σ₁₂' : RingHom.{u_9, u_13} R₁ R₂' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62))} => RingHomCompTriple.{u_9, u_12, u_13} R₁ R₁' R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₁₁' σ₁'₂' σ₁₂') inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.351 σ₁₂'_1 e_σ₁₂') (Eq.ndrec.{0, max (succ u_9) (succ u_13)} (RingHom.{u_9, u_13} R₁ R₂' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62))) σ₁₂' (fun {σ₁₂' : RingHom.{u_9, u_13} R₁ R₂' (Semiring.toNonAssocSemiring.{u_9} R₁ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50) (Semiring.toNonAssocSemiring.{u_13} R₂' (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62))} => RingHomCompTriple.{u_10, u_9, u_13} R₂ R₁ R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) σ₂₁ σ₁₂' σ₂₂') inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.356 σ₁₂'_1 e_σ₁₂') (Eq.ndrec.{0, max (succ u_10) (succ u_12)} (RingHom.{u_10, u_12} R₂ R₁' (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53) (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59))) ��₂₁' (fun {σ₂₁' : RingHom.{u_10, u_12} R₂ R₁' (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53) (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59))} => RingHomCompTriple.{u_10, u_13, u_12} R₂ R₂' R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_13} R₂' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.62) (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₂₂' σ₂'₁' σ₂₁') inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.361 σ₂₁'_1 e_σ₂₁') (Eq.ndrec.{0, max (succ u_10) (succ u_12)} (RingHom.{u_10, u_12} R₂ R₁' (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53) (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59))) σ₂₁' (fun {σ₂₁' : RingHom.{u_10, u_12} R₂ R₁' (Semiring.toNonAssocSemiring.{u_10} R₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53) (Semiring.toNonAssocSemiring.{u_12} R₁' (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59))} => RingHomCompTriple.{u_9, u_10, u_12} R₁ R₂ R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.50 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.53 (CommSemiring.toSemiring.{u_12} R₁' inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.59) σ₁₂ σ₂₁' σ₁₁') inst._@.Mathlib.Algebra.Module.Equiv.Basic.2562726778._hygCtx._hyg.366 σ₂₁'_1 e_σ₂₁') e₁_1 e₂_1)))","typeFull":"∀ {R₁ : Type u_9} {R₂ : Type u_10} {R₁' : Type u_12} {R₂' : Type u_13} {M₁ : Type u_17} {M₂ : Type u_18}\n  {M₁' : Type u_20} {M₂' : Type u_21} [inst : Semiring R₁] [inst_1 : Semiring R₂] [inst_2 : CommSemiring R₁']\n  [inst_3 : CommSemiring R₂'] [inst_4 : AddCommMonoid M₁] [inst_5 : AddCommMonoid M₂] [inst_6 : AddCommMonoid M₁']\n  [inst_7 : AddCommMonoid M₂'] [inst_8 : Module R₁ M₁] [inst_9 : Module R₂ M₂] [inst_10 : Module R₁' M₁']\n  [inst_11 : Module R₂' M₂'] {σ₁₂ : R₁ →+* R₂} {σ₂₁ : R₂ →+* R₁} {σ₁'₂' : R₁' →+* R₂'} {σ₂'₁' : R₂' →+* R₁'}\n  {σ₁₁' : R₁ →+* R₁'} {σ₂₂' : R₂ →+* R₂'} {σ₂₁' σ₂₁'_1 : R₂ →+* R₁'} (e_σ₂₁' : σ₂₁' = σ₂₁'_1) {σ₁₂' σ₁₂'_1 : R₁ →+* R₂'}\n  (e_σ₁₂' : σ₁₂' = σ₁₂'_1) [inst_12 : RingHomInvPair σ₁₂ σ₂₁] [inst_13 : RingHomInvPair σ₂₁ σ₁₂]\n  [inst_14 : RingHomInvPair σ₁'₂' σ₂'₁'] [inst_15 : RingHomInvPair σ₂'₁' σ₁'₂']\n  [inst_16 : RingHomCompTriple σ₁₁' σ₁'₂' σ₁₂'] [inst_17 : RingHomCompTriple σ₂₁ σ₁₂' σ₂₂']\n  [inst_18 : RingHomCompTriple σ₂₂' σ₂'₁' σ₂₁'] [inst_19 : RingHomCompTriple σ₁₂ σ₂₁' σ₁₁'] (e₁ e₁_1 : M₁ ≃ₛₗ[σ₁₂] M₂),\n  e₁ = e₁_1 → ∀ (e₂ e₂_1 : M₁' ≃ₛₗ[σ₁'₂'] M₂'), e₂ = 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σ₂₂']\n  [inst_18 : RingHomCompTriple σ₂₂' σ₂'₁' σ₂₁'] [inst_19 : RingHomCompTriple σ₁₂ σ₂₁' σ₁₁'] (e₁ e₁_1 : M₁ ≃ₛₗ[σ₁₂] M₂),\n  e₁ = e₁_1 → ∀ (e₂ e₂_1 : M₁' ≃ₛₗ[σ₁'₂'] M₂'), e₂ = e₂_1 → e₁.arrowCongr e₂ = e₁_1.arrowCongr 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x","typeReferences":[["IsLinearMap","mk'"],["RingHom"],["Equiv","instEquivLike"],["Module"],["RingHom","instFunLike"],["LinearMap","toAddHom"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["Equiv"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["EquivLike","toFunLike"],["instHSMul"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["AddHom","toFun"],["Eq"],["DistribSMul","toSMulZeroClass"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["Module","toDistribMulAction"],["AddCommMonoid","toAddCommSemigroup"],["HSMul","hSMul"],["IsLinearMap"],["AddZero","toZero"],["Semiring"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["IsLinearMap","mk'"],["Equiv","instEquivLike"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["EquivLike","toFunLike"],["LinearMap","map_smul'"],["DFunLike","coe"],["Equiv"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","automorphismGroup","_proof_11"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 : Module.