diff --git "a/data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.RingHom.sym.json" "b/data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.RingHom.sym.json" new file mode 100644--- /dev/null +++ "b/data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.RingHom.sym.json" @@ -0,0 +1 @@ +[{"isProp":true,"kind":"theorem","name":["Module","compHom","_proof_4"],"typeFallback":"forall {R : Type.{u_3}} {S : Type.{u_2}} (M : Type.{u_1}) [inst._@.Mathlib.Algebra.Module.RingHom.2523033993._hygCtx._hyg.6 : Semiring.{u_3} R] [inst._@.Mathlib.Algebra.Module.RingHom.2523033993._hygCtx._hyg.9 : AddCommMonoid.{u_1} M] [inst._@.Mathlib.Algebra.Module.RingHom.2523033993._hygCtx._hyg.12 : Module.{u_3, u_1} R M inst._@.Mathlib.Algebra.Module.RingHom.2523033993._hygCtx._hyg.6 inst._@.Mathlib.Algebra.Module.RingHom.2523033993._hygCtx._hyg.9] [inst._@.Mathlib.Algebra.Module.RingHom.2523033993._hygCtx._hyg.19 : Semiring.{u_2} S] (f : RingHom.{u_2, u_3} S R 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{R : Type.{u_1}} {S : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9 : Semiring.{u_2} S] (motive : (Subtype.{max (succ u_1) (succ u_2)} (Module.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (fun (_inst : Module.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) => IsScalarTower.{u_1, u_2, u_2} R S S (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (DistribMulAction.toDistribSMul.{u_1, u_2} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)) (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (Module.toDistribMulAction.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) _inst)))) (SMulZeroClass.toSMul.{u_2, u_2} S S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_2, u_2} S S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (instDistribSMul.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (DistribMulAction.toDistribSMul.{u_1, u_2} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)) (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (Module.toDistribMulAction.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) _inst)))))) -> Prop) (x._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx.94.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.102 : Subtype.{max (succ u_1) (succ u_2)} (Module.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (fun (_inst : Module.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) => IsScalarTower.{u_1, u_2, u_2} R S S (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (DistribMulAction.toDistribSMul.{u_1, u_2} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)) (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (Module.toDistribMulAction.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) _inst)))) (SMulZeroClass.toSMul.{u_2, u_2} S S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_2, u_2} S S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (instDistribSMul.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (DistribMulAction.toDistribSMul.{u_1, u_2} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)) (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (Module.toDistribMulAction.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) _inst)))))), (forall (val._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.112 : Module.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (property._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.113 : IsScalarTower.{u_1, u_2, u_2} R S S (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (DistribMulAction.toDistribSMul.{u_1, u_2} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)) (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (Module.toDistribMulAction.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) val._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.112)))) (SMulZeroClass.toSMul.{u_2, u_2} S S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_2, u_2} S S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (instDistribSMul.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (DistribMulAction.toDistribSMul.{u_1, u_2} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)) (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (Module.toDistribMulAction.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) val._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.112))))), motive (Subtype.mk.{max (succ u_1) (succ u_2)} (Module.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (fun (_inst : Module.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) => IsScalarTower.{u_1, u_2, u_2} R S S (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (DistribMulAction.toDistribSMul.{u_1, u_2} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)) (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (Module.toDistribMulAction.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) _inst)))) (SMulZeroClass.toSMul.{u_2, u_2} S S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_2, u_2} S S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (instDistribSMul.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (DistribMulAction.toDistribSMul.