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19] (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25), Eq.{succ u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (HMul.hMul.{u_2, u_2, u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (instHMul.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (LinearEquiv.automorphismGroup._proof_7.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (LinearEquiv.automorphismGroup._proof_7.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) g f))) (LinearEquiv.symm.{u_1, u_1, u_2, u_2} R R M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) f) f) (OfNat.ofNat.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) 1 (One.toOfNat1.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.refl.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25))))","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  f.symm * f = 1","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  f.symm * f = 1","typeReferences":[["Mul","mk"],["Module"],["One","mk"],["HMul","hMul"],["LinearEquiv","automorphismGroup","_proof_7"],["LinearEquiv"],["LinearEquiv","symm"],["OfNat","ofNat"],["LinearEquiv","trans"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["One","toOfNat1"],["RingHom","id"],["RingHomInvPair","ids"],["instHMul"],["Eq"],["LinearEquiv","refl"],["Semiring"]],"valueReferences":[["Mul","mk"],["RingHomCompTriple","ids"],["One","mk"],["HMul","hMul"],["LinearEquiv"],["LinearEquiv","symm"],["OfNat","ofNat"],["LinearEquiv","trans"],["LinearEquiv","ext"],["Semiring","toNonAssocSemiring"],["One","toOfNat1"],["RingHom","id"],["RingHomInvPair","ids"],["instHMul"],["LinearEquiv","left_inv"],["LinearEquiv","refl"]]},{"isProp":true,"kind":"theorem","name":["DistribMulAction","toModuleAut_apply"],"typeFallback":"forall (R : Type.{u_1}) {S : Type.{u_4}} (M : Type.{u_5}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.16 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.20 : Group.{u_4} S] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.23 : DistribMulAction.{u_4, u_5} S M (DivInvMonoid.toMonoid.{u_4} S (Group.toDivInvMonoid.{u_4} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.20)) (AddCommMonoid.toAddMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13)] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.27 : SMulCommClass.{u_4, u_1, u_5} S R M (SMulZeroClass.toSMul.{u_4, u_5} S M (AddZero.toZero.{u_5} M (AddZeroClass.toAddZero.{u_5} M (AddMonoid.toAddZeroClass.{u_5} M 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.16)))))) S (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : S) => LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.16 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.16) (Monoid.toMulOneClass.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.16) (DivInvMonoid.toMonoid.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.4191798717._hygCtx._hyg.10) M M 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Group S] [inst_4 : DistribMulAction S M] [inst_5 : SMulCommClass S R M] (s : S),\n  (DistribMulAction.toModuleAut R M) s = DistribMulAction.toLinearEquiv R M 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R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.15 : Semiring.{u_10} A] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.18 : Module.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.15)))] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.22 : SMulCommClass.{u_9, u_10, u_10} R A A (SMulZeroClass.toSMul.{u_9, u_10} R A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_9, u_10} R A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.15))))) (DistribMulAction.toDistribSMul.{u_9, u_10} R A (MonoidWithZero.toMonoid.{u_9} R (Semiring.toMonoidWithZero.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.12)) (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.15)))) (Module.toDistribMulAction.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.18)))) (SMulZeroClass.toSMul.{u_10, u_10} A A (AddZero.toZero.{u_10} A (AddZeroClass.toAddZero.{u_10} A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.15))))))) (DistribSMul.toSMulZeroClass.{u_10, u_10} A A (AddMonoid.toAddZeroClass.{u_10} A (AddMonoidWithOne.toAddMonoid.{u_10} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_10} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.15))))) (instDistribSMul.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.15)))))] (a : Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.15))) (x : A), Eq.{succ u_10} A (DFunLike.coe.{succ u_10, succ u_10, succ u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.18) A (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : A) => A) (EquivLike.toFunLike.{succ u_10, succ u_10, succ u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R 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(LinearEquiv.instEquivLike.{u_9, u_9, u_10, u_10} R R A A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.18 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R 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(MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.15)))) (MulOneClass.toMulOne.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A 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(RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.18) (DivInvMonoid.toMonoid.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R 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(Group.toDivInvMonoid.{u_10} (LinearEquiv.{u_9, u_9, u_10, u_10} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.12 (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.12)) (RingHom.id.{u_9} R (Semiring.toNonAssocSemiring.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.12)) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.12) (RingHomInvPair.ids.{u_9} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.12) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.15))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.18) (LinearEquiv.automorphismGroup.{u_9, u_10} R A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.12 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.15))) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.18)))))) (Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.15))) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : Units.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A 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(HMul.hMul.{u_10, u_10, u_10} A A A (instHMul.{u_10} A (Distrib.toMul.{u_10} A (NonUnitalNonAssocSemiring.toDistrib.{u_10} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_10} A (Semiring.toNonAssocSemiring.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.15))))) (Units.val.{u_10} A (MonoidWithZero.toMonoid.{u_10} A (Semiring.toMonoidWithZero.{u_10} A inst._@.Mathlib.Algebra.Module.Equiv.Basic.2798789870._hygCtx._hyg.15)) a) x)","typeFull":"∀ (R : Type u_9) {A : Type u_10} [inst : Semiring R] [inst_1 : Semiring A] [inst_2 : Module R A]\n  [inst_3 : SMulCommClass R A A] (a : Aˣ) (x : A), ((Units.mulLeftLinearEquiv R A) a) x = ↑a * x","typeReadable":"∀ (R : Type u_9) {A : Type u_10} [inst : Semiring R] [inst_1 : Semiring A] [inst_2 : Module R A]\n  [inst_3 : SMulCommClass R A A] (a : Aˣ) (x : A), ((Units.mulLeftLinearEquiv R A) a) x = ↑a * x","typeReferences":[["MulOneClass","toMulOne"],["Module"],["MonoidHom"],["MonoidHom","instFunLike"],["HMul","hMul"],["SMulZeroClass","toSMul"],["AddMonoidWithOne","toAddMonoid"],["instDistribSMul"],["LinearEquiv"],["DFunLike","coe"],["LinearEquiv","automorphismGroup"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Monoid","toMulOneClass"],["EquivLike","toFunLike"],["MonoidWithZero","toMonoid"],["Units","mulLeftLinearEquiv"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["LinearEquiv","instEquivLike"],["Eq"],["Group","toDivInvMonoid"],["NonAssocSemiring","toAddCommMonoidWithOne"],["Units"],["DistribSMul","toSMulZeroClass"],["NonUnitalNonAssocSemiring","toDistrib"],["Distrib","toMul"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["Units","instMulOneClass"],["AddZeroClass","toAddZero"],["SMulCommClass"],["Module","toDistribMulAction"],["DivInvMonoid","toMonoid"],["Units","val"],["RingHomInvPair","ids"],["instHMul"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["MulOneClass","toMulOne"],["rfl"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["MonoidHom"],["MonoidHom","instFunLike"],["Semiring","toMonoidWithZero"],["Units","instMulOneClass"],["LinearEquiv"],["DFunLike","coe"],["LinearEquiv","automorphismGroup"],["Semiring","toNonAssocSemiring"],["DivInvMonoid","toMonoid"],["RingHom","id"],["Monoid","toMulOneClass"],["EquivLike","toFunLike"],["MonoidWithZero","toMonoid"],["RingHomInvPair","ids"],["Units","mulLeftLinearEquiv"],["LinearEquiv","instEquivLike"],["Group","toDivInvMonoid"],["Units"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","domMulActCongrRight","_proof_1"],"typeFallback":"forall 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u_1} [inst : Semiring S], RingHomInvPair (RingHom.id Sᵈᵐᵃ) (RingHom.id Sᵈᵐᵃ)","typeReadable":"∀ {S : Type u_1} [inst : Semiring S], RingHomInvPair (RingHom.id Sᵈᵐᵃ) (RingHom.id Sᵈᵐᵃ)","typeReferences":[["Semiring","toNonAssocSemiring"],["RingHom","id"],["DomMulAct"],["RingHomInvPair"],["MulOpposite","instSemiring"],["DomMulAct","instSemiringOfMulOpposite"],["Semiring"]],"valueReferences":[["RingHomInvPair","ids"],["DomMulAct"],["MulOpposite","instSemiring"],["DomMulAct","instSemiringOfMulOpposite"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","toAddEquiv_toIntLinearEquiv"],"typeFallback":"forall {M : Type.