{u_1, u_2} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)) (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S 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Type u_1} {S : Type u_2} [inst : Semiring R] [inst_1 : Semiring S]\n (motive : { _inst // IsScalarTower R S S } → Prop) (x : { _inst // IsScalarTower R S S }),\n (∀ (val : Module R S) (property : IsScalarTower R S S), motive ⟨val, property⟩) → motive x","typeReferences":[["Subtype"],["Module"],["IsScalarTower"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["SMulZeroClass","toSMul"],["instDistribSMul"],["AddZeroClass","toAddZero"],["AddMonoidWithOne","toAddMonoid"],["Module","toDistribMulAction"],["Semiring","toNonAssocSemiring"],["MonoidWithZero","toMonoid"],["Subtype","mk"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["NonAssocSemiring","toAddCommMonoidWithOne"],["AddZero","toZero"],["DistribSMul","toSMulZeroClass"],["Semiring"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["Module"],["IsScalarTower"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["SMulZeroClass","toSMul"],["instDistribSMul"],["AddZeroClass","toAddZero"],["AddMonoidWithOne","toAddMonoid"],["Module","toDistribMulAction"],["Semiring","toNonAssocSemiring"],["MonoidWithZero","toMonoid"],["Subtype","casesOn"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["AddZero","toZero"],["NonAssocSemiring","toAddCommMonoidWithOne"],["DistribSMul","toSMulZeroClass"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["RingHom","smulOneHom_apply"],"typeFallback":"forall {R : Type.{u_1}} {S : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.RingHom.239643300._hygCtx._hyg.6 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.RingHom.239643300._hygCtx._hyg.9 : NonAssocSemiring.{u_2} S] [inst._@.Mathlib.Algebra.Module.RingHom.239643300._hygCtx._hyg.12 : Module.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.239643300._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.239643300._hygCtx._hyg.9))] [inst._@.Mathlib.Algebra.Module.RingHom.239643300._hygCtx._hyg.16 : IsScalarTower.{u_1, u_2, u_2} R S S (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.239643300._hygCtx._hyg.9)))))) 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(AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (DistribMulAction.toDistribSMul.{u_1, u_2} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)) (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (Module.toDistribMulAction.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S 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(AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (DistribMulAction.toDistribSMul.{u_1, u_2} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)) (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S 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(Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (property._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.74 : IsScalarTower.{u_1, u_2, u_2} R S S (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (DistribMulAction.toDistribSMul.{u_1, u_2} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)) (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (Module.toDistribMulAction.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) val._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.73)))) (SMulZeroClass.toSMul.{u_2, u_2} S S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_2, u_2} S S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (instDistribSMul.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (DistribMulAction.toDistribSMul.{u_1, u_2} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)) (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (Module.toDistribMulAction.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) val._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.73))))) => RingHom.smulOneHom.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9) val._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.73 property._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.74)))))) (SMulZeroClass.toSMul.{u_2, u_2} S S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_2, u_2} S S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (instDistribSMul.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (SMul.comp.{u_2, u_1, u_2} S R S (SMulZeroClass.toSMul.{u_2, u_2} S S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddCommMonoid.toAddMonoid.{u_2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (SMulWithZero.toSMulZeroClass.{u_2, u_2} S S (MulZeroClass.toZero.{u_2} S (MulZeroOneClass.toMulZeroClass.{u_2} S (MonoidWithZero.toMulZeroOneClass.{u_2} S (Semiring.toMonoidWithZero.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddCommMonoid.toAddMonoid.{u_2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (MulActionWithZero.toSMulWithZero.{u_2, u_2} S S (Semiring.toMonoidWithZero.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9) (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddCommMonoid.toAddMonoid.{u_2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (Module.toMulActionWithZero.{u_2, u_2} S S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) (Semiring.toModule.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (DFunLike.coe.{max (succ u_2) (succ u_1), succ u_1, succ u_2} (ZeroHom.{u_1, u_2} R S (MulZeroClass.toZero.{u_1} R (MulZeroOneClass.toMulZeroClass.{u_1} R (MonoidWithZero.toMulZeroOneClass.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)))) (MulZeroClass.toZero.{u_2} S (MulZeroOneClass.toMulZeroClass.{u_2} S (MonoidWithZero.toMulZeroOneClass.{u_2} S (Semiring.toMonoidWithZero.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) R (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : R) => S) (ZeroHom.funLike.