{u_5}} {M₂ : Type.{u_7}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1882754984._hygCtx._hyg.10 : AddCommGroup.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1882754984._hygCtx._hyg.13 : AddCommGroup.{u_7} M₂] {modM : Module.{0, u_5} Int M Int.instSemiring (AddCommGroup.toAddCommMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1882754984._hygCtx._hyg.10)} 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25) (x : M), Eq.{succ u_5} M (DFunLike.coe.{succ u_5, succ u_5, succ u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (EquivLike.toFunLike.{succ u_5, succ u_5, succ u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25) M M (LinearEquiv.instEquivLike.{u_1, u_1, u_5, u_5} R R M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10))) (HMul.hMul.{u_5, u_5, u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25) (instHMul.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25) (MulOne.toMul.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25) (MulOneClass.toMulOne.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25) (Monoid.toMulOneClass.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25) (DivInvMonoid.toMonoid.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25) (Group.toDivInvMonoid.{u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25) (LinearEquiv.automorphismGroup.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25))))))) f g) x) (DFunLike.coe.{succ u_5, succ u_5, succ u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (EquivLike.toFunLike.{succ u_5, succ u_5, succ u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25) M M (LinearEquiv.instEquivLike.{u_1, u_1, u_5, u_5} R R M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10))) f (DFunLike.coe.{succ u_5, succ u_5, succ u_5} (LinearEquiv.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.576582513._hygCtx._hyg.19 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[inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.13 : Semiring.{u_4} S] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.16 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.19 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.23 : Module.{u_4, u_5} S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.698665469._hygCtx._hyg.27 : SMulCommClass.{u_1, u_4, u_5} R S M (SMulZeroClass.toSMul.{u_1, u_5} R M (AddZero.toZero.{u_5} M (AddZeroClass.toAddZero.{u_5} M (AddMonoid.toAddZeroClass.{u_5} M 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module_M₂ module_M (LinearEquiv.symm.{u_1, u_2, u_5, u_7} R R₂ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1956577708._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1956577708._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1956577708._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1956577708._hygCtx._hyg.19 module_M module_M₂ σ₁₂ σ₂₁ re₁₂ re₂₁ (LinearEquiv.ofLinear.{u_1, u_2, u_5, u_7} R R₂ M M₂ inst._@.Mathlib.Algebra.Module.Equiv.Basic.1956577708._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1956577708._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1956577708._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1956577708._hygCtx._hyg.19 module_M module_M₂ σ₁₂ σ₂₁ re₁₂ re₂₁ f g h₁ h₂))) g","typeFull":"∀ {R : Type u_1} {R₂ : Type u_2} {M : Type u_5} {M₂ : Type u_7} [inst : Semiring R] [inst_1 : Semiring R₂]\n  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] {module_M : Module R M} {module_M₂ : Module R₂ M₂}\n  {σ₁₂ : R →+* R₂} {σ₂₁ : R₂ →+* R} {re₁₂ : RingHomInvPair σ₁₂ σ₂₁} {re₂₁ : RingHomInvPair σ₂₁ σ₁₂} (f : M →ₛₗ[σ₁₂] M₂)\n  (g : M₂ →ₛₗ[σ₂₁] M) {h₁ : f ∘ₛₗ g = LinearMap.id} {h₂ : g ∘ₛₗ f = LinearMap.id},\n  ↑(LinearEquiv.ofLinear f g h₁ h₂).symm = g","typeReadable":"∀ {R : Type u_1} {R₂ : Type u_2} {M : Type u_5} {M₂ : Type u_7} [inst : Semiring R] [inst_1 : Semiring R₂]\n  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] {module_M : Module R M} {module_M₂ : Module R₂ M₂}\n  {σ₁₂ : R →+* R₂} {σ₂₁ : R₂ →+* R} {re₁₂ : RingHomInvPair σ₁₂ σ₂₁} {re₂₁ : RingHomInvPair σ₂₁ σ₁₂} (f : M →ₛₗ[σ₁₂] M₂)\n  (g : M₂ →ₛₗ[σ₂₁] M) {h₁ : f ∘ₛₗ g = LinearMap.id} {h₂ : g ∘ₛₗ f = LinearMap.id},\n  ↑(LinearEquiv.ofLinear f g h₁ h₂).symm = g","typeReferences":[["RingHomInvPair","triples₂"],["RingHom"],["Module"],["LinearMap","comp"],["LinearEquiv","toLinearMap"],["LinearMap"],["LinearEquiv","symm"],["LinearMap","id"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["LinearEquiv","ofLinear"],["RingHomInvPair"],["Eq"],["Semiring"]],"valueReferences":[["rfl"],["LinearEquiv","ofLinear"],["LinearEquiv","toLinearMap"],["LinearMap"],["LinearEquiv","symm"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","ofSubsingleton","_proof_3"],"typeFallback":"forall (M : Type.{u_1}) (M₂ : Type.{u_2}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.19 : AddCommMonoid.{u_1} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.22 : AddCommMonoid.{u_2} M₂] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.33 : Subsingleton.{succ u_1} M] (x._@.Mathlib.Algebra.Module.Equiv.Basic.2084782062._hygCtx._hyg.83 : M), Eq.{succ u_1} M (OfNat.ofNat.{u_1} M 0 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x","typeReferences":[["Subsingleton"],["AddCommMonoid"],["Zero","toOfNat0"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["Eq"],["AddZero","toZero"],["OfNat","ofNat"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["Subsingleton","elim"],["Zero","toOfNat0"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["AddZero","toZero"],["OfNat","ofNat"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","applyDistribMulAction","_proof_2"],"typeFallback":"forall {R : Type.{u_2}} {M : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 : Semiring.{u_2} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 : AddCommMonoid.{u_1} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 : Module.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19] (x._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.72 : M), Eq.{succ u_1} M (HSMul.hSMul.{u_1, u_1, u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) M M (instHSMul.{u_1, u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) M (SMul.mk.{u_1, u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) M (fun (x1._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.51 : LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) (x2._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.51 : M) => DFunLike.coe.{succ u_1, succ u_1, succ u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (EquivLike.toFunLike.{succ u_1, succ u_1, succ u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) M M (LinearEquiv.instEquivLike.{u_2, u_2, u_1, u_1} R R M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10))) x1._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.51 x2._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.51))) (OfNat.ofNat.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) 1 (One.toOfNat1.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) (MulOne.toOne.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) (MulOneClass.toMulOne.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) (Monoid.toMulOneClass.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) (DivInvMonoid.toMonoid.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) (Group.toDivInvMonoid.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) (LinearEquiv.automorphismGroup.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25)))))))) x._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.72) (HSMul.hSMul.{u_1, u_1, u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) M M (instHSMul.{u_1, u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) M (SMul.mk.{u_1, u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) M (fun (x1._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.51 : LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) (x2._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.51 : M) => DFunLike.coe.{succ u_1, succ u_1, succ u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (EquivLike.toFunLike.{succ u_1, succ u_1, succ u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) M M (LinearEquiv.instEquivLike.{u_2, u_2, u_1, u_1} R R M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10))) x1._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.51 x2._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.51))) (OfNat.ofNat.{u_1} (LinearEquiv.{u_2, u_2, u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) (RingHomInvPair.ids.{u_2} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25) (LinearEquiv.automorphismGroup.