{u_1, u_2} R S (MulZeroClass.toZero.{u_1} R (MulZeroOneClass.toMulZeroClass.{u_1} R (MonoidWithZero.toMulZeroOneClass.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)))) (MulZeroClass.toZero.{u_2} S (MulZeroOneClass.toMulZeroClass.{u_2} S (MonoidWithZero.toMulZeroOneClass.{u_2} S (Semiring.toMonoidWithZero.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (MonoidWithZeroHom.toZeroHom.{u_1, u_2} R S (MonoidWithZero.toMulZeroOneClass.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)) (MonoidWithZero.toMulZeroOneClass.{u_2} S (Semiring.toMonoidWithZero.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)) (RingHom.toMonoidWithZeroHom.{u_1, u_2} R S (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6) (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9) (ringHomEquivModuleIsScalarTower.match_1.{u_1, u_2, max (succ u_1) (succ u_2)} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9 (fun (x._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx.55.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.63 : Subtype.{max (succ u_1) (succ u_2)} (Module.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (fun (_inst : Module.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S 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(AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (instDistribSMul.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S 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inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6) (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)) x._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.94 (fun (val._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.73 : Module.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (property._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.74 : IsScalarTower.{u_1, u_2, u_2} R S S (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) val._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.73)))) (SMulZeroClass.toSMul.{u_2, u_2} S S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_2, u_2} S S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (instDistribSMul.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (DistribMulAction.toDistribSMul.{u_1, u_2} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)) (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (Module.toDistribMulAction.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) val._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.73))))) => RingHom.smulOneHom.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9) val._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.73 property._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.74))))))","typeFull":"∀ {R : Type u_1} {S : Type u_2} [inst : Semiring R] [inst_1 : Semiring S] (x : { _inst // IsScalarTower R S S }),\n IsScalarTower R S S","typeReadable":"∀ {R : Type u_1} {S : Type u_2} [inst : Semiring R] [inst_1 : Semiring S] (x : { _inst // IsScalarTower R S S }),\n IsScalarTower R S S","typeReferences":[["RingHom"],["Subtype"],["IsScalarTower"],["Module"],["ZeroHom"],["MonoidWithZero","toMulZeroOneClass"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddMonoidWithOne","toAddMonoid"],["instDistribSMul"],["DFunLike","coe"],["RingHom","smulOneHom"],["Semiring","toNonAssocSemiring"],["MonoidWithZero","toMonoid"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Semiring","toModule"],["MulActionWithZero","toSMulWithZero"],["NonAssocSemiring","toAddCommMonoidWithOne"],["MonoidWithZeroHom","toZeroHom"],["DistribSMul","toSMulZeroClass"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["Module","toMulActionWithZero"],["SMul","comp"],["AddZeroClass","toAddZero"],["SMulWithZero","toSMulZeroClass"],["ZeroHom","funLike"],["Module","toDistribMulAction"],["MulZeroOneClass","toMulZeroClass"],["MulZeroClass","toZero"],["RingHom","toMonoidWithZeroHom"],["ringHomEquivModuleIsScalarTower","match_1"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["RingHom"],["ZeroHom"],["MonoidWithZero","toMulZeroOneClass"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddMonoidWithOne","toAddMonoid"],["instDistribSMul"],["DFunLike","coe"],["RingHom","smulOneHom"],["Semiring","toNonAssocSemiring"],["MonoidWithZero","toMonoid"],["DistribMulAction","toMulAction"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Semiring","toModule"],["MulActionWithZero","toSMulWithZero"],["NonAssocSemiring","toAddCommMonoidWithOne"],["MonoidWithZeroHom","toZeroHom"],["DistribSMul","toSMulZeroClass"],["IsScalarTower","left"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["SMul","comp","isScalarTower"],["Semiring","toMonoidWithZero"],["Module","toMulActionWithZero"],["AddZeroClass","toAddZero"],["SMulWithZero","toSMulZeroClass"],["ZeroHom","funLike"],["Module","toDistribMulAction"],["MulZeroOneClass","toMulZeroClass"],["MulZeroClass","toZero"],["RingHom","toMonoidWithZeroHom"],["ringHomEquivModuleIsScalarTower","match_1"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]]},{"isProp":false,"kind":"definition","name":["RingHom","toModule"],"typeFallback":"forall {R : Type.{u_1}} {S : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.RingHom.1426575160._hygCtx._hyg.6 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.RingHom.1426575160._hygCtx._hyg.9 : Semiring.{u_2} S], (RingHom.