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.25)))))))) x._@.Mathlib.Algebra.Module.Equiv.Basic.1747207001._hygCtx._hyg.72)","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"],["MulOne","toOne"],["Module"],["LinearEquiv"],["DFunLike","coe"],["OfNat","ofNat"],["LinearEquiv","automorphismGroup"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["DivInvMonoid","toMonoid"],["One","toOfNat1"],["RingHom","id"],["Monoid","toMulOneClass"],["HSMul","hSMul"],["EquivLike","toFunLike"],["RingHomInvPair","ids"],["instHSMul"],["LinearEquiv","instEquivLike"],["Eq"],["Group","toDivInvMonoid"],["Semiring"]],"valueReferences":[["MulOneClass","toMulOne"],["rfl"],["SMul","mk"],["MulOne","toOne"],["LinearEquiv"],["DFunLike","coe"],["OfNat","ofNat"],["LinearEquiv","automorphismGroup"],["Semiring","toNonAssocSemiring"],["DivInvMonoid","toMonoid"],["One","toOfNat1"],["RingHom","id"],["Monoid","toMulOneClass"],["HSMul","hSMul"],["EquivLike","toFunLike"],["RingHomInvPair","ids"],["instHSMul"],["LinearEquiv","instEquivLike"],["Group","toDivInvMonoid"]]},{"isProp":true,"kind":"theorem","name":["AddHom","mk","congr_simp"],"typeFallback":"forall {M : Type.{u_10}} {N : Type.{u_11}} [inst._@.Mathlib.Algebra.Group.Hom.Defs.450278985._hygCtx._hyg.22 : Add.{u_10} M] [inst._@.Mathlib.Algebra.Group.Hom.Defs.450278985._hygCtx._hyg.25 : Add.{u_11} N] (toFun : M -> N) (toFun_1 : M -> N) (e_toFun : Eq.{max (succ u_10) (succ u_11)} (M -> N) toFun toFun_1) (map_add' : forall (x : M) (y : M), Eq.{succ u_11} N (toFun (HAdd.hAdd.{u_10, u_10, u_10} M M M (instHAdd.{u_10} M inst._@.Mathlib.Algebra.Group.Hom.Defs.450278985._hygCtx._hyg.22) x y)) (HAdd.hAdd.{u_11, u_11, u_11} N N N (instHAdd.{u_11} N inst._@.Mathlib.Algebra.Group.Hom.Defs.450278985._hygCtx._hyg.25) (toFun x) (toFun y))), Eq.{max (succ u_10) (succ u_11)} (AddHom.{u_10, u_11} M N inst._@.Mathlib.Algebra.Group.Hom.Defs.450278985._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Group.Hom.Defs.450278985._hygCtx._hyg.25) (AddHom.mk.{u_10, u_11} M N inst._@.Mathlib.Algebra.Group.Hom.Defs.450278985._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Group.Hom.Defs.450278985._hygCtx._hyg.25 toFun map_add') (AddHom.mk.{u_10, u_11} M N inst._@.Mathlib.Algebra.Group.Hom.Defs.450278985._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Group.Hom.Defs.450278985._hygCtx._hyg.25 toFun_1 (Eq.ndrec.{0, max (succ u_10) (succ u_11)} (M -> N) toFun (fun (toFun : M -> N) => forall (x : M) (y : M), Eq.{succ u_11} N (toFun (HAdd.hAdd.{u_10, u_10, u_10} M M M (instHAdd.{u_10} M inst._@.Mathlib.Algebra.Group.Hom.Defs.450278985._hygCtx._hyg.22) x y)) (HAdd.hAdd.{u_11, u_11, u_11} N N N (instHAdd.{u_11} N inst._@.Mathlib.Algebra.Group.Hom.Defs.450278985._hygCtx._hyg.25) (toFun x) (toFun y))) map_add' toFun_1 e_toFun))","typeFull":"∀ {M : Type u_10} {N : Type u_11} [inst : Add M] [inst_1 : Add N] (toFun toFun_1 : M → N) (e_toFun : toFun = toFun_1)\n  (map_add' : ∀ (x y : M), toFun (x + y) = toFun x + toFun y),\n  { toFun := toFun, map_add' := map_add' } = { toFun := toFun_1, map_add' := ⋯ }","typeReadable":"∀ {M : Type u_10} {N : Type u_11} [inst : Add M] [inst_1 : Add N] (toFun toFun_1 : M → N) (e_toFun : toFun = toFun_1)\n  (map_add' : ∀ (x y : M), toFun (x + y) = toFun x + toFun y),\n  { toFun := toFun, map_add' := map_add' } = { toFun := toFun_1, map_add' := ⋯ }","typeReferences":[["HAdd","hAdd"],["instHAdd"],["Add"],["AddHom","mk"],["Eq","ndrec"],["AddHom"],["Eq"]],"valueReferences":[["HAdd","hAdd"],["instHAdd"],["Eq","refl"],["AddHom","mk"],["Eq","ndrec"],["AddHom"],["Eq"],["Eq","rec"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","smulOfNeZero_apply"],"typeFallback":"forall (K : Type.{u_3}) (M : Type.{u_5}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10 : Field.{u_3} K] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.13 : AddCommGroup.{u_5} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.16 : Module.{u_3, u_5} K M (DivisionSemiring.toSemiring.{u_3} K (Semifield.toDivisionSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10))) 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.13) (AddCommGroup.toAddCommMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.16) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (EquivLike.toFunLike.{succ u_5, succ u_5, succ u_5} (LinearEquiv.{u_3, u_3, u_5, u_5} K K (DivisionSemiring.toSemiring.{u_3} K (Semifield.toDivisionSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10))) (DivisionSemiring.toSemiring.{u_3} K (Semifield.toDivisionSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10))) (RingHom.id.{u_3} K (Semiring.toNonAssocSemiring.{u_3} K (DivisionSemiring.toSemiring.{u_3} K (Semifield.toDivisionSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10))))) (RingHom.id.{u_3} K (Semiring.toNonAssocSemiring.{u_3} K (DivisionSemiring.toSemiring.{u_3} K (Semifield.toDivisionSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10))))) (RingHomInvPair.ids.{u_3} K (DivisionSemiring.toSemiring.{u_3} K (Semifield.toDivisionSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10)))) (RingHomInvPair.ids.{u_3} K (DivisionSemiring.toSemiring.{u_3} K (Semifield.toDivisionSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10)))) M M (AddCommGroup.toAddCommMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.13) (AddCommGroup.toAddCommMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.16) M M (LinearEquiv.instEquivLike.{u_3, u_3, u_5, u_5} K K M M (DivisionSemiring.toSemiring.{u_3} K (Semifield.toDivisionSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10))) (DivisionSemiring.toSemiring.{u_3} K (Semifield.toDivisionSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10))) (AddCommGroup.toAddCommMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.13) (AddCommGroup.toAddCommMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.16 (RingHom.id.{u_3} K (Semiring.toNonAssocSemiring.{u_3} K (DivisionSemiring.toSemiring.{u_3} K (Semifield.toDivisionSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10))))) (RingHom.id.{u_3} K (Semiring.toNonAssocSemiring.{u_3} K (DivisionSemiring.toSemiring.{u_3} K (Semifield.toDivisionSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10))))) (RingHomInvPair.ids.{u_3} K (DivisionSemiring.toSemiring.{u_3} K (Semifield.toDivisionSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10)))) (RingHomInvPair.ids.{u_3} K (DivisionSemiring.toSemiring.{u_3} K (Semifield.toDivisionSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10)))))) (LinearEquiv.smulOfNeZero.{u_3, u_5} K M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.16 a ha) a._@._internal._hyg.0) (HSMul.hSMul.{u_3, u_5, u_5} K M M (instHSMul.{u_3, u_5} K M (SMulZeroClass.toSMul.{u_3, u_5} K M (AddZero.toZero.{u_5} M (AddZeroClass.toAddZero.{u_5} M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M (AddCommGroup.toAddCommMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.13))))) (DistribSMul.toSMulZeroClass.{u_3, u_5} K M (AddMonoid.toAddZeroClass.{u_5} M (AddCommMonoid.toAddMonoid.{u_5} M (AddCommGroup.toAddCommMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.13))) (DistribMulAction.toDistribSMul.{u_3, u_5} K M (MonoidWithZero.toMonoid.{u_3} K (Semiring.toMonoidWithZero.{u_3} K (CommSemiring.toSemiring.{u_3} K (Semifield.toCommSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10))))) (AddCommMonoid.toAddMonoid.{u_5} M (AddCommGroup.toAddCommMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.13)) (Module.toDistribMulAction.{u_3, u_5} K M (CommSemiring.toSemiring.{u_3} K (Semifield.toCommSemiring.{u_3} K (Field.toSemifield.{u_3} K inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.10))) (AddCommGroup.toAddCommMonoid.{u_5} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2940582495._hygCtx._hyg.16))))) a a._@._internal._hyg.0)","typeFull":"∀ (K : Type u_3) (M : Type u_5) [inst : Field K] [inst_1 : AddCommGroup M] [inst_2 : Module K M] (a : K) (ha : a ≠ 0)\n  (a_1 : M), (LinearEquiv.smulOfNeZero K M a ha) a_1 = a • a_1","typeReadable":"∀ (K : Type u_3) (M : Type u_5) [inst : Field K] [inst_1 : AddCommGroup M] [inst_2 : Module K M] (a : K) (ha : a ≠ 0)\n  (a_1 : M), (LinearEquiv.smulOfNeZero K M a ha) a_1 = a • a_1","typeReferences":[["Semifield","toCommSemiring"],["Module"],["Field"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["CommRing","toNonUnitalCommRing"],["LinearEquiv"],["DFunLike","coe"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["NonUnitalNonAssocCommRing","toNonUnitalNonAssocRing"],["EquivLike","toFunLike"],["instHSMul"],["Zero","toOfNat0"],["Semifield","toDivisionSemiring"],["Eq"],["LinearEquiv","instEquivLike"],["DistribSMul","toSMulZeroClass"],["Field","toCommRing"],["NonUnitalCommRing","toNonUnitalNonAssocCommRing"],["CommSemiring","toSemiring"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddCommGroup"],["DivisionSemiring","toSemiring"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["Module","toDistribMulAction"],["MulZeroClass","toZero"],["HSMul","hSMul"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["AddCommGroup","toAddCommMonoid"],["Field","toSemifield"],["RingHomInvPair","ids"],["Ne"],["AddZero","toZero"],["LinearEquiv","smulOfNeZero"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["DivisionSemiring","toSemiring"],["LinearEquiv"],["DFunLike","coe"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Eq","refl"],["EquivLike","toFunLike"],["Field","toSemifield"],["RingHomInvPair","ids"],["AddCommGroup","toAddCommMonoid"],["Semifield","toDivisionSemiring"],["LinearEquiv","instEquivLike"],["LinearEquiv","smulOfNeZero"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","automorphismGroup","_proof_9"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 : Module.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19] (x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.68 : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25), Eq.