{u_1, u_2} R S (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.1426575160._hygCtx._hyg.6) (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.1426575160._hygCtx._hyg.9)) -> (Module.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.1426575160._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.1426575160._hygCtx._hyg.9))))","typeFull":"{R : Type u_1} → {S : Type u_2} → [inst : Semiring R] → [inst_1 : Semiring S] → (R →+* S) → Module R S","typeReadable":"{R : Type u_1} → {S : Type u_2} → [inst : Semiring R] → [inst_1 : Semiring S] → (R →+* S) → Module R S","typeReferences":[["RingHom"],["Semiring","toNonAssocSemiring"],["Module"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["Semiring"]],"valueReferences":[["Semiring","toNonAssocSemiring"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["Semiring","toModule"],["Module","compHom"]]},{"isProp":true,"kind":"theorem","name":["ringHomEquivModuleIsScalarTower","_proof_2"],"typeFallback":"forall {R : Type.{u_1}} {S : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9 : Semiring.{u_2} S] (f : RingHom.{u_1, u_2} R S (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6) (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)), Eq.{max (succ u_1) (succ u_2)} (RingHom.{u_1, u_2} R S (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6) (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)) (ringHomEquivModuleIsScalarTower.match_1.{u_1, u_2, max (succ u_1) (succ u_2)} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9 (fun (x._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx.55.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.63 : Subtype.{max (succ u_1) (succ u_2)} (Module.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (fun (_inst : Module.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) => IsScalarTower.{u_1, u_2, u_2} R S S (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (DistribMulAction.toDistribSMul.{u_1, u_2} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)) (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (Module.toDistribMulAction.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) _inst)))) (SMulZeroClass.toSMul.{u_2, u_2} S S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_2, u_2} S S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (instDistribSMul.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (DistribMulAction.toDistribSMul.{u_1, u_2} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)) (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (Module.toDistribMulAction.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) _inst)))))) => RingHom.{u_1, u_2} R S (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6) (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)) (Subtype.mk.{max (succ u_1) (succ u_2)} (Module.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (fun (_inst : Module.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) => IsScalarTower.{u_1, u_2, u_2} R S S (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (DistribMulAction.toDistribSMul.{u_1, u_2} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)) (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (Module.toDistribMulAction.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) _inst)))) (SMulZeroClass.toSMul.{u_2, u_2} S S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_2, u_2} S S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (instDistribSMul.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (DistribMulAction.toDistribSMul.{u_1, u_2} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)) (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (Module.toDistribMulAction.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) _inst))))) (Module.compHom.{u_2, u_1, u_2} S R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) (Semiring.toModule.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9) inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 f) (ringHomEquivModuleIsScalarTower._proof_1.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9 f)) (fun (val._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.73 : Module.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (property._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.74 : IsScalarTower.{u_1, u_2, u_2} R S S (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (DistribMulAction.toDistribSMul.{u_1, u_2} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)) (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (Module.toDistribMulAction.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) val._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.73)))) (SMulZeroClass.toSMul.{u_2, u_2} S S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_2, u_2} S S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (instDistribSMul.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (DistribMulAction.toDistribSMul.{u_1, u_2} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)) (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (Module.toDistribMulAction.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) val._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.73))))) => RingHom.smulOneHom.