{succ u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (HMul.hMul.{u_2, u_2, u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (instHMul.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (Mul.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (fun (f : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (g : LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) => LinearEquiv.trans.{u_1, u_1, u_1, u_2, u_2, u_2} R R R M M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (LinearEquiv.automorphismGroup._proof_7.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (LinearEquiv.automorphismGroup._proof_7.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R 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inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) 1 (One.toOfNat1.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (One.mk.{u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10) M M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25) (LinearEquiv.refl.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.25)))) x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.68) x._@.Mathlib.Algebra.Module.Equiv.Basic.1265399338._hygCtx._hyg.68","typeFull":"∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (x : M ≃ₗ[R] M),\n  1 * x = x","typeReadable":"∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (x : M ≃ₗ[R] M),\n  1 * x = x","typeReferences":[["Mul","mk"],["Module"],["One","mk"],["HMul","hMul"],["LinearEquiv","automorphismGroup","_proof_7"],["LinearEquiv"],["OfNat","ofNat"],["LinearEquiv","trans"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["One","toOfNat1"],["RingHom","id"],["RingHomInvPair","ids"],["instHMul"],["Eq"],["LinearEquiv","refl"],["Semiring"]],"valueReferences":[["rfl"],["Mul","mk"],["RingHomCompTriple","ids"],["One","mk"],["HMul","hMul"],["LinearEquiv"],["DFunLike","coe"],["OfNat","ofNat"],["LinearEquiv","trans"],["LinearEquiv","ext"],["Semiring","toNonAssocSemiring"],["One","toOfNat1"],["RingHom","id"],["EquivLike","toFunLike"],["RingHomInvPair","ids"],["instHMul"],["LinearEquiv","instEquivLike"],["LinearEquiv","refl"]]},{"isProp":true,"kind":"theorem","name":["DistribMulAction","toLinearEquiv","_proof_3"],"typeFallback":"forall {S : Type.{u_2}} (M : Type.{u_1}) [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13 : AddCommMonoid.{u_1} M] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.20 : Group.{u_2} S] [inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.23 : DistribMulAction.{u_2, u_1} S M (DivInvMonoid.toMonoid.{u_2} S (Group.toDivInvMonoid.{u_2} S inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.20)) (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13)] (s : S), Function.LeftInverse.{succ u_1, succ u_1} M M (Equiv.invFun.{succ u_1, succ u_1} M M (AddEquiv.toEquiv.{u_1, u_1} M M (AddSemigroup.toAdd.{u_1} M (AddMonoid.toAddSemigroup.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13))) (AddSemigroup.toAdd.{u_1} M (AddMonoid.toAddSemigroup.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13))) (DistribMulAction.toAddEquiv.{u_2, u_1} S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.20 (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.23 s))) (Equiv.toFun.{succ u_1, succ u_1} M M (AddEquiv.toEquiv.{u_1, u_1} M M (AddSemigroup.toAdd.{u_1} M (AddMonoid.toAddSemigroup.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13))) (AddSemigroup.toAdd.{u_1} M (AddMonoid.toAddSemigroup.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13))) (DistribMulAction.toAddEquiv.{u_2, u_1} S M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.20 (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Equiv.Basic.2719555651._hygCtx._hyg.23 s)))","typeFull":"∀ {S : Type u_2} (M : Type u_1) [inst : AddCommMonoid M] [inst_1 : Group S] [inst_2 : DistribMulAction S M] (s : S),\n  Function.LeftInverse (DistribMulAction.toAddEquiv M s).invFun (DistribMulAction.toAddEquiv M s).toFun","typeReadable":"∀ {S : Type u_2} (M : Type u_1) [inst : AddCommMonoid M] [inst_1 : Group S] [inst_2 : DistribMulAction S M] (s : S),\n  Function.LeftInverse (DistribMulAction.toAddEquiv M s).invFun (DistribMulAction.toAddEquiv M s).toFun","typeReferences":[["Group"],["AddCommMonoid","toAddMonoid"],["AddEquiv","toEquiv"],["AddCommMonoid"],["DistribMulAction","toAddEquiv"],["DivInvMonoid","toMonoid"],["Equiv","invFun"],["AddMonoid","toAddSemigroup"],["Function","LeftInverse"],["Equiv","toFun"],["Group","toDivInvMonoid"],["DistribMulAction"],["AddSemigroup","toAdd"]],"valueReferences":[["Equiv","left_inv"],["DistribMulAction","toAddEquiv"],["AddMonoid","toAddSemigroup"],["AddCommMonoid","toAddMonoid"],["AddEquiv","toEquiv"],["AddSemigroup","toAdd"]]}]