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9) val._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.73 property._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.74)) f","typeFull":"∀ {R : Type u_1} {S : Type u_2} [inst : Semiring R] [inst_1 : Semiring S] (f : R →+* S),\n (match ⟨Module.compHom S f, ⋯⟩ with\n | ⟨val, property⟩ => RingHom.smulOneHom) =\n f","typeReadable":"∀ {R : Type u_1} {S : Type u_2} [inst : Semiring R] [inst_1 : Semiring S] (f : R →+* S),\n (match ⟨Module.compHom S f, ⋯⟩ with\n | ⟨val, property⟩ => RingHom.smulOneHom) =\n f","typeReferences":[["RingHom"],["IsScalarTower"],["Module"],["SMulZeroClass","toSMul"],["AddMonoidWithOne","toAddMonoid"],["instDistribSMul"],["RingHom","smulOneHom"],["Semiring","toNonAssocSemiring"],["MonoidWithZero","toMonoid"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["ringHomEquivModuleIsScalarTower","_proof_1"],["Eq"],["Semiring","toModule"],["NonAssocSemiring","toAddCommMonoidWithOne"],["DistribSMul","toSMulZeroClass"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["Module","toDistribMulAction"],["ringHomEquivModuleIsScalarTower","match_1"],["Subtype","mk"],["AddZero","toZero"],["Semiring"],["AddMonoid","toAddZeroClass"],["Module","compHom"]],"valueReferences":[["RingHom"],["IsScalarTower"],["Module"],["RingHom","instFunLike"],["MulZeroOneClass","toMulOneClass"],["ZeroHom"],["MonoidWithZero","toMulZeroOneClass"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddMonoidWithOne","toAddMonoid"],["instDistribSMul"],["DFunLike","coe"],["RingHom","smulOneHom"],["Semiring","toNonAssocSemiring"],["MonoidWithZero","toMonoid"],["DistribMulAction","toMulAction"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Semiring","toModule"],["MulActionWithZero","toSMulWithZero"],["NonAssocSemiring","toAddCommMonoidWithOne"],["NonAssocSemiring","toMulZeroOneClass"],["MonoidWithZeroHom","toZeroHom"],["DistribSMul","toSMulZeroClass"],["IsScalarTower","left"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["SMul","comp","isScalarTower"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["mul_one"],["Module","toMulActionWithZero"],["AddZeroClass","toAddZero"],["SMulWithZero","toSMulZeroClass"],["RingHom","ext"],["ZeroHom","funLike"],["Module","toDistribMulAction"],["MulZeroOneClass","toMulZeroClass"],["MulZeroClass","toZero"],["RingHom","toMonoidWithZeroHom"],["ringHomEquivModuleIsScalarTower","match_1"],["Subtype","mk"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Module","compHom"]]},{"isProp":false,"kind":"definition","name":["ringHomEquivModuleIsScalarTower","match_1"],"typeFallback":"forall {R : Type.{u_1}} {S : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9 : Semiring.{u_2} S] (motive : (Subtype.{max (succ u_1) (succ u_2)} (Module.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (fun (_inst : Module.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) => IsScalarTower.{u_1, u_2, u_2} R S S (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (DistribMulAction.toDistribSMul.{u_1, u_2} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)) (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (Module.toDistribMulAction.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) _inst)))) (SMulZeroClass.toSMul.{u_2, u_2} S S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_2, u_2} S S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (instDistribSMul.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (DistribMulAction.toDistribSMul.{u_1, u_2} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)) (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (Module.toDistribMulAction.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) _inst)))))) -> Sort.{u_3}) (x._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx.55.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.63 : Subtype.{max (succ u_1) (succ u_2)} (Module.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (fun (_inst : Module.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) => IsScalarTower.{u_1, u_2, u_2} R S S (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (DistribMulAction.toDistribSMul.{u_1, u_2} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)) (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (Module.toDistribMulAction.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) _inst)))) (SMulZeroClass.toSMul.{u_2, u_2} S S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_2, u_2} S S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (instDistribSMul.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (DistribMulAction.toDistribSMul.{u_1, u_2} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)) (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (Module.toDistribMulAction.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) _inst)))))), (forall (val._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.73 : Module.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (property._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.74 : IsScalarTower.{u_1, u_2, u_2} R S S (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (DistribMulAction.toDistribSMul.{u_1, u_2} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)) (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (Module.toDistribMulAction.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) val._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.73)))) (SMulZeroClass.toSMul.{u_2, u_2} S S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_2, u_2} S S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (instDistribSMul.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (DistribMulAction.toDistribSMul.{u_1, u_2} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)) (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (Module.toDistribMulAction.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) val._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.73))))), motive (Subtype.mk.{max (succ u_1) (succ u_2)} (Module.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (fun (_inst : Module.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) => IsScalarTower.{u_1, u_2, u_2} R S S (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) 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inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) _inst)))) (SMulZeroClass.toSMul.{u_2, u_2} S S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_2, u_2} S S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (instDistribSMul.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (SMulZeroClass.toSMul.{u_1, u_2} R S 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: Module R S] (x1 x2 : R),\n (x1 + x2) • 1 = x1 • 1 + x2 • 1","typeReferences":[["MulOneClass","toMulOne"],["Module"],["MulZeroOneClass","toMulOneClass"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["Semiring","toNonAssocSemiring"],["NonAssocSemiring"],["MonoidWithZero","toMonoid"],["instHSMul"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Eq"],["NonAssocSemiring","toMulZeroOneClass"],["DistribSMul","toSMulZeroClass"],["Distrib","toAdd"],["MulOne","toOne"],["NonUnitalNonAssocSemiring","toDistrib"],["instHAdd"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["HAdd","hAdd"],["Module","toDistribMulAction"],["AddCommMonoid","toAddCommSemigroup"],["One","toOfNat1"],["HSMul","hSMul"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["MulOneClass","toMulOne"],["MulOne","toOne"],["One","toOfNat1"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["MulZeroOneClass","toMulOneClass"],["NonAssocSemiring","toMulZeroOneClass"],["OfNat","ofNat"],["add_smul"]]},{"isProp":true,"kind":"theorem","name":["Module","compHom","_proof_1"],"typeFallback":"forall 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{R : Type.{u_1}} {S : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.RingHom.239643300._hygCtx._hyg.6 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.RingHom.239643300._hygCtx._hyg.9 : NonAssocSemiring.{u_2} S] [inst._@.Mathlib.Algebra.Module.RingHom.239643300._hygCtx._hyg.12 : Module.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.239643300._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.239643300._hygCtx._hyg.9))] [inst._@.Mathlib.Algebra.Module.RingHom.239643300._hygCtx._hyg.16 : IsScalarTower.{u_1, u_2, u_2} R S S (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.239643300._hygCtx._hyg.9)))))) 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inst._@.Mathlib.Algebra.Module.RingHom.239643300._hygCtx._hyg.12)))) (SMulZeroClass.toSMul.{u_2, u_2} S S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.239643300._hygCtx._hyg.9)))))) (DistribSMul.toSMulZeroClass.{u_2, u_2} S S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.239643300._hygCtx._hyg.9)))) (instDistribSMul.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.239643300._hygCtx._hyg.9)))) (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.239643300._hygCtx._hyg.9)))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.239643300._hygCtx._hyg.9)))) (DistribMulAction.toDistribSMul.{u_1, u_2} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.239643300._hygCtx._hyg.6)) (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.239643300._hygCtx._hyg.9))) (Module.toDistribMulAction.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.239643300._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.239643300._hygCtx._hyg.9)) inst._@.Mathlib.Algebra.Module.RingHom.239643300._hygCtx._hyg.12))))], RingHom.{u_1, u_2} R S (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.239643300._hygCtx._hyg.6) inst._@.Mathlib.Algebra.Module.RingHom.239643300._hygCtx._hyg.9","typeFull":"{R : Type u_1} →\n {S : Type u_2} →\n [inst : Semiring R] → [inst_1 : NonAssocSemiring S] → [inst_2 : Module R S] → [IsScalarTower R S S] → R →+* S","typeReadable":"{R : Type u_1} →\n {S : Type u_2} →\n [inst : Semiring R] → [inst_1 : NonAssocSemiring S] → [inst_2 : Module R S] → [IsScalarTower R S S] → R →+* S","typeReferences":[["RingHom"],["Module"],["IsScalarTower"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["SMulZeroClass","toSMul"],["instDistribSMul"],["AddZeroClass","toAddZero"],["AddMonoidWithOne","toAddMonoid"],["Module","toDistribMulAction"],["Semiring","toNonAssocSemiring"],["MonoidWithZero","toMonoid"],["NonAssocSemiring"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["AddZero","toZero"],["NonAssocSemiring","toAddCommMonoidWithOne"],["DistribSMul","toSMulZeroClass"],["Semiring"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["RingHom","smulOneHom","_proof_1"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["RingHom","smulOneHom","_proof_2"],["Semiring","toMonoidWithZero"],["MulZeroOneClass","toMulOneClass"],["AddCommMonoid","toAddMonoid"],["Module","toDistribMulAction"],["Semiring","toNonAssocSemiring"],["MonoidHom","smulOneHom"],["MonoidWithZero","toMonoid"],["DistribMulAction","toMulAction"],["RingHom","mk"],["NonAssocSemiring","toMulZeroOneClass"]]},{"isProp":true,"kind":"theorem","name":["ringHomEquivModuleIsScalarTower","_proof_4"],"typeFallback":"forall 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(AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (DistribMulAction.toDistribSMul.{u_1, u_2} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)) (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (Module.toDistribMulAction.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) _inst)))))) (Subtype.mk.{max (succ u_1) (succ u_2)} (Module.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (fun (_inst : Module.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) => IsScalarTower.{u_1, u_2, u_2} R S S (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (DistribMulAction.toDistribSMul.{u_1, u_2} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)) (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (Module.toDistribMulAction.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) _inst)))) (SMulZeroClass.toSMul.{u_2, u_2} S S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_2, u_2} S S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (instDistribSMul.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (DistribMulAction.toDistribSMul.{u_1, u_2} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)) (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (Module.toDistribMulAction.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) _inst))))) (Module.compHom.{u_2, u_1, u_2} S R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) (Semiring.toModule.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9) inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (ringHomEquivModuleIsScalarTower.match_1.{u_1, u_2, max (succ u_1) (succ u_2)} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9 (fun (x._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx.55.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.63 : Subtype.{max (succ u_1) (succ u_2)} (Module.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (fun (_inst : Module.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) => IsScalarTower.{u_1, u_2, u_2} R S S (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (DistribMulAction.toDistribSMul.{u_1, u_2} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)) (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (Module.toDistribMulAction.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) _inst)))) (SMulZeroClass.toSMul.{u_2, u_2} S S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_2, u_2} S S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (instDistribSMul.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (DistribMulAction.toDistribSMul.{u_1, u_2} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)) (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (Module.toDistribMulAction.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) _inst)))))) => RingHom.{u_1, u_2} R S (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6) (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)) x._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.94 (fun (val._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.73 : Module.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (property._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.74 : IsScalarTower.{u_1, u_2, u_2} R S S (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (DistribMulAction.toDistribSMul.{u_1, u_2} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)) (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (Module.toDistribMulAction.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) val._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.73)))) (SMulZeroClass.toSMul.{u_2, u_2} S S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_2, u_2} S S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (instDistribSMul.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (SMulZeroClass.toSMul.{u_1, u_2} R S (AddZero.toZero.{u_2} S (AddZeroClass.toAddZero.{u_2} S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R S (AddMonoid.toAddZeroClass.{u_2} S (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))))) (DistribMulAction.toDistribSMul.{u_1, u_2} R S (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6)) (AddMonoidWithOne.toAddMonoid.{u_2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9)))) (Module.toDistribMulAction.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} S (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9))) val._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.73))))) => RingHom.smulOneHom.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9) val._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.73 property._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.74))) (ringHomEquivModuleIsScalarTower._proof_3.{u_1, u_2} R S inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.6 inst._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.9 x._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.94)) x._@.Mathlib.Algebra.Module.RingHom.2238294897._hygCtx._hyg.94","typeFull":"∀ {R : Type u_1} {S : Type u_2} [inst : Semiring R] [inst_1 : Semiring S] (x : { _inst // IsScalarTower R S S }),\n ⟨Module.compHom S\n (match x with\n | ⟨val, property⟩ => RingHom.smulOneHom),\n ⋯⟩ =\n x","typeReadable":"∀ {R : Type u_1} {S : Type u_2} [inst : Semiring R] [inst_1 : Semiring S] (x : { _inst // IsScalarTower R S S }),\n ⟨Module.compHom S\n (match x with\n | ⟨val, property⟩ => RingHom.smulOneHom),\n ⋯⟩ =\n 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